Search

In this article we propose a theoretical investigation of the nonlinear dynamical response of a class of planar resonators dubbed the V-Shaped resonator. The resonators are intended for energy harvesting purpose and are designed to exhibit two-to-one internal resonance. In particular, we navigate the design space for the generalized V-shaped resonator to investigate the influence of shape parameters on the performance of the Vibration Energy Harvester. Notably, we introduce two metrics that help elucidating the role of the shape parameter in dictating the behavior of the system in terms of peak voltage and operational bandwidth width. For simplicity, we consider that the system is subjected to harmonic excitations near its primary resonances.

Kirigami is defined as the ancient Japanese art of cutting and folding paper to create three-dimensional structures, which is a subset of the larger term. Recent developments in kirigami-based structures have sparked interest in the engineering community for the development of mechanical metastructures with customized behavior such as negative Poisson’s ratio, out-of-plane buckling, and soft robot locomotion. In this manuscript, nonlinear springs based on kirigami are developed; the springs can be used to create customized nonlinear oscillators and vibration suppression systems. A Helmholtz-Duffing oscillator with nonlinear damping is created by attaching a mass to a smooth track with the kirigami springs attached to it. Kirigami springs were made by strategically cutting plastic sheets in predetermined patterns and arranging them in a ring. Identification of the unknown system parameters is accomplished through the use of a two-step procedure. To determine the quasi-static behavior of the spring, it was first subjected to tensile testing. These parameters serve as the foundation for developing a strategy for determining the unknown energy loss parameters in a system. In the second step, the Method of Multiple Scales is used to develop an approximate solution for the transient response, which is then tested. This solution is coupled with an optimization routine that, by modifying the unknown model parameters, seeks to reduce the error between the experimental free oscillations and the developed analytical solution as closely as possible.

The objective of this manuscript is to elucidate the role of topology on the nonlinear response of resonators. The resonators are composed of two beams and designed to exhibit two-to-one internal resonances. The manuscript explores the sensitivity to variations in the topological parameters, i.e., the relative orientation, and the ratio of lengths and heights, on the modal frequencies of the structure. The nonlinear governing equations are solved using the method of multiple scales when the system is excited near the first and second resonances. The occurrence of bifurcations and modal interactions has been shown both numerically and experimentally and related to the topological parameters. The effect of the topology on modal saturation has also been studied.

Spinal-driven locomotion was first hypothesized to exist in biological systems in the 1980s. However, only recently has the concept been applied to legged robots. In implementing spinal-driven locomotion in robots to-date, researchers have focused on bending in the spine. In this article, we propose an additional mode of spinal-driven locomotion: axial torsion via helical actuation patterns. To study torsional spinal-driven locomotion, a six-legged robot with unactuated legs is used. This robot is designed to be modular to allow for changes in the physical system, such as material stiffness of the spine and legs, and has actuators that spiral around the central elastomeric spine of the robot. A model is provided to explain torsional spinal-driven locomotion. Three spinal gaits are developed to allow the robot to walk forward, through which we demonstrate that the speed of the robot can be influenced by the stiffness of the spine and legs. We also demonstrate that a single gait can be used to drive the robot forward and turn the robot left and right by adjusting the leg positions or foot friction. The results indicate that the inclusion of helical actuation patterns can assist in movement. The addition of these actuation patterns or active axial torsion to future, more complex robots with active leg control may enhance the energy efficiency of locomotion or enable fast, dynamic maneuvering.

The objective of this study is to develop, simulate and verify experimentally a model of a nonlinear spring, based on the principle of a cantilevered beam with a mass on its tip, and whose overall lateral vibration is constrained by a specially shaped rigid boundary. The focus here is the use of this spring for vibration reduction applications. The modeling approach uses concepts of plane kinematics of rigid bodies, combined with quasi-static analysis to develop suitable equations of motion for a base-excited spring with a ninth-order geometric nonlinearity. In addition, a parametric identification procedure is implemented for obtaining the required coefficients for computational simulations. An approximated analytical solution to the model is completed with the aid of the method of harmonic balance and its stability is assessed through Floquet theory. Finally, the model is experimentally verified, with the use of two specimens, fabricated specifically for this study. The model, simulations and experimental measurements show the hardening and broadband behavior of the nonlinear spring.

