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This work concerns the numerical modeling of geometric nonlinear vibrations of slender structures in rotation using an original reduced order model based on the use of dual modes along with the implicit condensation method. This approach is an improvement of the classical ICE method in the sense that the membrane stretching effect is taken into account in the dynamic resolution. The dynamics equations are first presented and the construction of the reduced order model (ROM) is then proposed. The second part of the paper deals with numerical applications using the finite element method, first for a three-dimensional cantilever beam, then for an Ultra-High Bypass Ratio (UHBR) fan blade subject to aerodynamic loads. In the applications considered, the proposed method predicts more accurately the geometrically nonlinear behavior than the ICE method. [ABSTRACT FROM AUTHOR]

The analysis of the structural dynamics of multistage cyclic structures as linked components is required to model the interstage coupling. In turbomachinery, this can result in a collaboration between different compressor or turbine stages. This paper investigates the coupling between two rear drum blade integrated disk stages of an axial compressor to support the mechanical design process. Considering the vibration modeshapes of a multistage system, different components may coparticipate in the dynamics. For this reason, criteria to identify the modes affected by the coupling and to quantify this coupling are defined. This allows to distinguish between modes with interstage coupling, requiring the multistage system for their description, and uncoupled modes, involving a single stage. In addition, it is of interest to research methods to reduce the impact of the coupling on the vibrating system without drastically altering the geometry of the components. The vibration analyses of a two-stage compressor generalized geometry, representative of a compressor rear drum blisk, are presented as a study case. The use of a reducing method allows to describe the behavior of the nominal multistage system with a computationally efficient technique, enabling a parametric analysis of the stages' coupling. The investigation considers the effect of a set of geometrical and mechanical parameters on the dynamics, identifying the driving parameters of the coupled vibration characteristics. [ABSTRACT FROM AUTHOR]

The design of disk assemblies requires the capability to predict their dynamic behavior. To achieve this objective, knowledge of friction damping on the contact between blade and disk is of paramount importance. This paper proposes an experimental technique to measure the loss factor and the dynamics, in terms of natural frequencies, of blade-disk attachment. The free decay is used to infer the dynamic parameters from dummy blades. The identification method is based on the Hilbert transform that allows extracting the dynamic parameters from nonlinear system. This paper shows the test rig utilized in the experimental analysis and details the excitation system used to displace the dummy blade. This system must be a real or a "virtual" noncontact system to avoid injecting external damping into the blade under test. Tests were performed on both a dovetail and a fir-tree type attachment. On the dovetail, tests were performed both with dry contact surfaces and with contact surfaces covered by a film of lubricant to achieve a low coefficient of friction. This low coefficient of friction better simulates dry surfaces at high temperatures, as friction coefficients decrease with temperatures. This paper presents the results obtained on the first and second bending mode. The experimental results show the loss factor and the natural frequency for different axial loads. The measured loss factor depends on the amplitude of vibrations. As predicted with theoretical analyses the loss factor shows a maximum then approaching zero for large amplitude of vibrations. As a rule, it decreases with increasing centrifugal loads. [ABSTRACT FROM AUTHOR]

Hydraulic actuation systems have a broad range of applications covering almost all areas of manufacturing and production and also the service industry. However, it is usual for systems to have low energy efficiency. In recent decades, due to global environmental concerns, research in the field of digital hydraulics to develop more efficient hydraulic systems has increased. In this paper, an analysis of the possible combinations of chambers in a multichamber cylinder is presented. A mathematical expression is derived to verify the total number of combinations of chambers that it is possible to achieve for a cylinder with four or more chambers and that result in different constant velocities without cavitation occurring. In addition, a digital hydraulic pump is considered a supply unit and, since it has discrete output flow rates, an analytical method to combine the pump with a multichamber cylinder is developed resulting in a total number of cylinder velocities with a required resolution. For application in a positioning system, design guidelines for an actuator using a cylinder with four chambers and a digital hydraulic pump with three fixed displacement units are presented in which an optimization algorithm for the calculation of the cylinder areas and the volumetric displacement of the pumps is applied. The proposed approaches were applied to design a proof-of-concept and the experimental values presented very good accuracy when compared with the results obtained with the model. Closed-loop position control responses show that the system can achieve the required setting time with a smooth movement and steady-state error of around 1 mm. [ABSTRACT FROM AUTHOR]

Based on the guaranteed cost theory, this paper proposes a robust controller for the automotive electrohydraulic coupling system. However, parameter perturbation caused by the model linearization is a critical challenge for the nonlinear electrohydraulic coupling system. Generally, the electrical brake booster system (E-booster) can be separated into three parts, a permanent magnet synchronous motor (PMSM), a hydraulic model of the master cylinder, and the transmission mechanism. In this paper, the robust guaranteed cost controller (RGCC) is adopted to achieve an accurate regulation of the pushrod position of the E-booster and has strong robustness against internal uncertainties, and the linear extended state observer (LESO) is utilized to optimize E-booster's dynamic performance. Specifically, the tracking differentiator (TD) and LESO are used to improve the dynamic precision and reduce the hysteresis effect. The overshoot is suppressed by TD, and the disturbance caused by nonlinear uncertainty is restrained by LESO. The experimental results show that RGCC sacrifices a 6% phase lag in the low-frequency domain for a 10% and 40% reduction in first and second-order, respectively, compared with the proportion integration differentiation (PID). Results demonstrate that RGCC has higher precision and stronger robustness in dynamic behavior. [ABSTRACT FROM AUTHOR]

