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Abstract An improved method is proposed to combine the incremental harmonic balance method (IHBM) with the equivalent piecewise linearization for solving the dynamics of complicated nonlinear stiffness systems. Compared with the traditional IHBM, the proposed method has a wider application range and can provide a standard and unified procedure to deal with various forms of nonlinear stiffness systems. Firstly, the equivalent piecewise linearization is adopted to approximate the nonlinear restoring force of the system to the piecewise-linear restoring force and the linearized error is put forward to evaluate the computation error of this approximation. The procedure is suitable for any form of nonlinear stiffness expression that can be linearized into piecewise-linear stiffness expression. Then the IHBM procedure for the general piecewise-linear stiffness system is derived considering the sub-harmonic responses. The Duffing oscillator is presented to validate the proposed method. Finally, three cases of nonlinear stiffness systems are carried out. The results of these cases show that the proposed method is capable of analyzing the dynamics of these complicated nonlinear stiffness systems. [ABSTRACT FROM AUTHOR]

Abstract Prediction of a ship's roll motion in parametric roll and dead ship condition using CFD and experiments is time consuming and expensive, while a reliable equation based method can drastically decrease the computation time. The commonly used roll motion equation contains roll mass and added mass moment of inertia, damping and restoring terms and associated coefficients. Improving the prediction of these coefficients increases the accuracy of the method. There is a lack of precise calculation for the roll added mass moment of inertia, which is commonly estimated using semi-empirical techniques and as a percentage of the roll mass moment of inertia coefficient. This paper presents a new method to determine the roll added mass moment of inertia using CFD simulations based on a harmonic excitation roll motion technique and the results are compared against Bhattacharyya's method. The influences of excitation frequency, Froude number, roll angle and appendages on the roll motion characteristics and the roll added mass moment of inertia coefficient are investigated. In addition, the roll added mass moment of inertia coefficients on the model scale and full scale ship are computed to investigate the scale effect. [ABSTRACT FROM AUTHOR]

A nonparametric model is established to investigate the vibration characteristics of a motorized spindle system, where the bearing restoring force, the unbalanced magnetic pull, and the external bounded noise excitation are taken into account. Based on the Monte Carlo simulation, several numerical examples are used to study the effect of dispersion parameters from model uncertainty and strength of external bounded noise excitation on the whirl frequency and bifurcation behavior of the spindle. It is shown that the whirl frequency fluctuates due to the random uncertainty, and the fluctuation range grows wider as the dispersion parameters increase as anticipated. In the randomly uncertain case, the vibration of the spindle also exhibits periodic-dominant and bifurcation phenomena, of particular interest is the delay of bifurcation point following the increase of the rotation speed. Towards the vibration condition monitoring on the spindle system, the phase space reconstruction technique is also applied to identify the vibration signals by comparing the reconstructed deterministic phase-space orbits with those from the random uncertainty and the bounded noise excitation, and the inherent dynamical behavior can be revealed from the irregular one-dimension time series effectively. [ABSTRACT FROM AUTHOR]

A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort. [ABSTRACT FROM AUTHOR]

Highlights • Propose a novel isolation structure with flexible joints. • Introduce Origami mechanism in vibration isolation/protection structure. • Utilize asymmetrical nonlinearity to extend the effective isolation bandwidth. • Determine the optimal structural parameter of folds for isolation effectiveness improvement. • Carry out the experimental prototype with remarkable isolation/protection property. Abstract This paper proposes a novel isolation/protection structure inspired by structure and forcing method of leg parts of bipeds, the Origami-Joint Flexible (OJF) isolation structure. The vibration performances are studied under impact and ultralow-frequency excitations. According to the mechanical features of the legs of bipeds, the restoring force is considered mainly at the joints. Simulating the structure of bipeds, the flexibility of the proposed structure is realized by using an Origami structure with resilience at its folds. Based on the analysis of potential energy, the restoring and damping forces are nonlinear and symmetrical, depending on both magnitude and direction of motions. Then, solutions for transient and steady states are obtained for different high-energy excitations. Due to the large displacement and strong nonlinearity, the Method of Multiple Scales (MMS) with high-order approximation is utilized for theoretical study. The main theoretical results are verified by experiments. The relevant prototype displays remarkable isolation/protection effectiveness for impact and ultralow-frequency excitations. This study not only shows the advantages of strong asymmetrical nonlinearity of the novel isolation structure with flexible joints but also theoretically explains its control mechanism. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

The time-domain simulation follows the heaving of the conical float in waves and calculates the bag shape, ballast motion, adiabatic air pressure and the flow through the turbine. There are two independent oscillators, the float with its resonance and the bag/ballast with its resonance. The coupling of the two oscillators gives rise to a wide band response with two peaks in the capture width each reaching the theoretical λ/2π. In this new wave energy converter, apart from the turbine, there are no mechanical moving parts, no joints nor pistons, no end stops nor sliding seals, no flaps nor one-way valves. The expected life of the airtight flexible bag remains to be determined, but potential manufacturers are optimistic. [ABSTRACT FROM AUTHOR]