From the end of the nineteenth century to the first three decades of the twentieth century, the will to modernize Catalan literature favoured the translation of contemporary Spanish drama from Galdós to Casona into Catalan, and its performance. In the same period, some Catalan authors such as Àngel Guimerà, Santiago Rusiñol, and Josep M. de Sagarra were translated into Spanish and also performed on stages in Madrid. However, the exchange that took place between both Iberian dramas received a heavy blow with the establishment of Franco’s dictatorship in 1939. While emphasizing the importance of cultural promoters, playwrights, translators, and critics for contact between Catalan and Spanish drama, this chapter studies the presence of the latter in literary and dramatic collections translated into Catalan and, in turn, that of Catalan drama in the same type of collection translated into Spanish during a time marked by an unusually fruitful ‘complicity’ between both theatrical scenes.

Elastic metamaterials can be used in a variety of vibration and shock absorbing applications due to having mechanical properties that are not typically seen in nature. This work creates 2-dimensional metamaterial from a tessellation of unit cells composed of array Chi-springs. The Chi-springs exhibit a J shaped force displacement relationship or equivalently an effective stress strain relationship that is characterized by three regions: a linear stiffness/module, a quasi-zero stiffness/modulus region, and region of high tangent force/stress. The springs form the fundamental building block for a 2-dimensional unit cell and are created through a series of isometric transformations while meeting constraints on its effective constitutive behavior. The orientations of each unit cell are analyzed using Cayley diagrams, which are then used to determine various 2 × 2 tessellations of the structure. The resulting unit cells and their tessellations are manufactured through 3D printing. They exhibit a J shaped effective constitutive relationship in 2 material loading directions that resembles the force displacement relationship. Material testing indicates that the resulting structures are anisotropic. Furthermore, they have a dominant loading direction that displays larger values of linear modulus, plateau stress, and toughness. This work represents the first nascent steps toward the systematic design of metamaterial behavior in multiple load directions.

Objective To evaluate corpus callosum (CC) size by neurosonography (NSG) in fetuses with an isolated major congenital heart defect (CHD) and explore the association of CC size with the expected pattern of in-utero oxygen supply to the brain. Methods A total of 56 fetuses with postnatally confirmed isolated major CHD and 56 gestational-age-matched controls were included. Fetuses with CHD were stratified into two categories according to the main expected pattern of cerebral arterial oxygen supply: Class A, moderately to severely reduced oxygen supply (left outflow tract obstruction and transposition of the great arteries) and Class B, near normal or mildly impaired oxygenated blood supply to the brain (other CHD). Transvaginal NSG was performed at 32-36 weeks in all fetuses to evaluate CC length, CC total area and areas of CC subdivisions in the midsagittal plane. Results CHD fetuses had a significantly smaller CC area as compared to controls (7.91 +/- 1.30 vs 9.01 +/- 1.44 mm(2); P < 0.001), which was more pronounced in the most posterior part of the CC. There was a significant linear trend for reduced CC total area across the three clinical groups, with CHD Class-A cases showing more prominent changes (controls, 9.01 +/- 1.44 vs CHD Class B, 8.18 +/- 1.21 vs CHD Class A, 7.53 +/- 1.33 mm(2); P < 0.05). Conclusions Fetuses with major CHD had a smaller CC compared with controls, and the difference was more marked in the CHD subgroup with expected poorer brain oxygenation. Sonographic CC size could be a clinically feasible marker of abnormal white matter development in CHD. (c) 2021 International Society of Ultrasound in Obstetrics and Gynecology.

