Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory
TL;DR: In this article, the nonlinear forced vibrations of a microbeam are investigated by employing the strain gradient elasticity theory, and the geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach.
About: This article is published in International Journal of Engineering Science.The article was published on 2013-02-01. It has received 253 citations till now. The article focuses on the topics: Nonlinear system & Equations of motion.
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TL;DR: In this paper, a 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.
313 citations
TL;DR: In this paper, the nonlinear resonant dynamics of a microscale beam is studied 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.
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.
247 citations
TL;DR: In this paper, the authors investigated the nonlinear size-dependent behavior 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.
246 citations
TL;DR: In this paper, the authors investigated the nonlinear dynamics of a geometrically imperfect microbeam numerically on the basis of the modified couple stress theory and obtained the linear natural frequencies of the system.
244 citations
TL;DR: A critical review of nonlinear techniques which have been investigated for performance enhancement of energy harvesters in the past decade and the present state of the art of energy Harvesters which utilise this technique is conducted.
226 citations
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TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.
Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.
3,929 citations
3,323 citations
TL;DR: In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors in small-scale structures and a strain gradient elastic bending theory for plane-strain beams is developed.
Abstract: Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.
2,466 citations
01 Jan 2007
1,532 citations
01 Jan 1997
TL;DR: This is a guide to the software package AUTO for continuation and bifurcation problems in ordinary differential equations and the development of HomCont has much benefitted from various pieces of help and advice from, among others, W. W. Norton.
Abstract: Preface This is a guide to the software package AUTO for continuation and bifurcation problems in ordinary differential equations. graphics program PLAUT and the pendula animation program. An earlier graphical user interface for AUTO on SGI machines was written by Taylor & Kevrekidis (1989). Special thanks are due to Sheila Shull, California Institute of Technology, for her cheerful assistance in the distribution of AUTO over a long period of time. Over the years, the development of AUTO has been supported by various agencies through the California Institute of Technology. Work on this updated version was supported by a general research grant from NSERC (Canada). The development of HomCont has much benefitted from various pieces of help and advice from, among others, W. This manual uses the following conventions. command This font is used for commands which you can type in. PAR This font is used for AUTO parameters. filename This font is used for file and directory names. variable This font is used for environment variable. site This font is used for world wide web and ftp sites. function This font is used for function names.
1,417 citations