A recent study suggested that the nonlinear feedback loop (NFL) of the three-dimensional nondissipative Lorenz model (3D-NLM) serves as a nonlinear restoring force by producing nonlinear oscillatory solutions as well as linear periodic solutions near a nontrivial critical point. This study discusses the role of the extension of the NFL in producing quasi-periodic trajectories using a five-dimensional nondissipative Lorenz model (5D-NLM). An analytical solution to the locally linear 5D-NLM is first obtained to illustrate the association of the extended NFL and two incommensurate frequencies whose ratio is irrational, yielding a quasi-periodic solution. The quasi-periodic solution trajectory moves endlessly on a torus but never intersects itself. While the NFL of the 3D-NLM consists of a pair of downscaling and upscaling processes, the extended NFL within the 5D-NLM additionally introduces two new pairs of downscaling and upscaling processes that are enabled by two high wavenumber modes. One pair of downscaling and upscaling processes provides a two-way interaction between the original (primary) Fourier modes of the 3D-NLM and the newly-added (secondary) Fourier modes of the 5D-NLM. The other pair of downscaling and upscaling processes involves interactions amongst the secondary modes. By comparing the numerical simulations using one- and two-way interactions, we illustrate that the two-way interaction is crucial for producing the quasi-periodic solution. A follow-up study using a 7D nondissipative LM shows that a further extension of NFL, which may appear throughout the spatial mode-mode interactions rooted in the nonlinear temperature advection, is capable of producing one more incommensurate frequency. [ABSTRACT FROM AUTHOR]

A nonlinear oscillator, using a cubic-spring restoring function with high-deformation stiffening, is introduced and studied experimentally to improve passively the harnessed marine hydrokinetic power using Flow Induced Vibrations (FIVs) of a cylinder. In this research, the FIV of a single, rigid, circular cylinder on elastic end-supports is tested for Reynolds number 30,000 ≤  Re  ≤ 120,000. Damping, cubic stiffness, and flow-velocity are used as parameters. Selective roughness is applied to enhance FIV and increase the hydrokinetic energy converted by the oscillator. The second generation of the digital, virtual spring-damping system Vck, developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of the functions and values of viscous damping and spring stiffness. Cubic modeling of the oscillator stiffness in parametric form is thus realized and tested. Experimental results for amplitude response, frequency response, energy harvesting, efficiency and instantaneous energy of the converter are presented and discussed. All experiments are conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The cubic stiffness function is an effective way to raise the harnessed efficiency over a wider range of flow velocities. (2) At lower flow speed (upper and lower VIV branches), the harnessed power increases as the nonlinearity increases. A strongly nonlinear system exhibits a 100% increase in harnessed energy in this region. (3) At a higher flow speed (galloping), the cubic nonlinearity benefits the harnessed power in two ways because the natural frequency of the oscillator in water ( f n,water ) depends on the amplitude of oscillation. At low harness damping, the amplitude increases resulting in higher f n,water thus enhancing the harnessed power. At high harness damping, the harnessed power increases regardless of f n,water . [ABSTRACT FROM AUTHOR]

This paper presents an approach for restoring force enhancement to radio frequency (RF) micro-electro-mechanical systems (MEMS) switch with stiction-recovery actuation mechanism. It is based on additional anti-stiction electrodes which are inserted to the coplanar waveguide (CPW) between the signal line and ground planes of a RF MEMS switch. If the movable membrane sticks to the substrate, electrostatic force, as extra restoring force, generated by the bias voltage between the anti-stiction electrodes can promise restoring action. The designed device with the proposed approach is fabricated. The restoring force of the fabricated device had reached 75, 177 and 520 μN by the bias voltages of 0, 10 and 20 V, respectively. [ABSTRACT FROM AUTHOR]

Column is set on the stone base directly in traditional wooden structure, which forms to the very important column footing joint connecting the upper structure and stone base. Column foot transfers compressive force only without any tensile capacity. Columns can rotate around the edge of column foot under cyclic loads. Three 7 ts' ai full-scale column footing joint models based on Ying-tsao-fa-shih were established to study mechanical property of column footing joint under cyclic loads, such as earthquake or wind loads. The mechanical property, hysteretic characteristics, rotation stiffness, stiffness degradation law, equivalent radius and strain of edge point of column footing joint were analysed, and the effects of vertical loads on the above performances were also studied. Results show that compression deformation occurs at the edge of column foot, and rotation point of column foot changes from left to right under cyclic loads. Hysteretic curve with a Z-shape has pinching effect. Restoring moment and equivalent radius are increased with increase of rotation angle first and then constant. The stiffness with great initial value is decreased with increase of rotation angle. Stiffness degradation of column foot happens under cyclic loads. The rotation stiffness is positive during loading, which shows it has preferable rotation capability. Restoring moment, rotation stiffness and strain of edge point have a rising trend with the increase of vertical load. On the contrary, the equivalent radius is decreased with the increase of vertical load. The coefficient of vertical load on restoring moment and rotational stiffness were obtained by test results fitting. [ABSTRACT FROM AUTHOR]