Based on direct numerical simulations with point-like inertial particles, with Stokes numbers, $\textrm{St}=0, 0.5$, $3$, and $6$, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time evidence for the existence of Markov property in Lagrangian turbulence. We show that the Markov property is valid for a finite step size larger than a Stokes number-dependent Einstein-Markov coherence time scale. This enables the description of multi-scale statistics of Lagrangian particles by Fokker-Planck equations, which can be embedded in an interdisciplinary approach linking the statistical description of turbulence with fluctuation theorems of non-equilibrium stochastic thermodynamics and local flow structures. The formalism allows estimation of the stochastic thermodynamics entropy exchange associated with the particles' Lagrangian trajectories. Entropy consuming trajectories of the particles are related to specific evolution of velocity increments through scales and may be seen as intermittent structures. Statistical features of Lagrangian paths and entropy values are thus fixed by the fluctuation theorems., Accepted in EPL, 6 pages, 4 figures

Previous ultrasonic additive manufacturing (UAM) models ignore higher-order modes or do not simulate the entire weld cycle when studying the dynamics near critical height-to-width ratios. A multi-modal model was developed to study the dynamics near critical build heights. The cause for the critical height-to-width ratio is dynamic interaction between the substrate and sonotrode. As the build height approaches the critical height-width-ratio, the current model predicts a local maxima in the transverse velocity response directly under the moving load (simulated sonotrode excitation). This is validated by experimental observations from previous studies. However, the current model predicts that as the height is further increased, a maximum in the transverse velocity response occurs at a height-to-width ratio of 1.2 due to resonance of higher-order modes. This result indicates that a single mode-approximation is insufficient to describe the dynamics near critical build heights. In studying the time response for an entire weld cycle (1.5 s), the amplitude of the velocity response in the transverse direction varies greatly. This indicates that assuming a quasi-static or analyzing a short time period in a model excludes potential dynamics during an entire weld cycle (on the order of 1 s).

The exact periodic orbits of a conservative 2-degree-of-freedom vibro-impact system with stereo-mechanical impact model is studied using a piecewise continuation method. Feasible initial guesses are extracted from grazing solution points so that each branch of solution can be initiated smoothly from previously solved ones. Frequency-energy plots (FEPs) are produced where an emphasis is placed on enumerating potential bifurcations. Extra critical points are discovered on multiple-period duplicates of existing stable solution branches and lead to cascades of period-multiplying bifurcations. The results indicate that the system’s complete FEP can be viewed through a process of infinite fractals toward zero frequency where pseudo-periodic or chaotic responses are approached. Finally, it is shown both mathematically and through the comparison of FEPs that the impacting system can be represented explicitly as the extreme case of nonlinear systems with an odd-order polynomial internal force. It is thus proposed that as the counterpart to the superposition of linear normal modes, the free responses of a general conservative nonlinear system can be tracked via bifurcations from its nonlinear normal modes.

This note proposes a novel element removal method for ground structured based topology optimization that utilizes a double-filtering scheme based on a graph representation of the topology. Two types of systems: planar resonators and compliant mechanisms, are used to illustrate the method.

The objective of this study is to develop a novel methodology to assess the energy flow between a nonlinear energy sink (NES) and the primary system it is attached to in terms of energy orientation, which is directly related to the sign of the power present on the primary system. To extend the work done in previous studies, which have focused primarily on the analytical treatment, characterization, and performance evaluation of NES as passive nonlinear dampers for structures under different types of excitations, this study incorporates a methodology for determining whether energy is entering or leaving a primary oscillator when interacting with an NES, by means of considering the power flow of the primary oscillator. Several current measures for evaluating the effectiveness of the NES at extracting and dissipating energy irreversibly are considered through numerical simulations of systems with different damping cases of the NES. Each case provides a different dissipation scenario in the combined system, which is subjected to different types of base excitation signals such as impulse and seismic records. The methodology is further validated experimentally using a two degrees-of-freedom system with an NES attached to the second mass. Comparisons of the modeled responses versus the measured responses are provided for several physical damping realization scenarios in the NES.