Active base isolation has been studied in the last few decades to improve the control performance of base isolation. As a two-degree-of-freedom active disturbance-rejection method, the equivalent-input-disturbance (EID) approach shows its validity for structural control. It uses a state observer to estimate the effect of disturbances on a control input channel. However, since the model of a base-isolated building has high degrees-of-freedom, the resulting control system has a high order. Thus, the use of a full-order state observer results in the complexity of a control-system implementation. To solve this problem, this paper presents an EID control system that uses a reduced-order state observer (ROSO) to reduce the expense of control-system implementation and ensure system reliability. First, the condition of using an ROSO in an EID control system is derived, and the configuration of an ROSO-based EID control system is presented. Next, the concept of perfect regulation is used to design the gain of the state observer. A stability condition of the system with prescribed control performance is derived in the form of a linear matrix inequality (LMI) that is used to design the gain of the state feedback. Finally, the seismic control of a base-isolated building demonstrates the validity of the method. [ABSTRACT FROM AUTHOR]

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve. [ABSTRACT FROM AUTHOR]

This paper has been written to develop closed-form equations for describing the theoretical displacement of a check-valve type, digital displacement pump. In theory, the digital displacement pump is used to alter the apparent volumetric displacement of the machine by short circuiting the flow path for reciprocating pistons within the machine that would ordinarily deliver a full volumetric flow rate to the discharge side of the pump. The short circuiting for the pistons is achieved by opening and closing a digital valve connected to each piston chamber at a desired time during the kinematic cycle for each reciprocating piston. Experience with these machines has shown that the expected volumetric displacement for the machine tends to decrease with pressure. This paper presents a theoretical explanation for the reduced volumetric displacement of the pump and quantifies the expected behavior based upon the digital valve command, the residual volume of fluid within a single piston chamber, and the fluid bulk modulus-of-elasticity. In summary, it shown that the apparent volumetric displacement of the machine may be reduced by as much as 10% for high-displacement commands and by as much as 30% for low-displacement commands. [ABSTRACT FROM AUTHOR]

This paper describes a unique design concept that is capable of electronically controlling the flow delivered by an external gear pump (EGP). The principle used for varying the flow relies on the variable timing concept which has been previously demonstrated by the author's research team for EGP's operating at high pressures (HPs) (p > 100 bar). This principle permits to vary the flow within a certain range, without introducing additional sources of power loss. In this paper, the above concept has been applied to formulate a design for a variable delivery EGP for low pressure (LP) applications (p < 30 bar), suitable for direct electric actuation. Specific design principles for the gear and the flow variation mechanisms are introduced to limit the force required by the electric actuation, and for maximizing the flow variation range. Also, the low target pressure allows the variable timing principle to be realized with an asymmetric solution, with only one variable timing element present at one side of the gears. A detailed analysis concerning the relationship between the electrically commanded position of the flow varying element and the theoretical flow delivered by the pump is also presented. This analysis is used to formulate analytical expressions for the instantaneous flow rate and the flow nonuniformity of the pump. The paper details the design principle of the proposed variable flow pump and describes the multi-objective optimization approach used for sizing the gears and flow variation mechanism. The paper also discusses the experimental activity performed on a prototype of the proposed unit, able to achieve a flow variation of 31%. [ABSTRACT FROM AUTHOR]

Many engineering applications utilize periodic lattice structures to take advantage of their favorable and tailorable mechanical properties. However, manufacturing the structures and evaluating their mechanical properties are still challenging. Additive manufacturing (AM) processes offer an alternative method to fabricate periodic lattice structures but the processes only approximate bounding part surfaces. Periodic lattice structures generally have two important geometrical characteristics, large bounding surfaces, and a large number of joints. Since geometric approximation errors on large bounding surfaces critically affect mechanical properties of the structures, designers and engineers should incorporate this degradation into mechanical property estimation procedures. In addition, the effects of joints should be analyzed in the estimation process, because joints reduce struts lengths, and as a result, they add stiffness to lattice structures. This paper presents a new homogenization approach to estimate mechanical properties of additively manufactured periodic lattice structures that is based on semirigid joint frame elements, and it takes into account effects of geometric approximation errors and joint stiffening. Effective structural parameters of a semirigid joint frame element are calculated from an as-fabricated voxel model to incorporate the geometric approximation errors. The semirigid joint frame element is integrated into a discrete homogenization process to evaluate joint stiffening effects. This paper reports results of parametric studies that investigate effects of AM process and joint properties on periodic lattice structures fabricated by material extrusion. This paper also compares estimates from the proposed approach and conventional homogenization approaches with test results. The comparison shows that the proposed method provides estimates that are more accurate. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach for characterizing the interfacial region using the molecular dynamics (MD) simulations and the shear deformation model (SDM). The bulk-level mechanical properties of graphene-reinforced nanocomposites strongly depend on the interfacial region between the graphene and epoxy matrix, whose thickness is about 6.8-10.0 Å. Because it is a challenge to experimentally investigate mechanical properties of this thin region, computational MD simulations have been widely employed. By pulling out graphene from the graphene/epoxy system, pull-out force and atomic displacement of the interfacial region are calculated to characterize the interfacial shear modulus. The same processes are applied to 3% grafted hydroxyl and carboxyl functionalized graphene (OH-FG and COOH-FG)/epoxy (diglycidyl ether of bisphenol F (DGEBF)/triethylenetetramine (TETA)) systems, and influences of the functionalization on the mechanical properties of the interfacial region are studied. Our key finding is that, by functionalizing graphene, the pull-out force moderately increases and the interfacial shear modulus considerably decreases. We demonstrate our results by comparing them with literature values and findings from experimental papers. [ABSTRACT FROM AUTHOR]

The hybrid computational fluid dynamics/computational aeroacoustics (CFD/CAA) approach represents an effective method to assess the stability of noncompact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized finite element method (sFEM). One main advancement presented in this study is the elimination of the nonphysical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results. [ABSTRACT FROM AUTHOR]

