Topic
Multiple-scale analysis
About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.
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TL;DR: In this article, a doubly clamped viscoelastic microbeam actuated by one-sided electrode is investigated in detail, based on a modified couple stress theory, which is essentially nonlinear due to its midplane stretching effect and electrostatic force.
Abstract: Viscoelastic phenomena widely exist in MEMS materials, which may have certain effects on quasi-static behaviors and transition mechanism of nonlinear jumping phenomena. The static and dynamic behaviors of a doubly clamped viscoelastic microbeam actuated by one sided electrode are investigated in detail, based on a modified couple stress theory. The governing equation of motion is introduced here, which is essentially nonlinear due to its midplane stretching effect and electrostatic force. Through quasi-static analysis, the equilibrium position, pull-in voltage and pull-in location of the system are obtained with differential quadrature method and finite element method. The equivalent geometric nonlinear parameter is presented to explain the influence of the scale effect on the pull-in location. Different from elastic material, there are two kinds of pull-in voltages called as instantaneous pull-in voltage and the durable pull-in voltage in viscoelastic system. Then, Galerkin discretization and the method of multiple scales are applied to determine the response and stability of the system for small vibration amplitude. A new perturbation method to deal with viscoelastic term is presented. Theoretical expressions about the parameter spaces of linear-like vibration, hardening-type vibration and softening-type vibration are then deduced. The influence of viscoelasticity and scale effect on nonlinear dynamic behavior is studied. Results show that the viscoelasticity can reduce the effective elastic modulus and make the system tend to softening-type vibration; the scale effect can increase effective elastic modulus and make the system tend to hardening-type vibration. And most of all, simulation results of case studies are used to realize parameter optimization. Then parameter conditions of linear-like vibration, which is desired for many applications, are obtained. In this paper, the results of multi-physical field coupling simulation are used to verify the theoretical analysis.
22 citations
TL;DR: In this paper, the geometrically exact equations of motion of prewisted rotating composite beams parametrized by one space coordinate are derived from three-dimensional theory.
22 citations
TL;DR: In this paper, the nonlinear responses and stability of double-layered nanoplate embedded in the elastic medium are investigated in the presence of 3:1 internal resonance, and the effect of small scale effect and viscous damping on nonlinear vibration is explored in details.
22 citations
TL;DR: The phase shift caused by the dispersive perturbation is a remarkable feature that has never been observed in the collision process of algebraic solitons in the Benjamin-Ono equation.
Abstract: A direct perturbation theory is developed to study the effects of small perturbations on the interaction process of algebraic solitons of the Benjamin-Ono (BO) equation. Using the method of multiple scales, the modulation equations for the amplitude and the phase of each soliton are derived in the lowest approximation. As practical applications of the theory, the interaction of two solitons is investigated for the two different types of perturbations that appear in real physical systems. One is a dissipative perturbation (BO--Burgers equation) and the other is a dispersive perturbation (higher-order BO equation). In both cases, the changes of the soliton parameters due to small perturbation are calculated by numerical integrations and their characteristics are elucidated in detail. Among them, the phase shift caused by the dispersive perturbation is a remarkable feature that has never been observed in the collision process of algebraic solitons.
22 citations
TL;DR: In this paper, the response of a weakly nonlinear, single-degree-of-freedom system with cubic nonlinearities to multifrequency excitations is studied analytically and numerically.
Abstract: The response of a weakly nonlinear, single-degree-of-freedom system with cubic nonlinearities to multifrequency excitations is studied analytically and numerically The method of multiple scales is used to obtain uniformly valid, approximate solutions of the governing equation for various combination resonances The analytical and numerical solutions are in virtually perfect agreement for all cases considered, but difer markedly from the exact solution of the linearized equation of motion The peak amplitudes in the solutions of the nonlinear equation can be several times those in the solutions of the linearized equation, and they can occur rather more often; moreover, the addition of a static load can affect the natural frequency and, hence, either tune or detune a resonance, producing profound changes in the response The present results demonstrate that the actual response of a structure can lead to a fatigue life that is much shorter than what is predicted by linear analysis Hence, the conventional structural engineering practice of considering the structure to be safe from resonant responses when none of the frequencies of the excitation matches the natural frequency is shown to be fraught with danger; a practicing engineer, therefore, cannot afford to be ignorant of nonlinear phenomena
22 citations