Polyethylene (PE) foam is a material used commonly in protective packaging for its shock absorption properties. When developing a package design intended to mitigate shock to the product, decisions are typically made based on established cushion evaluation procedures performed at standard laboratory conditions. Distribution environment temperatures, however, can vary greatly from the condition at which these materials are assessed. The research presented in this paper utilizes the stress–energy method of cushion evaluation and highlights trends in the stress–energy equations of PE foam tested at 12 different temperatures, ranging from −20°C to 50°C. A quadratic polynomial is used to describe the variation in the stress–energy equation coefficients over the temperature range evaluated. The model developed enables cushion curve prediction for any static stress, drop height, material thickness and temperature expected over the intended range of use of the material. This model is validated by performing additional impact testing of samples at various temperatures and comparing experimentally obtained acceleration values to those predicted by the model. Further model analysis is performed to estimate the optimal static stress for the material at any temperature within the range tested and to study the variation with temperature of this optimal point. Results reveal that the model developed is capable of predicting the shock absorption properties of the material within the range of parameters tested and that the optimal static stress of the material decreases as temperature increases from −20°C to 50°C. Application to cushion design is made to recommend an approach to designing a PE cushion system for use over a range of temperatures. Copyright © 2016 John Wiley & Sons, Ltd.

Knowledge of the evaporative loss from lakes and reservoirs is critical to water resources managers as well as to the overall understanding of the water balance in a given basin, geographical region, or continent. Existing methods for ascertaining evaporation from lakes and reservoirs include point measurements, water balance and mass transfer calculations, and proxy measurements using a pan. Point measurements using the eddy flux covariance method can be accurate, but are resource intensive and unsuited for determining spatial variation over a lake, or for obtaining measurements over many lakes. Mass balance methods cannot provide spatial variability and their accuracy depends on other portions of the water balance that can be challenging to obtain, such as leakage. Similarly, relatively recently deployed scintillation methods provide only an average for a strip across a lake and are also resource intensive and not suited for multi-lake studies. Evaporation pan measurements can also be used, though their accuracy is poor. Herein, we use a combination of Moderate Resolution Imaging Spectroradiometer (MODIS) satellite measurements of water surface temperature, measurements of wind speed, air temperature, and relative humidity from local NWS stations, and a mass transfer method, to demonstrate multi-lake evaporation measurements. Specifically, the seasonal variation in evaporation is obtained for the five major lakes in the Savannah River Basin (in South Carolina, USA): Lakes Jocassee, Keowee, Hartwell, Russell, and Thurmond. Since this approach requires only an existing satellite resource with global coverage and existing NWS stations, this method can potentially be ported to any lake where there is a nearby meteorology station. Hence, this method could be used by both water resource managers and limnologists alike. The possibility is discussed of extending this approach beyond a single basin to encompass an entire geographical region or continent.

With the introduction of renewable energy sources into the power system, transmission system operators need extremely reliable and flexible simulation tools that should also be fast. Sinusoidal predictor method, aims to meet this need by simulating the full-waveform of AC power systems by integrating the arising systems of DAE by trying to free the time step limitation introduced by the frequency of some electrical components. The searched solution is split in a predicted sinusoidal part and a corrector DAE solution part. This paper presents the mathematical convergence of this approach leading to the choice of computing Fourier coefficients by minimizing a function that captures the distance of the desired sinusoidal part of the solution with respect to its oscillating steady state. Using the Dynaωo framework that aims to completely separate the modeling and the solving aspects of power systems, It details latest developments of an add-on in the IDA solver of SUNDIALS and the implementation optimisations. Results on performance speed up of the method computational time using much larger time steps than those used by classical DAE integration methods.

Triboelectric energy harvesters or nanogenerators exploit both contact electrification and electrostatic induction to scavenge excess energy from random motions of mechanical structures. This study focuses on the modeling of triboelectric energy harvesters in the configuration of contact-separation impact oscillators. While mechanical and electrostatic elements in such systems can be satisfactorily modeled based on existing theories, the underlying physics of contact electrification is still under debate. The aim of this work is to introduce the surface charge density of dielectric layers as a variable into the macroscopic equations of motion of triboelectric impact oscillators by experimentally investigating the relation between the impact force and the charge transfer during contact electrification. Specifically, specimens with selected pairs of materials are put under a solenoid-driven pressing tester which charges the specimens with a vertical force whose magnitude, frequency and duty cycle can be controlled. An electrometer is used to monitor the short circuit charge ow between the electrodes from which the charge accumulation on dielectric layers can be extracted. With results from parameter-sweep tests, the produced map from contact force to surface charge density can be integrated into equations of motion via curve fitting or interpolation.