This study deals with analysis of stochastic crosswind response of tall buildings with bilinear hysteretic restoring force character at the vicinity of vortex lock-in speed where nonlinear negative aerodynamic damping is significant. The nonlinear aerodynamic damping at a given wind speed and the hysteretic damping resulted from hysteretic restoring force are modelled as polynomial functions of amplitude of narrow-band building response. It permits analytical estimations of response statistics by using equivalent nonlinear equation (ENEL) approach, which include root-mean-square value, kurtosis, extreme value distribution and fatigue damage. Response history analysis is also performed to prove the accuracy of this analytical framework. A comprehensive parameter study is carried out to shed insights on the characteristics of inelastic crosswind response. This study also illustrates the advantage of the ENLE approach over the statistical linearization approach with assumption of Gaussian response distribution when applied to estimate inelastic crosswind response at wind speed region with negligible aerodynamic damping. This study not only presents an effective analytical approach but also sheds new insights towards improved understanding of inelastic crosswind response of tall buildings, contributing to a safer and more economical design of tall buildings against strong winds. [ABSTRACT FROM AUTHOR]

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate. [ABSTRACT FROM AUTHOR]

In this paper, the problem of positive periodic solutions is studied for the Liénard equation with a singularity of repulsive type, where $f:(0,+\infty)\rightarrow R$ is continuous, α, h are continuous with T-periodic and $\alpha(t)\ge0$ for all $t\in R$ , $\mu \in(0,+\infty)$ is a constant. By means of a Manásevich-Mawhin's continuation theorem, a sufficient and necessary condition is obtained for the existence of positive T-periodic solutions of the equation. The interesting point is that the weak singularity of restoring force $\frac{\alpha(t)}{x^{\mu}}$ at $x=0$ is allowed and f may have a singularity at $x=0$ . [ABSTRACT FROM AUTHOR]

Restoring force model is the foundation of the elasto-plastic time history analysis of the steel structure or the member. However, the restoring force curves obtained from the experiments are complex and difficult to be directly used for the seismic calculation of the structure. In order to simplify the restoring force characteristics of the outer shell beam-column joints of a steel structure, a computational model based on the properties of the test curves and described by a mathematical method was presented. Through the quasi-static test method, the seismic performance of four outer shell joints under cyclic loading was studied, and the stress stage and failure mode were analyzed. Then, a tri-linear restoring force model accorded with the skeleton curve characteristics was established. Based on this model, the stiffness degradation rules of the specimens under reciprocating load were deduced by regression statistical method. In addition, the hysteresis curve models of the joints were calculated and compared with the experimental results. The results show that the stress process of the specimen is divided into three stages: elasticity, yield, and plasticity. Moreover, the tri-linear skeleton curve models are in good agreement with the experimental results, which reflect the stress properties of the joints at different stages. Meanwhile, the hysteresis models considering stiffness degradation describe the hysteresis rules, these rules are approximately the same as the hysteresis curves obtained from the tests. The proposed restoring force model can accurately reflect the moment-rotation relationships of the specimens, providing theoretical references for the nonlinear seismic response analysis of the outer shell joints. [ABSTRACT FROM AUTHOR]

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

The effects of the polarization force on the self-similar expansion into vacuum of an unmagnetized, collisionless dusty plasma are addressed. It is found that the polarization force may drastically influence the general trends of the self-similar expansion. It is noticed that when the polarization force dominates over the electrical one, the self-similar expansion of the dusty plasma cannot set in because the net force experienced by the dust grains is not a restoring force. Dust wave breaking and inherent dust bunching then occur preventing therefore the expansion of the dust grains. For any value of the polarization parameter R ranging from zero to a critical value Rcr, the sound-speed increases as the dust number density increases. As R increases, the values of the plasma soundspeed are shifted towards higher values before decreasing beyond the critical value Rcr. As R increases from zero to Rc, the plasma expansion becomes faster compared to those of the other cases, and larger velocities are communicated to the dust grains. This is attributed to the fact that as R increases from 0 to Rcr, the electrostatic potential and thus the electric field are sustained over a larger distance allowing therefore the dust particles to expand over a much farther distance. [ABSTRACT FROM AUTHOR]