The application of explicit dynamics to simulate quasi-static events often becomes impractical in terms of computational cost. Different solutions have been investigated in the literature to decrease the simulation time and a family of interesting, increasingly adopted approaches are the ones based on the proper orthogonal decomposition (POD) as a model reduction technique. In this study, the algorithmic framework for the integration of the equation of motions through POD is proposed for discrete linear and nonlinear systems: a low dimensional approximation of the full order system is generated by the so-called proper orthogonal modes (POMs), computed with snapshots from the full order simulation. Aiming to a predictive tool, the POMs are updated in itinere alternating the integration in the complete system, for the snapshots collection, with the integration in the reduced system. The paper discusses details of the transition between the two systems and issues related to the application of essential and natural boundary conditions (BCs). Results show that, for one-dimensional (1D) cases, just few modes are capable of excellent approximation of the solution, even in the case of stress-strain softening behavior, allowing to conveniently increase the critical time-step of the simulation without significant loss in accuracy. For more general three-dimensional (3D) situations, the paper discusses the application of the developed algorithm to a discrete model called lattice discrete particle model (LDPM) formulated to simulate quasi-brittle materials characterized by a softening response. Efficiency and accuracy of the reduced order LDPM response are discussed with reference to both tensile and compressive loading conditions. [ABSTRACT FROM AUTHOR]

In the past decades, various novel functions (i.e., negative Poisson's ratio, zero thermal expansion) have been obtained by tailoring the microstructures of the cellular structures. Among all the microstructures, the horseshoe topology shows a J-shaped stress-strain curve, which is quite different from the conventional materials. It can be inferred that the 2D lattice structure with horseshoe microstructure will also exhibit excellent out-of-plane impact resistance since the spider silk also exhibits the J-shaped stress-strain curve. In this paper, the out-of-plane sphere impact of 2D truss lattice structure is conducted using finite element method (FEM) simulation. The point has been made that, by replacing the direct-line beam to horseshoe curved beam, the out-of-plane impact resistance has been greatly improved. The most curved beam structure is found to have the best out-of-plane performs with the maximum energy absorption and the minimum passing through velocity. [ABSTRACT FROM AUTHOR]

This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force-displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system. [ABSTRACT FROM AUTHOR]

Variable displacement axial piston units are the core components of many hydrostatic and hydraulic hybrid drive trains. Therein, the fast and accurate control of the swash plate angle, utilizing the full possible dynamics of the displacement system, is essential for a good performance of the overall drive train. This paper describes the development, implementation, and the experimental validation of a control strategy for the swash plate angle based on nonlinear model predictive control (NMPC). A tailored mathematical model, which serves as the basis for the NMPC, is described in the first part of the paper. Two versions of NMPC, an indirect and a direct method, are compared with respect to their numerical complexity and their capability of handling input and state constraints. An observer strategy, which is designed to obtain the nonmeasurable states and varying parameters of the system, completes the overall control strategy. To reduce the negative influence of stick-slip friction, the concept of dithering is applied in the experimental implementation. The differences of the NMPC methods are analyzed by simulation studies and experiments. Finally, the experimental results, using an industrial electronic control unit (ECU), prove the practical feasibility and the improved control accuracy and robustness in comparison to classical (nonlinear) control strategies. [ABSTRACT FROM AUTHOR]

The weak form quadrature element method (QEM) combines the generality of the finite element method (FEM) with the accuracy of spectral techniques and thus has been projected by its proponents as a potential alternative to the conventional finite element method. The progression on the QEM and its applications is clear from past research, but this has been scattered over many papers. This paper presents a state-of-the-art review of the QEM employed to analyze a variety of problems in science and engineering, which should be of general interest to the community of the computational mechanics. The difference between the weak form quadrature element method (WQEM) and the time domain spectral element method (SEM) is clarified. The review is carried out with an emphasis to present static, buckling, free vibration, and dynamic analysis of structural members and structures by the QEM. A subroutine to compute abscissas and weights in Gauss-Lobatto-Legendre (GLL) quadrature is provided in the Appendix. [ABSTRACT FROM AUTHOR]

In view of the stronger vulnerability of horizontally irregular structures during earthquakes, numerous studies have been made since mid-1950?s. Unfortunately, research progress in this subject does not appear encouraging. This is evident from the current wisdom embodied in modern codes in the form of design guidelines. Beginning with a critical review of the earlier works and the available code-provisions, the present paper emphasizes on the prevalent controversies and the fundamental fallacies in research studies and traditional design. The review intends to address the strength vis-a-vis weakness of the studies accomplished so far and helps streamlining future research. The present paper also summarizes the updated views for selecting and processing appropriate set of ground motions. This is a key input in seismic response assessment and a major reason of the existing controversies in the subject of asymmetry. A prognostic scrutiny of the research progress recognizes the prospective challenges ahead. [ABSTRACT FROM AUTHOR]

This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method. [ABSTRACT FROM AUTHOR]

An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure's macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force-displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force-displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption. [ABSTRACT FROM AUTHOR]