The objective of the manuscript is to explore the effects of geometry on the dynamics of an internally resonant vibrational energy harvester (VEH). Recently, the authors of this manuscript unveiled the existence of ∞6N solutions to design multi-members resonators which exhibit N commensurate frequencies equal to the number of members of the structure. The generalized topology of this family of resonators which exhibit 1:2 resonance resembles a V -shaped structure, i.e., a structure with two members adjoined at an angle φ, denoted as the folding angle. The classic 1:2 internally resonant L-shaped structure is a subset of solutions in this family. This work investigates the effect of the folding angle on the dynamic response of these oscillators. The nonlinear equations of motion are derived by means of Lagrange’s equation, the beams are inextensible yielding second order nonlinearities. Approximate solutions of the model are obtained using the method of multiple scales. The effect of the folding angle on the nonlinear modal interaction in the power- frequency response curves is investigated.

Ultrasonic vibration has been observed to lower the flow stress necessary to initiate plastic deformation, a phenomenon known as "acoustic softening". This unique effect of ultrasound has been extensively applied in welding, machining, forming of metals, and ultrasonic additive manufacturing to lower the yield stress necessary to initiate plastic deformation, it nevertheless lacks fundamental investigation. Some prior studies showed experimental errors due to the design of experimental setups and the associated testing methods that have been introduced, leading to questions about their observations and conclusions. Therefore, an experimental setup described in this paper is designed to minimize the constraints identified from the setups in prior studies. Three types of aluminum are studied: Al 1100-O a commercially pure aluminum, Al 6061-O an aluminum alloy without precipitate strengthening, and Al 6061-T6 a precipitate-strengthened aluminum alloy. The acoustic softening and residual effect are compared based on the similarities and differences in microstructures of the three types of aluminum. In both acoustic softening and residual effect, linear relations are obtained between stress change and ultrasound intensities. The slope defined by the linear relations, i.e. the acoustic softening factor, depends on the microstructure of the specific material. The underlying mechanism of acoustic softening is associated with the activation of dislocations by ultrasonic energy and subsequently their interactions with other dislocations and precipitates, whereas the residual effects are attributed to the permanent changes in dislocation density due to dislocation annihilation, dynamic annealing, and dislocation-precipitate interaction.

This paper seeks to address the implications on putting a golf ball with an off-center mass by analyzing the effect of unbalanced mass of ball on its impact and subsequent rolling. We present the general formulation of a rigid golf ball rolling with slip that is able to transition to rolling friction on an arbitrary surface. Particular attention is given to the effects of the offset center of mass on the golf ball’s path. An experimental setup based on a USGA Stimpmeter is used to calibrate the position of contact point as the ball rolls on the green. The trajectories of the ball due to the mass imbalance were studied by numerically solving the equations of motion during putting. Theoretical predictions show that a mass imbalance has little effect on the launch conditions of the ball. However, on a level green a mass offset center of 0.2 % of the ball’s radius can impact the path of the ball with the consequences of missing the hole in a 5.8 m putt. Changing golf ball trajectories with mass offset center has implications on the development of balls and putting.

In this paper, the free and forced vibration response of a linearized, distributed-parameter model of a viscoelastic rod with an applied tip-mass is investigated. A nonlinear model is developed from constitutive relations and is linearized about a static equilibrium position for analysis. A classical Maxwell–Weichert model, represented via a Prony series, is used to model the viscoelastic system. The exact solution to both the free and forced vibration problem is derived and used to study the behavior of an idealized packaging system containing Nova Chemicals׳ Arcel ® foam. It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss modulii necessitate the use of additional Prony series terms. It is also shown that the model is able to predict the modal frequencies and the primary resonance response at low acceleration excitation, both with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a nonlinear elastic model that extends beyond the scope of this work. Solution analysis and experimental data indicate little material vibration energy dissipation close to the first modal frequency of the mass/rod system.

