Mergen H. Ghayesh

Bio: Mergen H. Ghayesh is an academic researcher from University of Adelaide. The author has contributed to research in topics: Nonlinear system & Galerkin method. The author has an hindex of 60, co-authored 254 publications receiving 9691 citations. Previous affiliations of Mergen H. Ghayesh include University of Wollongong & Tarbiat Modares University.

Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory

Abstract: The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton’s principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency–response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.

Nonlinear dynamics of a microscale beam based on the modified couple stress theory

Abstract: In the present study, the nonlinear resonant dynamics of a microscale beam is studied numerically. The nonlinear partial differential equation governing the motion of the system is derived based on the modified couple stress theory, employing Hamilton’s principle. In order to take advantage of the available numerical techniques, the Galerkin method along with appropriate eigenfunctions are used to discretize the nonlinear partial differential equation of motion into a set of nonlinear ordinary differential equations with coupled terms. This set of equations is solved numerically by means of the pseudo-arclength continuation technique, which is capable of continuing both the stable and unstable solution branches as well as determining different types of bifurcations. The frequency–response curves of the system are constructed. Moreover, the effect of different system parameters on the resonant dynamic response of the system is investigated.

Nonlinear behaviour of electrically actuated MEMS resonators

Abstract: The present study investigates the nonlinear size-dependent behaviour of an electrically actuated MEMS resonator based on the modified couple stress theory; the microbeam is excited by an AC voltage which is superimposed on a DC voltage. A high-dimensional reduced order model of the continuous system is obtained by applying the Galerkin scheme to the nonlinear partial differential equation of motion. The pseudo-arclength continuation technique is employed to examine the nonlinear static and dynamic behaviour of the system. Specifically, the nonlinear static behaviour of the system is investigated when the microbeam is excited by the electrostatic excitation (DC voltage); this analysis yields the static deflected configuration of the system and the value of the DC voltage corresponding to the static pull-in instability. The size-dependent dynamic behaviour of the system is examined under primary and superharmonic excitations; the frequency- and force-response curves of the system as well as time histories and phase-plane portraits are constructed. Moreover, the effect of taking into account the length-scale parameter on the static and dynamic behaviour of the system is examined by comparing the results obtained by means of the classical and modified couple stress theories.

Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory

Abstract: The present study investigates the nonlinear dynamics of a geometrically imperfect microbeam numerically on the basis of the modified couple stress theory. Hamilton’s principle is used to obtain the nonlinear partial differential equation of motion for an initially curved beam. The equation of motion is discretized and reduced to a set of nonlinear ordinary differential equations by means of the Galerkin scheme. This set of equations is solved numerically by means of the pseudo-arclength continuation technique which allows the continuation of both stable and unstable solution branches as well as determination of different types of bifurcation. An eigenvalue analysis is also conducted to obtain the linear natural frequencies of the system. The frequency-response curves are constructed for the system with different initial imperfections. Moreover, the frequency-response curves of the system are plotted together as a specific system parameter is varied, in order to highlight the effect of each parameter on the resonant dynamics of the system.

Ambient vibration energy harvesters: A review on nonlinear techniques for performance enhancement

Abstract: Vibration energy harvesters are emerging as a promising solution for powering small-scale electronics, such as sensors and monitoring devices, especially in applications where batteries are costly or difficult to replace. However, current vibration energy harvesters are only effective within a limited frequency bandwidth, whereas most ambient vibrations occur randomly over a wide frequency range. Many techniques, such as tuning, coupling between modes, multimodal arrays and hybrid transduction methods, can be used for performance enhancement of vibration-based energy harvesters. Among these techniques is the introduction of nonlinearities to the energy harvesting system. In most cases, using nonlinear techniques for energy harvesting results in a larger frequency bandwidth when compared to a linear system. In certain systems, the introduction of nonlinearities can also result in a higher amplitude response. The aim of this paper is to conduct a critical review of nonlinear techniques which have been investigated for performance enhancement of energy harvesters in the past decade and present state of the art of energy harvesters which utilise this technique. This includes discussions of several techniques that have been employed for enhancing energy harvesting, such as stochastic loading, internal resonances, being multi-degree-of-freedom, mechanical stoppers and parametric excitations, which all lead to nonlinear behaviour and enhancement of the system. These techniques are capable of significantly extending the frequency bandwidth and, in some cases, increasing the amplitude response. The enhancement in performance results in devices that can harvest energy more efficiently from ambient vibrations.