Microbond tests have been widely used for studying the interfacial mechanical properties of fiber-reinforced composites. However, experimental results reveal that the interfacial shear strength (IFSS) depends on the length of microdroplet-embedded fiber (le). Thus, it is essential to provide an insight into this size effect on IFSS. In this paper, microbond tests are conducted for two kinds of widely used composites, i.e., glass fiber/epoxy matrix and carbon fiber/epoxy matrix. The lengths of microdroplet-embedded glass fiber and carbon fiber are in the ranges from 114.29 µm to 557.14 µm and from 63.78 µm to 157.45 µm, respectively. We analyze the representative force-displacement curves, the processes of interfacial failure and frictional sliding, and the maximum force and the frictional force as functions of le. Experimental results show that IFSS of both material systems monotonically decreases with le and then approaches a constant value. The finite element model is used to analyze the size effect on IFSS and interfacial failure behaviors. For both material systems, IFSS predicted from simulations is consistent with that obtained from experiments. Moreover, by analyzing the shear stress distribution, a transition of interface debonding is found from more or less uniform separation to crack propagation when le increases. This study reveals the mechanism of size effect in microbond tests, serving as an effective method to evaluate the experimental results and is critical to guidelines for the design and optimization of advanced composites. [ABSTRACT FROM AUTHOR]

This paper introduces mechanical networks as a tool for modeling complex unidirectional vibrations. Networks of this type have branches containing massless linear springs and dampers, with masses at the nodes. Tree and ladder configurations are examples demonstrating that the overall dynamics of infinite systems can be represented using implicitly defined integro-differential operators. Results from the proposed models compare well to numerical results from finite systems, so this approach may have advantages over high-order differential equations. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear vibrations of rotating beams with large displacements are investigated by the use of the co-rotational (C-R) finite element method. In the C-R approach, the full motion is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange's equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

We theoretically study the electromechanical behaviors of a laminated thin-film piezoelectric semiconductor (PS) composite plate with flexural deformation. The nonlinear equations for drift currents of electrons and holes are linearized for a small carrier concentration perturbation. Following the structural theory systemized by R. D. Mindlin, a system of two-dimensional (2D) equations for the laminated thin-film PS plate, including the lowest order coupled extensional and flexural motion, are presented by expanding the displacement, potential, and the incremental concentration of electrons and holes as power series of the plate thickness. Based on the derived 2D equations, the analytical expressions of the electromechanical fields and distribution of electrons in the thin-film PS plate with an n-type ZnO layer subjected to a static bending are presented. The numerical results show that the electromechanical behaviors and piezotronic effects can be effectively controlled by the external applied force and initial concentration of carriers. The derived 2D equations and numerical results in this paper are helpful for developing piezotronic devices. [ABSTRACT FROM AUTHOR]

Advancement of additive manufacturing is driving a need for design tools that exploit the increasing fabrication freedom. Multimaterial, three-dimensional (3D) printing allows for the fabrication of components from multiple materials with different thermal, mechanical, and "active" behavior that can be spatially arranged in 3D with a resolution on the order of tens of microns. This can be exploited to incorporate shape changing features into additively manufactured structures. 3D printing with a downstream shape change in response to an external stimulus such as temperature, humidity, or light is referred to as four-dimensional (4D) printing. In this paper, a design methodology to determine the material layout of 4D printed materials with internal, programmable strains is introduced to create active structures that undergo large deformation and assume a desired target displacement upon heat activation. A level set (LS) approach together with the extended finite element method (XFEM) is combined with density-based topology optimization to describe the evolving multimaterial design problem in the optimization process. A finite deformation hyperelastic thermomechanical model is used together with an higher-order XFEM scheme to accurately predict the behavior of nonlinear slender structures during the design evolution. Examples are presented to demonstrate the unique capabilities of the proposed framework. Numerical predictions of optimized shape-changing structures are compared to 4D printed physical specimen and good agreement is achieved. Overall, a systematic design approach for creating 4D printed active structures with geometrically nonlinear behavior is presented which yields nonintuitive material layouts and geometries to achieve target deformations of various complexities. [ABSTRACT FROM AUTHOR]

The structural synthesis of planetary gear trains (PGTs) is helpful for innovating transmission systems in machinery. A great deal of research has been devoted to the synthesis of one-degree-of-freedom (1-DOF) PGTs over the past half century. However, most synthesis methods are limited to PGTs with no more than eight links. Moreover, the synthesis results are not consistent with each other. Until now, the inconsistency of synthesis results is still unresolved and exact synthesis results remain elusive. This paper presents a systematic and fully automatic method based on parent graphs to synthesize 1-DOF PGTs. The complete database of rotation graphs (r-graphs) and displacement graphs (d-graphs) of 1-DOF PGTs with up to nine links is established for the first time. All possible reasons for the contradictory synthesis results in the literature are analyzed and the controversy in the existing synthesis results which has lasted for nearly half a century is completely resolved. The exact results of the 6-, 7-, and 8-link r-graphs are confirmed to be 27, 152, and 1070, respectively. The exact results of the 6-, 7-, and 8-link d-graphs are confirmed to be 81, 647, and 6360, respectively. Additionally, the new results of 8654 r-graphs and 71,837 d-graphs of 9-link PGTs are provided for the first time. [ABSTRACT FROM AUTHOR]

In this paper, a control scheme is developed and evaluated for stable bilateral haptic teleoperation of a single-rod hydraulic actuator subjected to base disturbance. The proposed controller, based on Lyapunov stability technique, is capable of reducing position errors at master and slave sides, and provides a feel of the contact force between the actuator and the task environment to the operator without a need for direct measurement. The controller requires only the measurements of the actuator line pressures and displacements of the master and slave. The system stability is insensitive to the uncertainties of the physical parameters and of the measurement of the base point motion. Stability of the proposed controller incorporating hydraulic nonlinearities and operator dynamics with an estimated upper value for the base disturbance is analytically proven. Simulation studies validate that the proposed control system is stable while interacting with a task environment. Experimental results demonstrate the effectiveness of control scheme in maintaining stability, while having good position tracking by the hydraulic actuator as well as providing a haptic feel to the operator without direct measurement of interaction force, while the hydraulic actuator is subjected to base disturbance. [ABSTRACT FROM AUTHOR]

