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 paper, the nonlinear vibrations of fractional viscoelastic plate with Kelvin-Voigt fractional order constitutive relationship are investigated. And the structural dynamic of the plate is modeled by using the Newton's second law.
Abstract: Nonlinear vibrations of fractional viscoelastic plate with Kelvin–Voigt fractional order constitutive relationship is investigated in this paper. Based on the Kirchhoff hypothesis for thin shells and von Karman’s assumption, the structural dynamic of the plate is modeled by using the Newton’s second law. The nonlinear coupled equations of motion are obtained by introducing the Airy stress function and the Galerkin method is used to discretize the partial differential equations. Analytical solutions for fully simply supported and clamped plate are obtained by using the method of multiple scales and finally the equations of amplitude–frequency and phase–frequency are obtained for primary, super-harmonic and sub-harmonic resonance. The obtained amplitude–frequency and phase–frequency equations are used for studying the effects of excitation, fractional parameters and nonlinearity on the frequency responses of the fractional viscoelastic plate and finally some conclusions are outlined.
47 citations
TL;DR: In this paper, the nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory and the governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam.
Abstract: The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory. The governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam. The method of multiple scales is applied to the governing equation to evaluate the nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and highlight the contributions of the nonlinear term and nonlocal effect.
47 citations
TL;DR: In this article, the authors deal with the internal resonances originated from parametric excitation of a slender pipe conveying fluid for marine applications, which corresponds to an excitation frequency that is equal to the double of the structure's first lateral natural frequency.
47 citations
TL;DR: In this paper, the steady-state periodic response of an axially moving viscoelastic beam in the supercritical speed range is investigated under the quasi-static stretch assumption, where the excitation of the forced vibration is spatially uniform and temporally harmonic.
47 citations
TL;DR: In this article, the response of two-degree-of-freedom systems with quadratic nonlinearities to a principal parametric resonance in the presence of two to one internal resonances is investigated.
47 citations