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 nonlinear dynamic equation of space cable net structures is developed using the extended Hamilton principle, which belongs to the self-excited vibration with quadratic and cubic nonlinearities.
Abstract: The nonlinear dynamic analysis of cable net structures becomes more and more significant for their space applications required high surface accuracy, especially mesh reflector antennas. In this work, the resonant multi-modal dynamics due to 1:1 internal resonances in the finite-amplitude vibrations of cable net structures subjected to harmonic loads are investigated. The nonlinear dynamic equation of space cable net structures is first developed using the extended Hamilton principle, which belongs to the self-excited vibration with quadratic and cubic nonlinearities. Linear modal analysis is then performed to decouple the nonlinear differential equations, and yields a complete set of system quadratic/cubic coefficients. With the aim of parametrically revealing nonlinear behaviors of space cable net structures, the second-order asymptotic analysis under 1:1 internal resonance is accomplished by the method of multiple scales. The nonlinear phenomena of a planar cable net and cable net reflector, such as the bending of response curve, jump phenomena, instability regions, saddle-node bifurcation, are verified by means of numerical analysis.
10 citations
TL;DR: In this paper, the electrohydrodynamic Kelvin-Helmholtz instability of a cylindrical interface separating two dielectric streaming fluids, stressed by an axial electric field in the absence of surface charges on the interface, is studied.
Abstract: The electrohydrodynamic Kelvin–Helmholtz instability of a cylindrical interface separating two dielectric streaming fluids, stressed by an axial electric field in the absence of surface charges on the interface, is studied. We have used the method of multiple scales. Two nonlinear Schrodinger equations are obtained, one of them leads to the determination of the cut-off wavenumber and the cut–off electric field. The other Schrodinger equation is used to analyze the stability of the system. The stability conditions of the perturbed system is discussed analytically and numerically. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein—Gordon equation. The various stability criteria are derived from this equation.
10 citations
TL;DR: In this paper, a dual proof mass accelerometer is proposed by introducing mode localization in two electrostatically coupled resonators, where the levering mechanism is utilized to amplify the inertial force applied axially to the two weakly coupled Resonators.
10 citations
TL;DR: An analysis on nonlinear oscillations and chaotic dynamics is presented for a simply-supported symmetric cross-ply composite laminated rectangular thin plate with parametric and forcing excitations in the case of 1:3:3 internal resonance.
Abstract: An analysis on nonlinear oscillations and chaotic dynamics is presented for a simply-supported symmetric cross-ply composite laminated rectangular thin plate with parametric and forcing excitations in the case of 1:3:3 internal resonance. Based on Reddy's third-order shear deformation plate theory and the von Karman-type equations, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate can be established via the Hamilton's principle. Such partial differential equations are further discretized by the Galerkin method to form a three-degree-of-freedom coupled nonlinear system including the cubic nonlinear terms. The method of multiple scales is then employed to derive a set of averaged equations. Through the stability analysis, the steady-state solutions of the averaged equations are provided. An illustrative case of 1:3:3 internal resonance and fundamental parametric resonance, 1/3 subharmonic resonance is considered. Numerical simulation is applied to investigate the intrinsically nonlinear behavior of the composite laminated rectangular thin plate. With certain external load excitations, the simulation results demonstrate that the nonlinear dynamical system of the composite laminated plate exhibits different kinds of periodic and chaotic motions.
10 citations
TL;DR: In this article, the primary resonance of a Duffing oscillator with two distinct time delays in the linear feedback control under narrow-band random excitation was analyzed and the analytical results were in well agreement with the numerical results.
Abstract: The paper presents analytical and numerical results of the primary resonance of a Duffing oscillator with two distinct time delays in the linear feedback control under narrow-band random excitation. Using the method of multiple scales, the first-order and the second-order steady-state moments of the primary resonance are derived. For the case of two distinct time delays, the appropriate choices of the combinations of the feedback gains and the difference between two time delays are discussed from the viewpoint of vibration control and stability. The analytical results are in well agreement with the numerical results.
10 citations