Bioinspired design of robotic systems can offer many potential advantages in comparison to traditional architectures including improved adaptability, maneuverability, or efficiency. Substantial progress has been made in the design and fabrication of bioinspired systems. While many of these systems are bioinspired at a system architecture level, the design of linkage connections often assumes that motion is well approximated by ideal joints subject to designer-specified box constraints. However, such constraints can allow a robot to achieve unnatural and potentially unstable configurations. In contrast, this paper develops a methodology, which identifies the set of admissible configurations from experimental observations and optimizes a compliant structure around the joint such that motions evolve on or close to the observed configuration set. This approach formulates an analytical-empirical (AE) potential energy field, which "pushes" system trajectories toward the set of observations. Then, the strain energy of a compliant structure is optimized to approximate this energy field. While our approach requires that kinematics of a joint be specified by a designer, the optimized compliant structure enforces constraints on joint motion without requiring an explicit definition of box-constraints. To validate our approach, we construct a single degree-of-freedom elbow joint, which closely matches the AE and optimal potential energy functions and admissible motions remain within the observation set. [ABSTRACT FROM AUTHOR]

Axial piston pumps with variable volumetric displacement are often used to control flow and pressure in hydraulic systems. The displacement control mechanism in these pumps occupies significant space and accounts for significant cost in the pump design. Fixed displacement pumps have lower cost and a more compact design but suffer from a significant energy consumption disadvantage due to the need to control flow and pressure by throttling flow and bypassing unused flow to pressures below the discharge pressure. An inlet metering valve-controlled pump marks a recent development in pumping technology for hydraulic systems. In this design, an inlet metering valve restricts inlet flow reducing inlet pressure so that the specific volume of the fluid is increased as it enters a fixed displacement pump. By altering the specific volume of the working fluid, the inlet metering valve permits precise control over the pump discharge flow. This paper presents a theoretical model for inlet metered pump efficiency. The work considers additional sources of energy loss unique to the inlet metering system. Experimental results associated with inlet metered pump efficiency are presented. A comparison of the theoretical model and the experimental results is also included. It is determined that the current efficiency model accurately predicts efficiencies determined using experimental data. [ABSTRACT FROM AUTHOR]

Flow of gas in pipelines is subject to thermodynamic conditions which produces two-phase bulks (i.e., slugs) within the axial pipeline flow. These moving slugs apply a moving load on the free spanning pipe sections, which consequently undergo variable bending stresses, and flexural deflections. Both the maximum pipeline stress and deflection due to the slug flow loads need to be understood in the design of pipeline spans. However, calculation of a moving mass on a free spanning pipeline is not trivial and the required mathematical model is burdensome for general pipeline design engineering. The work in this paper is intended to investigate the conditions under which simplified analysis would produce a safe pipeline design which can be used by practicing pipeline design engineers. The simulated finite element models presented here prove that replacing the moving mass of the slug by a moving force will produce adequately accurate results at low speeds where the mass of the slug is much smaller than the mass of the pipe section. This result is significant, as the assumption of point load simplifies the analysis to a considerable extent. Since most applications fall within the speed and mass ratio which justify employing this simplified analysis, the work presented here offers a powerful design tool to estimate fatigue stresses and lateral deflections without the need of expensive time-consuming inputs from specialized practitioners. [ABSTRACT FROM AUTHOR]

In addition to processing a troubling agricultural by-product and reducing demands on our landfills, prepared agro-waste composites are suitable for a variety of practical applications. However, enhancing value-added options for these agricultural by-products can necessitate ability to assess their mechanical integrity. This paper accordingly describes the preparation of a cellulosic-manure composite and demonstrates ability to determine stresses in a perforated structure of the material from measured displacement data. Processing digital image correlation (DIC) recorded displacement information with an Airy stress function gives reliable results full-field as well as at the edge of geometric discontinuities without having to differentiate the recorded data. Required constitutive properties are evaluated in situ and results are substantiated independently. [ABSTRACT FROM AUTHOR]

Mussel adhesion is a problem of great interest to scientists and engineers. Recent microscopic imaging suggests that the mussel material is porous with patterned void distributions. In this paper, we study the effect of the pore distribution on the interfacial-to-the overall response of an elastic porous plate, inspired from mussel plaque, glued to a rigid substrate by a cohesive interface. We show using a semi-analytical approach that the existence of pores in the vicinity of the crack reduces the driving force for crack growth and increases the effective ductility and fracture toughness of the system. We also demonstrate how the failure mode may switch between edge crack propagation and inner crack nucleation depending on the geometric characteristics of the bulk in the vicinity of the interface. Numerically, we investigate using the finite element method two different void patterns; uniform and graded. Each case is analyzed under displacement-controlled loading. We show that by changing the void size, gradation, or volume fraction, we may control the peak pulling force, maximum elongation at failure, as well as the total energy dissipated at complete separation. We discuss the implications of our results on design of bulk heterogeneities for enhanced interfacial behavior. [ABSTRACT FROM AUTHOR]

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links. [ABSTRACT FROM AUTHOR]

For a number of emerging mechatronics applications, dielectric elastomers (DEs) appear as a more energy efficient, lightweight, and low-cost solution with respect to established actuation technologies based, e.g., on solenoids or pneumatic cylinders. In addition to large strain, low power consumption, and high flexibility, DE actuators (DEA) are also highly scalable. Since DE membranes can be easily manufactured in different sizes and shapes, an effective approach to scale their performance is based on properly designing the material geometry. Clearly, to perform an optimal scaling the relation between material geometry and performance has to be properly investigated. In this paper, performance scaling by means of geometry is studied for circular out-of-plane (COP) DEAs. Such actuators consist of a silicone elastomer membrane sandwiched between two electrodes (carbon black silicone mixture). DEAs with six different geometries are manufactured, and a model-based strategy is used to find an experimental relationship between geometry and electro-mechanical behavior. In addition, an effective and computationally efficient method for predicting force-displacement characteristics of different geometries is presented. The proposed method allows to easily adapt DEAs to different applications in terms of stroke and force requirement, while minimizing at the same time both characterization and prototyping effort. [ABSTRACT FROM AUTHOR]