The state-of-the-art review on energy harvesting from flow-induced vibrations

Abstract: In this paper, the currently popular flow-induced vibrations energy harvesting technologies are reviewed, including numerical and experimental endeavors, and some existing or proposed energy capture concepts and devices are discussed. The energy harvesting mechanism and current research progress of four types of flow-induced vibrations, such as vortex-induced vibrations, galloping, flutter and buffeting, are introduced. To enhance the performance of the harvesters and broaden the operating range, the researchers have proposed various mechanical designs, methods of the structures’ surfaces optimization and concepts with incorporated magnets for multistability. The paper summarizes the works led to the current wind energy and hydro energy harvesters based on the principle of flow-induced vibrations, including bladeless generator Vortex Bladeless, University of Michigan vortex-induced vibrations aquatic clean energy, Australian BPS company's airfoil tidal energy capture device bioSTREAM, and others. This shows the gradual progress and maturity of the flow-induced vibrations energy harvesters. The article concludes with a discussion on the current problems in the area of the flow-induced vibration energy capture and the challenges faced.

Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach

Abstract: In this study, a novel size-dependent beam model is proposed for nonlinear free vibration of a functionally graded (FG) nanobeam with immovable ends based on the nonlocal strain gradient theory (NLSGT) and Euler-Bernoulli beam theory in conjunction with the von-Karman's geometric nonlinearity. It is assumed the material properties of the nanobeam changes continuously in the thickness direction according to simple power-law form. To remove the stretching and bending coupling due to the unsymmetrical material variation along the thickness, the formulation of the problem is developed based on a new reference surface. The Hamilton's principle is utilized to derive the equations of the motion and the corresponding boundary conditions. The partial nonlinear differential equation describes the nonlinear vibration of FG nanobeam is reduced to an ordinary nonlinear differential equation with cubic nonlinearity via Galerkin's approach under the assumption that the axial inertia is negligible. A closed-form solution is obtained for nonlinear frequency by the novel Hamiltonian approach, and some illustrative numerical examples are given in order to study the effects of the strain gradient length scale, the nonlocal parameters, vibration amplitude and various material compositions on the ratio of nonlinear frequency to linear frequency (the nonlinear frequency ratio).

Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory

Abstract: A size-dependent nonlinear Euler–Bernoulli beam is considered in the framework of the nonlocal strain gradient theory. The geometric nonlinearity due to the stretching effect of the mid-plane of the size–dependent beam is considered here. The governing equations and boundary conditions are derived by employing the Hamilton principle. The post-buckling deflections and critical buckling forces of simply supported size-dependent beams are analytically derived. The derived results are compared with those of strain gradient theory, nonlocal elasticity theory and classical elasticity theory. It is found that the post-buckling deflections can be increased by increasing the nonlocal parameter or decreasing the material characteristic parameter. The high-order buckling deflections are more sensitive to size-dependent parameters than the low-order buckling deflections. Furthermore, the critical buckling force can be increased by decreasing the nonlocal parameter when the nonlocal parameter is larger than the material characteristic parameter, or increasing the nonlocal parameter when the nonlocal parameter is smaller than the material characteristic parameter.

A review of continuum mechanics models for size-dependent analysis of beams and plates

Abstract: This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro- and nano-structures.

Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory

Abstract: The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton’s principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency–response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.