Influence Of Beam Thickness Research Articles

Shock Reliability of Vacuum-Packaged Piezoelectric Vibration Harvester for Automotive Application

This paper reports for the first time the shock reliability of vacuum-packaged piezoelectric vibration harvesters for automotive application. Experimental study on >80 devices shows that the failure is induced by the impact between seismic mass and glass package. The statistical results obtained for various types of harvesters have shown a trend of higher shock reliability for a higher resonance frequency. The influence of beam thickness on the shock reliability is then discussed. The trade-off between the power output and shock reliability is elaborated. To further improve the reliability to the level of automotive application, the idea of stepped cavity is discussed and implemented. The experimental results confirmed a significantly enhanced reliability increased by ~50%, up to maximum 2000 g, for the same type of device under shock excitations.

Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions

In this research, buckling analysis of three microbeam models are investigated based on modified couple stress theory. Using Euler–Bernoulli beam theory (EBT), Timoshenko beam theory (TBT) and Reddy beam theory (RBT), the effect of shear deformation is presented. To examine the effect of boundary condition, three kinds of boundary conditions i.e. hinged–hinged, clamped–hinged and clamped–clamped boundary conditions, are considered. These nonclassical microbeam models incorporated with Poisson effect, contain a material length scale parameter and can capture the size effect. These models can degenerate into the Classical models if the material length scale parameter and Poisson’s ratio are both taken to be zero. Governing equations and boundary conditions are derived by using principle of minimum potential energy. Generalized differential quadrature (GDQ) method is employed to solve the governing differential equations. Also an analytical solution is applied to determine the critical buckling load of microbeams with hinged–hinged boundary condition. Comparison between the results of GDQ and analytical methods reveals the accuracy of GDQ method. Some numerical results are exhibited to indicate the influences of beam thickness, material length scale parameter and Poisson’s ratio on the critical buckling load of these microbeams.

A sixth-order compact finite difference method for non-classical vibration analysis of nanobeams including surface stress effects

A non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed in this study. Based on Gurtin–Murdoch elasticity theory, the influence of surface stress is incorporated into the Euler–Bernoulli beam theory. A compact finite difference method (CFDM) of sixth order is employed for discretizing the non-classical governing differential equation to obtain the natural frequencies of nanobeams subject to different boundary conditions. To check the validity of the present numerical solution, based on an exact solution, an explicit formula for the fundamental frequency of simply-supported nanobeams is obtained. Good agreement between the results of exact and numerical solutions is achieved, confirming the validity and accuracy of the present numerical scheme. The comparison between the results generated by CFDM with those obtained by the conventional finite difference method (FDM) further reveals the advantages of the compact method over its classical counterpart. The influences of beam thickness, surface density, surface residual stress, surface elastic constants, and boundary conditions on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

Investigated herein is the free vibration characteristics of microbeams made of functionally graded materials (FGMs) based on the strain gradient Timoshenko beam theory. The material properties of the functionally graded beams are assumed to be graded in the thickness direction according to the Mori–Tanaka scheme. Using Hamilton’s principle, the equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FGM microbeams including size effect. A detailed parametric study is performed to indicate the influences of beam thickness, dimensionless length scale parameter, and slenderness ratio on the natural frequencies of FGM microbeams. Moreover, a comparison between the various beam models on the basis of the classical theory (CT), modified couple stress theory (MCST), and strain gradient theory (SGT) is presented for different values of material property gradient index. It is observed that the value of gradient index play an important role in the vibrational response of the microbeams of lower slenderness ratios. It is further observed that by increasing the length-to-thickness ratio of the microbeam, the value of dimensionless natural frequency tends to decrease for all amounts of the gradient index.