Stress concentration in porous materials is one of the most crucial culprits of mechanical failure. This paper focuses on planar porous materials with porosity less than 5%. We present a stress-prediction model of an arbitrarily rotated elliptical hole in a rhombus shaped representative volume element (RVE) that can represent a class of generic planar tessellations, including rectangular, triangular, hexagonal, Kagome, and other patterns. The theoretical model allows the determination of peak stress and distribution of stress generated near the edge of elliptical holes for any arbitrary tiling under displacement loading and periodic boundary conditions. The results show that the alignment of the void with the principal directions minimizes stress concentration. Numerical simulations support the theoretical findings and suggest the observations remain valid for porosity as large as 5%. This work provides a fundamental understanding of stress concentration in low-porosity planar materials with insight that not only complements classical theories on the subject but also provides a practical reference for material design in mechanical, aerospace, and other industry. [ABSTRACT FROM AUTHOR]

In this paper, the theoretical analysis and the inversion of the contact stress on the finite thickness rubber contact surface with the friction effect are investigated. First, an explicit expression of deformation and stress on the surface of rubber under a rigid spherical indenter is developed by means of theoretical model, dimensional analysis, and nonlinear finite element simulation. Second, the inverse approach for obtaining the contact stress on the finite thickness rubber contact surface is presented and verified theoretically. Also, the displacement, the stress field, and the friction coefficient are obtained by means of three-dimensional digital image correlation (3D DIC) method. Finally, the applicability to other hyperelastic models, general boundary conditions, and loading modes are discussed. The results will provide an important theoretical and experimental basis for evaluating the contact stress on the finite thickness rubber layer. [ABSTRACT FROM AUTHOR]

Flexible pipes are structures composed by many layers that vary in composition and shapes. The structural behavior of each layer is defined by the role it must play. The construction of flexible pipes is such that the layers are unbounded, with relative movement between them. Even though this characteristic is what enables its high bending compliant behavior, if the displacements involved are small, a bonded analysis is interesting to grasp the general characteristics of the problem. The bonded hypothesis means that there is no movement relative between layers, which is fine for a small displacement analysis. It also creates a lower bound for the movement, since when considering increasingly friction coefficient values, it tends to the bonded situation. The main advantage of such hypothesis is that the system becomes linear, leading to fast solving problems (when compared to full frictional analysis) and giving insights to the pipe behavior. The authors have previously developed a finite element based one called macroelements. This model enables a fast-solving problem with less memory consumption when compared to multipurpose software. The reason behind it is the inclusion of physical characteristics of the problem, enabling the reduction in both number of elements and memory used and, since there are less elements and degrees-of-freedom, faster solved problems. In this paper, the advantages of such model are shown by using examples that are representative of a simplified, although realistic, flexible pipe. Comparisons between the macroelement model and commercial software are made to show its capabilities. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic model for steel catenary risers (SCRs) based on the principle of virtual work, where the equations of motion are obtained by combining Euler's equation and initial conditions. The motion equations of the floating platform are transformed and combined with those of the riser to establish the complete model. Vertical structure and dispersion of the internal wave are calculated to obtain the internal wave load and combined with the floating platform motion. The whole motion equation of the riser was solved by the Newmark ß method. A proprietary matlab algorithm was written to analyze the influence of different factors on the dynamic response of the riser in an internal wave field. Top tension had a significant effect on the riser dynamic characteristics and response. Floating platform movement determines the vibration frequency of the riser, considering the internal wave as an external force, to promote the whole movement of the riser. The maximum riser displacement was mainly affected by the internal wave, where the top corner was mainly from the floating platform movement. [ABSTRACT FROM AUTHOR]

The layers of unbounded flexible pipes have relative movement, enhancing its capabilities to handle curvatures and moment loads. In a simplified approach, those pipes can be described using bonded elements; but to really capture this behavior, a frictional contact is utterly needed. In general, dealing with contact problems in computational mechanics is complicated, since it involves the constant evaluation of its status and can lead to convergence problems or simulation failure, due to intrinsically problematic and inefficient contact models or due to contact models that are insufficient to capture the desired details. The macroelement formulation, which was created to deal with flexible pipes in a simplified way, needed a frictional contact element to enhance the quality of results and closeness to real behavior. The major drawback for developing such element is the different nature of the nodal displacements descriptions. The first approach possible is the simplest contact model: it involves only the nodes in each contacting elements. The gap information and distances are evaluated using exclusively the nodal information. This kind of model provides good results with minimum computational effort, especially when considering small displacements. This paper proposes such element: a node-to-node contact formulation for macroelements. It considers that the nodal displacements of both nodes are in cylindrical coordinates with one of them using Fourier series to describe the displacements. To show model effectiveness, a case study with a cylinder using Fourier series and multiple helical elements connected with the contact element is done and shows great results. [ABSTRACT FROM AUTHOR]