This manuscript highlights an analytical solution to a nonlinear, viscoelastic model of expanded polymer foam. The governing partial differential equation is discretized into a single-mode nonlinear ordinary differential equation (ODE). Solution of the nonlinear ODE is analytically approximated using the method of multiple scales. Comparison to experimental data reveals that the single-mode analytical solution is capable of capturing the nonlinear bending behaviour missed by a previously solved linearized model. It is also shown that limitations due to the system-identification data-collection method affect the ability of the model to capture the degree of nonlinearity present at lower strain levels. While this limitation has no observable effect on the previously studied linearized system response, nonlinear modelling can benefit from further work performed in the low strain characterization of expanded polymer foam. Lastly, the nonlinear solution is used to study the effect of varying excitation acceleration and static stress on the frequency response of expanded polymer foam. Copyright © 2015 John Wiley & Sons, Ltd.

Despite the ubiquity of both linear and nonlinear multimember resonators in MEMS and kinetic energy harvesting devices very few research efforts examine the orientation of members in the resonator on its dynamic behavior. Previous efforts to design this type of resonator constrains the members to have relative orientations that are 0 ○ or 90○ to each other, i.e., the elements are connected inline with adjoining members or are perpendicular to adjoining members. The work expands upon the existing body of research by considering the effect of the relative orientation between members on the dynamic behavior of the system. In this manuscript, we derive a generalized reduced-order model for the design of a multi-member planar resonator that has integer multiple modal frequencies. The model is based on a Rayleigh Ritz approximation where the number of degrees of freedom equals the number of structural members in the resonator. The analysis allows the generation of design curves, representing all the possible solutions for modal frequencies that are commensurate. The generalized model, valid for an N-DOF structure, is then restricted for a 2- and 3-DOF system/member resonator, where the linear dynamic behavior of the resonator is investigated in depth. Furthermore, this analysis demonstrates a rule of thumb; relaxing restrictions on the relative orientation of members in a planar structure, allows the structure to exhibit exactly N commensurable frequencies if it contains N members.

This review stands in the larger framework of functional materials by focussing on heterostructures of rare-earth nickelates, described by the chemical formula RNiO

Electret based energy scavenging devices utilize electro-static induction to convert mechanical energy into electrical energy. Uses for these devices include harvesting ambient energy in the environment and acting as sensors for a range of applications. These types of devices have been used in MEMS applications for over a decade. However, recently there is an interest in triboelectric generators/harvesters, i.e., electret based harvesters that utilize triboelectrification as well as electrostatic induction. The literature is filled with a variety of designs for the latter devices, constructed from materials ranging from paper and thin films; rendering the generators lightweight, flexible and inexpensive. However, most of the design of these devices is ad-hoc and not based on exploiting the underlying physics that govern their behavior; the few models that exist neglect the coupled electromechanical behavior of the devices. Motivated by the lack of a comprehensive dynamic model of these devices this manuscript presents a generalized framework based on a Lagrangian formulation to derive electromechanical equation for a lumped parameter dynamic model of an electret-based harvester. The framework is robust, capturing the effects of traditional MEMS devices as well as triboelectric generators. Exploiting numerical simulations the predictions are used to examine the behavior of electret based devices for a variety of loading conditions simulating real-world applications such as power scavengers under simple harmonic forcing and in pedestrian walking.

Cushion curves enable packaging designers to optimize a design solution for a given product fragility and expected distribution environment drop height. The industry accepted techniques for developing these curves are time intensive and devoid of a physical understanding of the materials and the physics involve in energy absorption. This paper delves into a qualitative understanding of the dynamics of a platen impacting an open cell foam cushion material. An hyperelastic material model is used to describe the foam's nonlinear stress–strain relationship, while its damping and hysteretic behaviour are represented with linear viscoelasticity. Using a simple nonlinear, discontinuous model of a drop test along with numerical simulations, the study examines the physics of the impact. The numerical studies show that the model is able to provide predictions of the shock pulse's shape, duration and amplitude at various static stresses and drop heights. The dynamic cushion curves generated by the model retain the characteristic concave upward ‘trough’ shape of the experimental curves. Furthermore, the model shows that the optimal amplitude of shock absorbed for a given set of drop conditions depends on the foam's thickness and cross-sectional area. Lastly, the model is validated using the comparison of a predicted curve and experimental data captured using a cushion tester. Copyright © 2014 John Wiley & Sons, Ltd.