Flow Induced Motions (FIMs) of a single, rigid, circular cylinder with piecewise continuous restoring force are investigated for Reynolds number 24,000≤ Re ≤120,000 with damping, and different piecewise functions as parameters. Selective roughness is applied to enhance FIM and increase the hydrokinetic energy captured by the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) Converter at higher Reynolds numbers. The second generation of virtual spring-damping system Vck, developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of viscous-damping and spring-stiffness for fast and precise oscillator modeling. Experimental results for amplitude response, frequency response, energy harvesting, and efficiency are presented and discussed. All experiments were conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinear piecewise spring Converter can harness energy from flows as slow as 0.275 m/s with no upper limit. (2) In galloping, the nonlinear spring Converter has up to 76% better performance than its linear spring counterpart. (3) The FIM response is predominantly periodic for all nonlinear spring functions used. (4) Optimal power harnessing is achieved by changing the nonlinear piecewise spring function and the linear viscous damping. (5) VIVACE exhibits local maxima in power conversion at the end of the upper branch in VIV and the highest velocity reached in galloping. (6) The efficiency optima though are at the beginning of the VIV initial branch and at the beginning of galloping. [ABSTRACT FROM AUTHOR]

Due to difficulties in determining modulus of elasticity of wood, only strain or deflection profiles caused by relaxation of internal stress are normally evaluated for industrial kiln-dried lumber. To directly assess the level of internal stress within the lumber, a new technique of measuring the restoring force on a half-split specimen has been presented and the corresponding device has been designed and constructed. Kiln-dried rubberwood specimens with dimensions of 30 or 50 mm (thickness), 130 mm (width) and 50 mm (length) were used in the study. The measured restoring force appears to vary with half-split length and specimen thickness. A mathematical model based on an elastic cantilever beam theory has been successfully developed to describe the restoring force behavior in a flexural response regime. The magnitude of the maximum linearly averaged internal stress σ can be derived without prior knowledge of the modulus of elasticity of wood. For the 30-mm-thick lumber, the derived values of σ are in general agreement with the ones obtained from the conventional McMillen slice test. Very close agreement is observed when the internal stress is at a relatively low level and its profile is approximately linear. But for the 50-mm-thick lumber, the determination of σ is less appropriate because of its relatively short flexural range. A restoring force-internal stress chart has been proposed for practical use in the lumber industry. This assessment was performed to investigate the evolution of internal stress during the conditioning and storage stages of kiln-dried rubberwood lumber. [ABSTRACT FROM AUTHOR]

The synchronous interaction between a sloshing fluid and its container may take place when the motion of the container is not prescribed a priori . When a partially-filled container is suspended as a bifilar pendulum, the fluid contributes to the restoring force by its weight through the wire suspensions and may either augment or diminish the restoring force through hydrodynamic interaction with the container. Here we report on linearized shallow-water theory and experiments for multi-chamber box containers, a cylinder and an upright 90° wedge. The nature of system response at low fluid mass is analyzed in detail using linear theory and shallow-water simulations. These results show that the system frequency smoothly transitions through successive higher frequency eigenmodes so that, in the limit where the fluid mass tends to zero, the system frequency is that of the dry container. [ABSTRACT FROM AUTHOR]

In the dynamic time-history analysis of structural elastoplasticity, it is important to develop a universal mathematical model that can describe the force-displacement characteristics for restoring force. By defining three control parameters (stiffness degradation, slip closure γ, energy degradation β), the Park restoring force mathematical model can simulate various components. In this study, the Park restoring force has been improved by adding two control parameters (energy-based strength degradation βe and ductility-based strength degradation βd). Based on the testing data, the constitutive model is input and 55 numerical models are developed to analyze the effects of various parameters on structural behavior. Conclusion. (1) β has determinative effect on structural behavior; the effect of βe is basically consistent with that of β; α has significant effect on shear forces and bending moments; γ has significant effect on displacements and accelerations; βd has significant effect on shearing forces, acceleration, and total energy consumptions. (2) Based on the classification of four types of damage level, the recommended values for α, γ, β, βe, and βd are presented. (3) Based on the testing data of high-strength columns, the recommended values for the five control parameters of the improved Park restoring force model are presented. [ABSTRACT FROM AUTHOR]

This article presents a parametric study on the lateral-torsional coupling behaviour of the simplified bidirectional asymmetric multistorey dual lateral load-resisting model. The implementation process for establishing the simplification model is shown in an illustrative example on a three-storey reinforced concrete building system. Combined with the force–displacement relationships of the lateral load-resisting members and the inter-story restoring force models, the dynamic stiffness matrix and the equations of motion under different loading conditions can also be determined. On this basis, parametric analyses for the systems are carried out through the whole loading process from the elastic stage to the inelastic stage. Effects of uncoupled torsion to lateral frequency ratios (Ω) and the stiffness eccentricities on the frequencies are investigated. The analysis shows that the asymmetrical system with a smaller Ω value has a smaller torsional stiffness and a stronger lateral-torsional coupling effect. The effects of the eccentricities in both directions on the frequencies are remarkably different. Smaller Ω values and greater eccentricities lead to greater reductions in the effects of Ω and eccentricities on the frequencies in the inelastic stage. [ABSTRACT FROM AUTHOR]