In this paper, a hierarchical control logic for two-channel hydraulic active roll control (ARC) system, which includes vehicle level control and actuator level control is proposed. Vehicle level control consists of antiroll torque controller and antiroll torque distributor. The antiroll torque controller is designed with "PID + feedforward" algorithm to calculate the total antiroll moment. The antiroll torque distributor is devised based on fuzzy control method to implement an antiroll moment allocation between the front and rear stabilizer bar. Actuator level control is designed based on pressure and displacement, respectively. The contrastive analysis of the two proposed actuator control method is presented. The hardware-in-the-loop (HIL) test platform is proposed to evaluate the performance of the devised control algorithm. The HIL simulation result illustrates that actuator displacement control could generate a relatively accurate antiroll moment, and the vehicle roll stability, yaw stability can be enhanced by the proposed ARC control method. [ABSTRACT FROM AUTHOR]

In this study, the governing equation of motion for a general arbitrary higher-order theory of rods and tubes is presented for a general material response. The impetus for the study, in contrast to the classical Cosserat rod theories, comes from the need to study bulging and other deformation of tubes (such as arterial walls). While Cosserat rods are useful for rods whose centerline motion is of primary focus, here we consider cases where the lateral boundaries also undergo significant deformation. To tackle these problems, a generalized curvilinear cylindrical coordinate (CCC) system is introduced in the reference configuration of the rod. Furthermore, we show that this results in a new generalized frame that contains the well-known orthonormal moving frames of Frenet and Bishop (a hybrid frame) as special cases. Such a coordinate system can continuously map the geometry of any general curved three-dimensional (3D) structure with a reference curve (including general closed curves) having continuous tangent, and hence, the present formulation can be used for analyzing any general rod or pipe-like 3D structures with variable cross section (e.g., artery or vein). A key feature of the approach presented herein is that we utilize a non-coordinate "Cartan moving frame" or orthonormal basis vectors, to obtain the kinematic quantities, like displacement gradient, using the tools of exterior calculus. This dramatically simplifies the calculations. By the way of this paper, we also seek to highlight the elegance of the exterior calculus as a means for obtaining the various kinematic relations in terms of orthonormal bases and to advocate for its wider use in the applied mechanics community. Finally, the displacement field of the cross section of the structure is approximated by general basis functions in the polar coordinates in the normal plane which enables this rod theory to analyze the response to any general loading condition applied to the curved structure. The governing equation is obtained using the virtual work principle for a general material response, and presented in terms of generalized displacement variables and generalized moments over the cross section of the 3D structure. This results in a system of ordinary differential equations for quantities that are integrated across the cross section (as is to be expected for any rod theory). [ABSTRACT FROM AUTHOR]

Programmable multistable mechanisms (PMM) exhibit a modifiable stability behavior in which the number of stable states, stiffness, and reaction force characteristics are controlled via their programming inputs. In this paper, we present experimental characterization for the concept of stability programing introduced in our previous work (Zanaty et al., 2018, "Programmable Multistable Mechanisms: Synthesis and Modeling," ASME J. Mech. Des., 140(4), p. 042301.) A prototype of the T-combined axially loaded double parallelogram mechanisms (DPM) with rectangular hinges is manufactured using electrodischarge machining (EDM). An analytical model based on Euler-Bernoulli equations of the T-mechanism is derived from which the stability behavior is extracted. Numerical simulations and experimental measurements are conducted on programming the mechanism as monostable, bistable, tristable, and quadrastable, and show good agreement with our analytical derivations within 10%. [ABSTRACT FROM AUTHOR]

Rigid-body discretization of continuum elements was developed as a method for simplifying the kinematics of otherwise complex systems. Recent work on pseudo-rigid-body (PRB) models for compliant mechanisms has opened up the possibility of using similar concepts for synthesis and design, while incorporating various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within planar compliant mechanisms is developed to create a set of equations that can be used to analyze various designs and topologies. A PRB model with three revolute joints is derived to approximate the behavior of initially curved compliant beams, while treating straight beams as a special case (zero curvature). The optimized model parameter values are tabled for a range of arc angles. The general kinematic and static equations for a single-loop mechanism are shown, with an example to illustrate accuracy for shape and displacement. Finally, this framework is used for the design of a compliant constant force mechanism to illustrate its application, and comparisons with finite element analysis (FEA) are provided for validation. [ABSTRACT FROM AUTHOR]

This is a series of two papers in which the nonlinear stability behavior of sandwich panels is investigated. This part presents the buckling behavior and focuses on the critical load and the buckling mode. The buckling analysis is based on the extended high-order sandwich panel theory (EHSAPT) which takes transverse compressibility and axial rigidity of the core into account. It allows for the interaction between the faces and the core. The geometric nonlinearity, i.e., large displacement with moderate rotation, is considered in both faces and core. The weak form governing equations are derived based on the EHSAPT-based element. Detailed formulations and analysis procedures are provided. It presents a general approach for arbitrary buckling type without decoupling it into isolated global buckling and wrinkling. There are no additional assumptions made about the prebuckling state and buckling mode shape, which are commonly presumed in the literature. In addition, edge effects which are also commonly neglected are included. The prebuckling state is determined via a nonlinear static analysis. Solving an eigenvalue problem yields the critical load and the corresponding eigenvector gives the buckling mode. Sandwich panels with different lengths are studied as examples. Both global buckling and wrinkling are observed. It shows that the axial rigidity of the core has a pronounced effect on both the critical load and the buckling mode. [ABSTRACT FROM AUTHOR]