The demand to lower costs and reduce the amount of packaging materials utilized in a packaged product system has placed increased importance on the development of tools to model the behaviour of packaging systems. This manuscript examines the accuracy and convergence of a reduced-order model (ROM). The ROM is derived from an idealized packaging system consisting of a rod of polymer foam with an attached end mass. The work begins with an introduction to the complex cyclic softening and the viscoelastic and nonlinear stress–strain behaviour exhibited by expanded polymer foam. The partial differential equations and associated boundary conditions governing the motion of the system are obtained. The equations are reduced to an ROM using the assumed modes method. Approximate eigenvalues are compared with both exact and experimental eigenvalues reported in literature. Finally, the ROM is compared with the frequency response functions of the exact solution and those obtained experimentally. Both results are used to determine the number of modal equations needed for the ROM to accurately capture the steady-state dynamic behaviour of the packaging system. Copyright © 2014 John Wiley & Sons, Ltd.

Precision mechanisms that require repeatable and friction free motion utilize numerous types of flexural bearing joints. This manuscript expands the pool of existing flexure designs by presenting a type of two-degree of freedom (DOF) flexural joint, dubbed the hybrid bi-directional flexure joint (HBFJ), along with the evolution of its design, possible applications and experimental results for stiffness, range of motion, and vibration damping. The HBFJ has a dominant plane of deformation. However, unlike most of its traditional counterparts, the flexure can deflect in other planes. It contains an open, thin walled cavity as the base joint that can be filled with an elastomeric filler material. The filler limits axial deflection, while still permitting the mechanism to have bending deformations in and out of plane. Additionally, the elastomer provides vibration damping to the joint.

When competing in performance with their pneumatic counterparts, nonpneumatic tires should have several critical features, such as low energy loss when rolling over obstacles, low mass, low stiffness, and low contact pressure. In recent years, a nonpneumatic tire design was proposed to address each of these critical issues [1]. In this study, the steady state and transient energy losses due to rolling resistance for the proposed nonpneumatic tire are considered. Typically, such an analysis is complex because of the coupling of temperature on the structural deformation and the viscoelastic energy dissipation, which requires an iterative procedure. However, researchers have proposed a simplified analysis by using the sensitivity of the tire's elastic response to changes in material stiffness through a deformation index [2–4]. In the current study, the method is exploited to its full potential for the nonpneumatic tire due to the relatively simple nature of deformation in the tire's flexible ring and the lack of several complicating features present in pneumatic tires, namely, a heated air cavity and the complex stress state due to its composite structure. In this article, two models were developed to predict the transient and steady-state temperature rise. The first is a finite element model based on the deformation index approach, which can account for thermo-mechanical details in the tire. Motivated by the simplicity of the thermo-behavior predicted by this finite element model, a simple lumped parameter model for temperature prediction at the center of the shear band was developed, which in many cases compares very well with the more detailed finite element approach due to the nature of the nonpneumatic tire. The finite element model can be used to, for example, explore the design space of the nonpneumatic tire to reach target temperatures by modifying heat transfer coefficients and/or material properties.

National Urbanization Policies (NUPs) are of particular importance in countries with rapid urbanization. Both for diagnosis for development of NUPs and for planning of implementation of NUPs we present a new methodology called the Spatial Development Framework (SDF). The SDF analyzes and describes with stakeholders the regional structure and interdependencies between settlements and evaluates the strengths and weaknesses of settlements. This is the basis for action planning by national, regional and local stakeholders. We describe the methodology and show the preliminary results of the ongoing implementation of the methodology for the NUP implementation in Rwanda. We discuss the empirical value of the methodology, its integrative nature, the applicability to any spatial policy development and implementation, its data requirements, and its time input requirements. We conclude that the Spatial Development Framework methodology complements NUPs be providing an empirical, integrated and by stakeholders shared understanding of the spatial structure of the country’s settlements and development corridors. It serves realistic urban and regional development planning based on this shared understanding. Keywords —matrix of functions, national urban policy, spatial multi-criteria evaluation, urban and regional planning.