A strongly nonlinear pendulum mechanism is considered in which the restoring force is approximately a cubic function of the displacement variable. Its free oscillation frequency is approximately proportional to the amplitude of oscillation and distinctly lower than that of a simple pendulum. The mechanism has therefore been named infra-pendulum. The forced undamped oscillation response of the mechanism to non-harmonic periodic loading is studied under the assumption of small displacements. The loading function is derived from the free oscillation response whose time course follows a Jacobi elliptic function. It is chosen such that exact analytical solutions are obtained for the steady-state response and the amplitude–frequency relation. The equation describing the amplitude–frequency relation is a cubic polynomial equation. Its solutions are presented. The general approach of using non-harmonic periodic loading functions is transferable to other types of nonlinear oscillators. [ABSTRACT FROM AUTHOR]

A semi-analytical approach to the simulation of the parametric roll motions of container ships in head seas is presented. In the proposed 1.5-degree of freedom model, the nonlinear change in the transverse stability induced by the vertical motions and wave elevation is approximated by investigating the relationship between the restoring lever ( GZ ) and the metacentric height ( GM ) in waves. In particular, the variations in the GM in irregular waves are modeled by the transfer functions of the mean value and first harmonic component on the basis of the assumption of superposition. Using the derived formula, the quantitative prediction of parametric roll motion as well as the susceptibility to such motion in regular and irregular waves is conducted. A comparison with the results of a weakly nonlinear time-domain method, namely, the impulse response function method based on the hydrodynamic coefficients of strip theory, is carried out to validate the proposed model. Not only the accuracy and efficiency of the present approach but also the stochastic properties of parametric roll in random seas are examined considering the sensitivities and uncertainties in the computations. [ABSTRACT FROM AUTHOR]

Based on Euler–Bernoulli beam theory and Hamilton’s principle, the differential equation of a vertical cantilevered pipe conveying fluid is derived when the pipe has deploying or retracting motion. The resulting equation is discretized via the Galerkin method in which the eigenfunctions of a clamped-free Euler–Bernoulli beam are utilized. Then, the dynamic responses and stability are discussed with regard to the deploying or retracting speed, mass ratio, and fluid velocity. Numerical results reveal that the dynamical behavior of the system is mainly affected by the flow velocity, instantaneous length of pipe, gravity, and mass ratio. For the small flow velocity, the fluid and higher mass ratio helps to stabilize the transverse vibration of the cantilevered pipe conveying fluid in both deployment and retraction modes, and the system will lose stability with the further increase of flow velocity. The critical flow velocity is mainly influenced by the instantaneous length of pipe. The additional restoring force due to gravity causes critical flow velocity to be higher for the vertically cantilevered pipe conveying fluid. Therefore, gravity is conducive to the stability the transverse vibration of the system in both deployment and retraction modes. [ABSTRACT FROM AUTHOR]

This paper focuses on a horizontal-vertical coupling effect observed in a full-scale shake table experiment of a 5-story moment frame building isolated with triple pendulum bearings. A significant increase or amplification of the horizontal floor accelerations was observed during three-dimensional (3D) shaking compared to XY (horizontal only) shaking with comparable input motions. The coupling phenomenon is explained by analytical and numerical simulation of a single degree-of-freedom (rigid mass) structure and multistory cantilever structure subjected to simplified sinusoidal motions, both isolated with triple pendulum bearings. The results of the simplified numerical study are extended to explain the horizontal-vertical coupling in the full-scale experiment, which are also validated by numerical modeling of the test structure. The vertical component of ground acceleration is shown to introduce a high-frequency component into the base shear that can excite higher modes of the base-isolated structure. The phenomenon is possible in anymultistory structure isolated with friction bearings, and should be evaluated on a case-by-case basis. [ABSTRACT FROM AUTHOR]

Pitching motion is one of the most important characteristics in the longitudinal plane for the maneuvering supercavitating vehicle. In this case, supercavity is unsteady to dramatically change hydrodynamic distribution of its vehicle because of some factors such as changes of ambient pressure and control surfaces, gravity, inertial force, and so on. More importantly, planing force is usually produced to provide restoring force and moment for motion stability. The maneuvering supercavity model is applied to model supercavitating vehicle with planing force in the longitudinal plane. The corresponding numerical algorithm is developed to simulate uncontrolled vehicle making a diving motion in the longitudinal plane and calculate planing force based on the model. The algorithm includes two intercoupling sub-algorithms: the self-developed cavitation number embedded coefficient correction algorithm for unsteady supercavity and Runge–Kutta algorithm for vehicle’s trajectory. The model and numerical algorithm are validated to some extent by comparing numerical results with ones of the empirical supercavity model applied widely. [ABSTRACT FROM AUTHOR]