A major challenge in designing a perfect invisibility cloak for elastic waves is that the mass density and elasticity tensor need to be independent functions of its radius with a linear transformation medium. The traditional cloak for out-of-plane shear waves in elastic membranes exhibits material properties with inhomogeneous and anisotropic shear moduli and densities, which yields a poor or even negative cloaking efficiency. This paper presents the design of a cylindrical cloak for elastic shear waves based on a nonlinear transformation. This excellent broadband nonlinear cloak only requires variation of its shear modulus, while the density in the cloak region remains unchanged. A nonlinear ray trajectory equation for out-of-plane shear waves is derived and a parameter to adjust the efficiency of the cylindrical cloak is introduced. Qualities of the nonlinear invisibility cloak are discussed by comparison with those of a cloak with the linear transformation. Numerical examples show that the nonlinear cloak is more effective for shielding out-of-plane elastic shear waves from outside the cloak than the linear cloak and illustrate that the nonlinear cloak for shear waves remains highly efficient in a broad frequency range. The proposed nonlinear transformation in conjunction with the ray trajectory equation can also be used to design nonlinear cloaks for other elastic waves. [ABSTRACT FROM AUTHOR]

This paper presents an engineering approach to study the effects of soil profile variation and scour on structural response of an offshore monopile wind turbine. A wind-wave model for finite water depth is proposed to obtain the corresponding sea-state based on the incident wind. Different wind, wave, and current loads on the wind turbine for the operational conditions are considered. The interaction between the foundation and the soil is simulated by nonlinear springs, for which stiffness properties are obtained from the axial load transfer curve, the tip load-displacement curve, and the lateral load-deflection curve. Four types of soil conditions are considered, i.e., 100% sand layer, 50% sand layer (top) and 50% clay layer (bottom), 50% clay layer (top), and 50% sand layer (bottom), as well as 100% clay layer. For a given current speed, the variations of the structural response of the wind turbine due to the effects of different wind-wave load combinations, soil conditions and scour have been investigated. Different wind-wave load combinations directly affect the mean internal bending moment and mean displacement vertically along the support structure. Different soil conditions change the eigenfrequency of the structure significantly. The top layer of the soil appears to have a strong influence on the mean internal bending moment and the mean shear force distribution along the foundation. Moreover, the effect of scour alters the eigenfrequency of the structure significantly. The maximum mean bending moment and displacement increase for the cases with a scour hole as compared to the cases with scour protection. [ABSTRACT FROM AUTHOR]

This paper presents the substructure-based dynamic analysis of an offshore platform with compressor packages. Three typical substructure methods, the Guyan condensation method, the fixed-interface component mode synthesis (CMS) method and the free-interface CMS method, were compared to identify the appropriate substructure method for this application. A mode truncation criterion was proposed to ensure the accuracy of the recommended substructure method. The results indicated that the free-interface CMS method could generate almost the same results as the fully coupled method and save more than 50% in calculation time and more than 60% in storage space. When the same amount of time was used, the free-interface CMS method obtained more accurate results than the fixed-interface CMS method and Guyan condensation method; thus, the use of this method for evaluating the dynamics of an offshore platform with compressor packages was recommended. The cutoff frequency of the substructure was suggested to be 1.25 times the highest frequency of interest when conducting a dynamic analysis of an offshore platform with compressor packages using the free-interface CMS method. In addition, the offshore platform is a flexible structure with low and dense mechanical natural frequencies (MNFs), with approximately 4500 orders vibration modes in the frequency range of 0-40 Hz, and the displacement response at the area around the compressor package exceeded the allowable value under the excitation of the compressor package. [ABSTRACT FROM AUTHOR]

Understanding the buckling and post-buckling behavior of rods confined in a finite space is of both scientific and engineering significance. Under uniaxial compression, an initially straight and slender rod confined in a tube may buckle into a sinusoidal shape and subsequently evolve into a complicated, three-dimensional (3D) helical shape. In this paper, we combine theoretical and numerical methods to investigate the post-buckling behavior of confined rods. Two theoretical models, which are based on the inextensible and extensible rod theories, respectively, are proposed to derive the analytical expressions for the axial compressive stiffness in the sinusoidal post-buckling stage. The former is concise in formulation and can be easily applied in engineering, while the latter works well in a broader scope of post-buckling analysis. Both methods can give a good approximation to the sinusoidal post-buckling stiffness and the former model is proved to be a zeroth-order approximation of the latter. The flexible multibody dynamics method based on the Timoshenko's geometrically exact beam theory is used to examine the accuracy of the two models. The methods presented in this work can be used in, for example, drilling engineering in oil and gas industries. [ABSTRACT FROM AUTHOR]

In this paper, a microsystem with prescribed functional capabilities is designed and simulated. In particular, the development of a straight line path generator micro electro mechanical system (MEMS) device is presented. A new procedure is suggested for avoiding branch or circuit problems in the kinematic synthesis problem. Then, Ball's point detection is used to validate the obtained pseudo-rigid body model (PRBM). A compliant MEMS device is obtained from the PRBM through the rigid-body replacement method by making use of conjugate surfaces flexure hinges (CSFHs). Finally, the functional capability of the device is investigated by means of finite element analysis (FEA) simulations and experimental testing at the macroscale. [ABSTRACT FROM AUTHOR]

The membrane structure has been applied throughout different fields such as civil engineering, biology, and aeronautics, among others. In many applications, large deflections negate linearizing assumptions, and linear modes begin to interact due to the nonlinearity. This paper considers the coupling effect between vibration modes and develops the theoretical analysis of the free vibration problem for orthotropic rectangular membrane structures. Von Kármán theory is applied to model the nonlinear dynamics of these membrane structures with sufficiently large deformation. The transverse displacement fields are expanded with both symmetric and asymmetric modes, and the stress function form is built with these coupled modes. Then, a reduced model with a set of coupled equations may be obtained by the Galerkin technique, which is then solved numerically by the fourth-order Runge-Kutta method. The model is validated by means of an experimental study. The proposed model can be used to quantitatively predict the softening behavior of amplitude-frequency, confirm the asymmetric characters of mode space distribution, and reveal the influence of various geometric and material parameters on the nonlinear dynamics. [ABSTRACT FROM AUTHOR]