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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.

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 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.

A procedure for the characterization of low velocity impact damage and its effect on residual tensile and buckling behaviour of composite structures is presented. A simplified analytical method is used to enhance the damage simulation and a degradation model is introduced in the subsequent finite element analysis. Different degradation coefficients are defined for three impact energy stages. Two different types of analysis are performed using MD.Nastran software: the non-linear progressive failure analysis to estimate the residual tensile strength and the linear analysis to predict the critical uniaxial and shear buckling loads after impact. Tensile and buckling experiments are used to validate the present methodology. A good correlation is obtained for all the cases under investigation.

Purpose This paper aims to present a systematic performance-oriented procedure to predict structural responses of composite layered structures. The procedure has a direct application in the preliminary design of aerospace composite structures evaluating the right and most effective material. Design/methodology/approach The aforementioned procedure is based upon the definition of stiffness invariants. In the paper, the authors briefly recall the definition and the physical explanation of the invariants, i.e. the trace; then they present the scaling procedure for the selection of the best material for a fixed geometrical shape. Findings The authors report the basic principles of the scaling procedure and several examples pertaining typical responses sought in the preliminary design of aeronautic structures Research limitations/implications Typically, during early stages, engineers had to perform the daunting task of balancing among functional requirements and constraints and give the optimum solution in terms of structural concept and material selection. Moreover, preliminary design activities require evaluating different responses as a function of as less as possible parameters, ensuring medium to high fidelity. The importance of incorporating as much physics and understanding of the problem as early as possible in the preliminary design stages is therefore fundamental. A robust and systematic procedure is necessary. Practical implications The time/effort reduction in the preliminary design of composite structures can increase the overall quality of the configuration chosen. Social implications Reduction in design costs and time. Originality/value In spite of the well-known invariant properties of composites, the application and extension to the preliminary design of composite structures by means of a scaling rule is new and original.

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.

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.

In this paper a revised algorithm, derived by the Stud GA, to optimize the stacking sequence of layered composite structures is presented. The constrained combinatorial problem is formulated and hence solved by means of the algorithm presented herein. Unlike the Stud GA, the proposed algorithm uses a fitness-proportionate selection to find potential mates to the Stud and a self-adaptive extinction to avoid premature convergence. Elitism is also allowed. Standard benchmark problems have been used to fully assess the validity of the proposed algorithm. Results in terms of reliability and efficiency are compared against three GAs and a Permutation Search (PS) algorithm. It has been demonstrated, by means of a parametric study, that a low probability of extinction is sufficient to ensure fast convergence as well as reliable results. Finally the optimization of a more complex aeronautic structure is addressed aiming to prove the validity of the proposed algorithm in a two level optimization strategy. Results in terms of efficiency are compared against those of an in-house standard GA.