In this study, we investigated the scaling behavior of dynamic hysteresis with frequency f and electric field E in epitaxial PbZrO 3 antiferroelectric film on (111)-oriented SrTiO 3 substrate. The scaling relation for the saturated hysteresis loops takes the form of hysteresis area ∝ f 0.03 ( E − 499) 0.20 at relatively low testing f . However, when frequency exceeds 30 Hz, the shows stronger dependence on f while remains basically unchanged relation with E , leading to a form of ∝ f 0.10 ( E − 499) 0.20 . The scaling behavior is modeled as occurring in a viscous medium where several forces, such as viscous and restoring forces, act on the phase transition process. [ABSTRACT FROM AUTHOR]

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η, that maximizes the clustering of the particles. [ABSTRACT FROM AUTHOR]

Abstract.: One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. Graphical abstract: [ABSTRACT FROM AUTHOR]

In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge weakly to an Itô differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a nonlinear approach to identify the structural parameters of a vertical riser. To carry out this task, Kalman-like observers are proposed so that they can deal with the nonlinear behavior that is exhibited in the restoring force of a riser and the noise of the measurement signals that are used to perform the identification. The observers are designed from a spatial discretization of a nonlinear model with distributed parameters that is described by a system of quasi-linear partial differential equations. Some results from numerical simulations—showing the feasibility of the proposed approach—are presented. [ABSTRACT FROM AUTHOR]

Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is validated experimentally, analytically, and numerically. As compared to the 3 dB bandwidth of the corresponding linear system with the same linear damping ratio, the M-shaped oscillator offers 3200, 5600, and 8900 percent bandwidth enhancement at the root-mean-square base excitation levels of 0.03 g , 0.05 g , and 0.07 g , respectively. The M-shaped configuration can easily be exploited in piezoelectric and electromagnetic energy harvesting as well as their hybrid combinations due to the existence of both large strain and kinetic energy regions. A demonstrative case study is given for electromagnetic energy harvesting, revealing the importance of higher harmonics and the need for multi-term harmonic balance analysis for predicting the electrical power output accurately. [ABSTRACT FROM AUTHOR]

The hysteresis behavior of a cast-in-situ recycled aggregate concrete (RAC) frame was analyzed based on shaking table tests on a one-fourth scaled model of a two-bay, two-span and 6-storey RAC frame. Then feature points and the stiffness degradation were defined and the deteriorating four-line-typed restoring force model was put forward. In the hysteresis model, the monotonic behavior is described by a four-line-typed skeleton curve which accounts for concrete cracking, yielding of reinforcing bars, maximum and ultimate point of the RAC frame model. The hysteresis behavior is described through a number of rules for unloading and reloading. Therefore, the restoring force model proposed in this study can capture the hysteresis response of the frame under seismic actions. Moreover, the displacement ductility of the RAC frame structure is evaluated based on the proposed restoring force model. It can be concluded from this investigation that the RAC frame structure with proper design and construction has favorable load-carrying capacity, deformation capacity, energy dissipation ability and seismic performance, and can be applied and popularized in the area with the requirement of aseismic fortification intensity. [ABSTRACT FROM AUTHOR]

Abstract: Chain-like systems have been studied by many researchers for their simple structure and wide range of application. Previously, the damage in a chain-like system was detected by the reduction of the mass-normalized stiffness coefficient for certain elements as reported by Nayeri et al. (2008 [16]). However, some shortcomings exist in that approach and for overcoming them; an improved approach is derived and presented in this paper. In our improved approach, the mass normalized stiffness coefficients under two states (baseline state and potentially damaged state) are first estimated by a least square method, then these mass-stiffness coupled coefficients are decoupled to derive stiffness and mass relative change ratios for individual elements. These ratios are assembled in a vector, which is defined as damage indication vector (DIV). Each component in DIV is normalized individually to one to get multiple solutions. These solutions are averaged for estimating relative system changes, while abnormal solutions are discarded. The work of judging a solution as normal or abnormal is done by a cluster analysis algorithm. The most intriguing merit of this improved approach is that the relative stiffness and mass changes, which are coupled in the previous approach, can be separately identified. By this approach, the damage (single or multiple) extent and location can be correctly detected under operational conditions, meanwhile the proposed damage index has a clear physical meaning and is directly related to the stiffness reduction of corresponding structural elements. For illustrating the effectiveness and robustness of the improved approach, numerical simulation of a four floor building was carried out and experimental data from a structure tested at the Los Alamos National Laboratory was employed. Identified structural changes with both simulation and experimental data properly indicated the location and extent of actual structural damage, which validated the proposed approach. [Copyright &y& Elsevier]