In this manuscript, we investigate the use topology optimization to design planar resonators with modal fre- quencies that occur at 1 : n ratios for kinetic energy scavenging of ambient vibrations that exhibit at least two frequency components. Furthermore, we are interested in excitations with a fundamental component containing large amounts of energy and secondary component with smaller energy content. This phenomenon is often seen in rotary machines; their frequency spectrum exhibits peaks on multiple harmonics, where the energy is primarily contained in the rotation frequency of the device. Several theoretical resonators are known to exhibit modal frequencies that at integer multiples 1:2 or 1:3. However, designing manufacturable resonators for other geometries is still a daunting task. With this goal in mind, we utilize topology optimization to determine the layout of the resonator. We formulate the problem in its non-dimensional form, eliminating the constraint on the allowable frequency. The frequency can be obtained a posteriori by means of linear scaling. Conversely, to previous research, which use the clamped beam as initial guess, we synthesize the final shape starting from a ground structure (or structural universe) and remove of the unnecessary beams from the initial guess by means of a graph-based filtering scheme. The algorithm determines the simplest structure that gives the desired frequency’s ratio. Within the optimization, the structural design is accomplished by a linear FE analysis. The optimization reveals several trends, the most notable being that having members connected orthogonally as in the L-shaped resonator is not the preferred topology of this devices. In order to fully explore the angle of orientation of connected members on the modal characteristics of the device; we derive a reduced-order model that allows a bifurcation analysis on the effect of member orientation on modal frequency. Furthermore, the reduced order approximation is used solve the coupled electro-mechanical equation of a vibration based energy harvester (VEH). Finally, we present the performance of the VEH under various base excitations. These results show an infinite number of topologies that can have integer ratio modal frequencies, and in some cases harvest more power than a nominal L shaped harvester, operating in the linear regime.

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

International audience

In the field of meta-materials engineering, asymptotic homogenization has proven to be a valuable tool to estimate material properties for many different design needs. Homogenization is used in the design of an object to tie the global material properties to the local material microstructure of the meta-material. The governing equations of the theory are derived from a small-parameter expansion that assumes the scaling length of the unit cell, the smallest repeatable structure found in the material, is much smaller than the entire material length scale. However, for those design problems that do not meet this scaling requirement, the meta-material properties given by homogenization may be inaccurate, leading to error in the material design process. To demonstrate some of these limitations, the more general set of macroscopic analyses derived from the average stress and average strain theorems are applied to several designs in which the assumptions of homogenization theory are no longer valid, those chiefly being materials made of a single or a few layers of unit cells. Then, by applying both materials analyses to simple design problems, the necessity of using a meta-material design method to link global and local properties in a manner consistent with global design methods is demonstrated. In particular, the use of homogenization in designing single layer materials is shown to incur a very large error in the design process, whereas the averaging method is much more accurate.

Cotton fabrics were dyed with dyes generated in situ by laccase-catalyzed oxidative coupling of the colorless 2,5-diaminobenzenesulfonic acid (2,5-DABSA) and 1-hydroxyphenol (catechol). The enzymatic oxidation of the dye intermediates led to cross-coupling reaction products when the reaction was conducted with an excess of catechol. At least fourfold excess of catechol was necessary to achieve satisfactory dye fixation on cotton. Formation of the same colored product using either an equimolar ratio of the reagents or tenfold excess of catechol was observed. Most probably, homo-molecular reactions predominate over the cross-coupling at equimolar ratio of the precursors, while with an excess of catechol, the cross-coupling occurs in higher yield. The reaction was followed using UV-Vis spectroscopy, HPLC, FTIR and MALDI-TOF MS. A reaction pathway for laccase-induced cross-coupling of catechol and 2,5-DABSA yielding a major colored product was proposed.