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.

Nonlinear Electrohydrodynamic Stability of Two Superposed Streaming Finite Dielectric Fluids in Porous Medium with Interfacial Surface Charges

Abstract: A weakly nonlinear stability analysis of wave propagation in two superposed dielectric fluids streaming through porous media in the presence of vertical electric field producing surface charges is investigated in three dimensions. The method of multiple scales is used to obtain a dispersion relation for the linear problem and a nonlinear Klein–Gordon equation with complex coefficients describing the behavior of the perturbed system at the critical point of the neutral curve. In the linear case, we found that the system is always unstable for all physical quantities (including the dimension l), even in the presence of electric fields and porous medium, in the nonlinear case, novel stability conditions are obtained, and the effects of various parameters on the stability of the system are discussed numerically in detail.

Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations

Abstract: In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.Copyright © 2003 by ASME

Vibration suppression of nonlinear rotating metamaterial beams

Abstract: In this paper, we investigate the nonlinear vibration of a metamaterial structure that consists of a rotating cantilever beam attached to a periodic array of spring–mass–damper subsystems deployed for vibration suppression. The full nonlinear model of the system is developed. The nonlinear response due to a primary resonance excitation is investigated, and the capability of the metastructure to suppress vibration is examined. The mass of the resonators (absorbers) comes at the expense of the host structure’s mass itself, which makes the total mass of the system conservative. Free and forced vibration analyses are performed. We first use the method of multiple scales to analyze the nonlinear behavior of rotating beams. The perturbation solutions are validated against their numerical counterparts. Results show the presence of a critical rotational speed at which the beam undergoes bifurcation and starts to flutter. The addition of the absorbers is observed to slightly reduce this critical speed. Nevertheless, the amplitude of limit-cycle oscillations beyond bifurcation is found to decrease when equipping the rotating beam with local absorbers. The results demonstrate the capability of the metamaterial structure as an efficient damping treatment. Furthermore, we show that careful placement of the absorbers along the cantilever beam (close to the tip) enables further vibration mitigation.