In this paper pole assignment control method is used to modify dynamic properties of damaged buildings. Since the eigenvalues of open-loop system, known as poles, are related to the dynamic properties of the system, damage causes changes in their values. In terms of pole assignment, a controller will modify dynamic properties of damaged structure by moving the eigenvalues to their initial place. Using the proposed gain matrix calculation algorithm and restoring the initial eigenvalues, dynamic properties of undamaged building, which have been lost due to damage, can be restored. When feedback controller restores all the eigenvalues, damaged elements and connections can be verified from the large control forces concentrated in the nodes of damaged elements. The algorithm also represents a new approach for partial pole assignment and the effect of restoring some undesired eigenvalues can be studied individually. For numerical simulation, a typical ten-story moment frame building is employed which has experienced some damages during the 1971 Newhall earthquake. Three states of damage are defined for the finite element model of the building to consider damage in elements and connections. [ABSTRACT FROM AUTHOR]

The restoring force method (RFM), a nonparametric identification technique established in applied mechanics, was used to maximize the information obtained from moment-rotation hysteresis curves under pure moment flexion-extension testing of human lumbar spines. Data from a previous study in which functional spine units were tested intact, following simulated disk injury, and following implantation with an interspinous process spacer device were used. The RFM was used to estimate a surface map to characterize the dependence of the flexion-extension rotation on applied moment and the resulting axial displacement. This described each spine response as a compact, reduced-order model of the complex underlying nonlinear biomechanical characteristics of the tested specimens. The RFM was applied to two datasets, and successfully estimated the flexion-extension rotation, with error ranging from 3 to 23%. First, one specimen, tested in the intact, injured, and implanted conditions, was analyzed to assess the differences between the three specimen conditions. Second, intact specimens (N=12) were analyzed to determine the specimen variability under equivalent testing conditions. Due to the complexity and nonlinearity of the hysteretic responses, the mathematical fit of each surface was defined in terms of 16 coefficients, or a bicubic fit, to minimize the identified (estimated) surface fit error. The results of the first analysis indicated large differences in the coefficients for each of the three testing conditions. For example, the coefficient corresponding to the linear stiffness (a01) had varied magnitude among the three conditions. In the second analysis of the 12 intact specimens, there was a large variability in the 12 unique sets of coefficients. Four coefficients, including two interaction terms comprised of both axial displacement and moment, were different from zero (p < 0.05), and provided necessary quantitative information to describe the hysteresis in three dimensions. The results suggest that further work in this area has the potential to supplement typical biomechanical parameters, such as range of motion, stiffness, and neutral zone, and provide a useful tool in diagnostic applications for the reliable detection and quantification of abnormal conditions of the spine. [ABSTRACT FROM AUTHOR]

Electrostatically-driven, cantilever-shaped resonators under a pair of parallel-plate electrodes with the ‘pull–pull drive’ scheme have been demonstrated and characterized. Theoretical analyses have been established based on the force balance among the electrostatic excitation, the mechanical elastic restoring force and air damping reactions. It is found that the ‘pull–pull drive’ setup can exhibit nonlinear characteristic in the output response, and consequently achieve about 3.8 times the maximum resonance amplitude as compared with the conventional single electrode setup. Furthermore, by adjusting the position of the cantilever between the parallel-plate electrodes, the magnitude of pull-in voltage as well as the maximum resonance amplitude can be changed. As such, the ‘pull–pull drive’ scheme provides an easy and alternative way to increase the response of the electrostatically-actuated resonators for various potential applications in resonator-based sensors and actuators. [ABSTRACT FROM AUTHOR]

Abstract: The hysteresis exhibited by short steel wire ropes is shown to lend itself as an effective restoring force for nonlinear monodirectional tuned mass dampers. Experiment-driven modeling based on the identified hysteretic restoring forces together with continuation tools enables an optimal design of these dampers through construction of families of frequency–response curves over a wide range of excitation amplitudes. Semi-analytical/numerical and experimental studies are carried out considering a base-excited test structure represented by a simply supported beam together with a prototype of the hysteretic damper subject to either harmonic or filtered Gaussian white noise excitations. [Copyright &y& Elsevier]

A self-centering concrete wall with distributed friction devices is proposed to achieve seismic resilient building structures. Unbonded post-tensioned tendons, running vertically through wall panels, provide a restoring force that pulls the structure back toward its undeformed plumb position after earthquake. Two steel jackets are installed at wall toes to prevent concrete spalling and crushing. Friction devices are distributed between the wall and its adjacent gravity columns to achieve controllable energy dissipation, and these devices are readily replaceable. Desirable self-centering and energy dissipation capacities were observed in low-cyclic loading tests, and influences of various parameters on the hysteretic behavior were investigated. [ABSTRACT FROM AUTHOR]

Abstract: In my research a 3D model was created to investigate the restoring force arising and the self-alignment occurring during reflow soldering; and simulations were performed to examine the assumptions given by the model. Besides, experiments were carried out to verify both the assumptions and the simulation predictions. Passive components with the size of 0603 (1.5×0.75mm) were placed with intended misplacements and their position was measured before and after soldering. Three cases were examined: how misplacements perpendicular to the longer sides of components affects the restoring force, how parallel misplacements affect the same, and how a sidewall metallization on the component influences that. Based on the results, it is shown that the degree of restoring force is higher in the case of misplacements perpendicular to the longer side of components (x-direction) than in the case of misplacements parallel to that (y-direction). However, in the case of y-direction misplacements, the restoring force increases when sidewall metallization on the components is present. [Copyright &y& Elsevier]

The present authors have earlier reported the employment of varying section fixed-fixed beam for achieving lower pull-in voltage with marginal fall in restoring force. Reducing Young's modulus also reduces the pull-in voltage but with lesser degree of reduction in restoring force. Composite beams are ideal alternatives to achieve decreased Young's modulus. Hence new varying section composite fixed-fixed beam type RF MEMS switch has been proposed. The main advantage of this RF MEMS switch is that lower pull-in voltages can be achieved with marginal fall in stiction immunity. Spring constant of the proposed switch has been obtained using simulation studies and it has been shown that the spring constant and therefore the pull-in voltage (Vpi) can be considerably reducedwith the proposed switch. Simulation studies conducted on the proposed switch clearly demonstrate that the pull-in voltage can be reduced by 31.17% when compared to the varying section monolayer polysilicon fixed-fixed beam. Further this approach enables the designer to have more freedom to design lower pull-in voltage switches with improved stiction immunity. [ABSTRACT FROM AUTHOR]

Performance characteristics of tunable-gap electromechanical actuators depend on the complex interaction of forcing function (voltage versus charge actuation), restoring force (linear versus nonlinear spring), and electrode geometry (planar versus nanostructured electrodes); and have been studied on a case-by-case basis. In this paper, we unify the performance characteristics of electromechanical actuators through scaling relationships for pull-in (PI) instability, PI voltage/charge, and resonance frequency. These scaling relationships depend only on two scaling parameters, n and p, related to the electrostatic force and the nature of spring, respectively. This scaling theory not only explains a broad range of experimental data within a single theoretical framework, but can also be used to characterize electrode geometry and nature of spring for any new actuator. The scaling relationships should enable the design of electrode geometry, actuation mechanism, and/or spring for desired performance. [ABSTRACT FROM PUBLISHER]

The theoretically predicted vanishment of the macroscopic contact angle hysteresis is found experimentally along with a small but finite force of adhesion (FAd≈-0.5 μN) that, unexpectedly, is independent of the history of the preload. Our results agree with the prediction of a model in which the surface tension of the liquid provides the counterpart of the restoring force of an elastic solid, evidencing that the dewetting of a liquid in the absence of strong pinning points is equivalent to the detachment of an elastic solid. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a vertical quasi-zero stiffness (QZS) vibration isolator with a mechanism for adjusting restoring force. QZS vibration isolators have high initial stiffness and QZS around the static equilibrium position. This way, excessive deformation due to self-weight can be avoided while having enough vibration reduction capability to dynamic excitations. One of the main issues left for QZS vibration isolators is the difficulty in keeping the vibration reduction capability when the vibration isolated object is replaced. In such a case, adjustment of its restoring force becomes necessary in accordance with the self-weight of the newly placed vibration isolated object. This paper attempts to address this issue by proposing a mechanism that enables quick and easy adjustment of the restoring force of a QZS vibration isolator. The proposed mechanism consists of cranks and a screw jack. With the present mechanism, the restoring force provided by horizontally placed springs can be converted into the vertical restoring force of the vibration isolator. In the conversion, the vertical resisting force can be adjusted simply by applying and removing torque to the screw jack to change and hold the angle of inclined bars placed in the cranks. In this study, a prototype of a class of QZS vibration isolator having the proposed mechanism is produced. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the produced prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the produced prototype can reduce the response acceleration within the same tolerance even when the mass of the vibration isolated object is changed. [Copyright &y& Elsevier]

We predict that a low-permittivity oblate body (disk-shaped object) above a thin metal substrate (plate with a hole) immersed in a fluid of intermediate permittivity will experience a metastable equilibrium (restoring force) near the center of the hole. Stability is the result of a geometry-induced transition in the sign of the force, from repulsive to attractive, that occurs as the disk approaches the hole—in planar or nearly planar geometries, the same material combination yields a repulsive force at all separations, in accordance with the Dzyaloshinskiĭ-Lifshitz-Pitaevskiĭ condition of fluid-induced repulsion between planar bodies. We explore the stability of the system with respect to rotations and lateral translations of the disks and demonstrate interesting transitions (bifurcations) in the rotational stability of the disks as a function of their size. Finally, we consider the reciprocal situation in which the disk-plate materials are interchanged and find that in this case the system also exhibits metastability. The forces in the system are sufficiently large to be observed in experiments and should enable measurements based on the diffusion dynamics of the suspended bodies. [ABSTRACT FROM AUTHOR]