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 kelvin-helmholtz instability of two superposed dielectric finite fluids in porous medium under vertical electric fields

Abstract: A weakly nonlinear theory of wave propagation in two superposed dielectric fluids streaming through porous media in the presence of vertical electric field and in the absence of surface charges at their interface is investigated in three dimensions. The method of multiple scales is used to obtain a dispersion relation for the linear problem and a Ginzburg-Landau equation with complex coefficients for the nonlinear problem, describing the behavior of the system. The stability of the system is discussed both analytically and numerically in both cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the stability criterion is independent of the medium permeability and that the medium porosity, surface tension, and dimension all have stabilizing effects the fluid viscosities, velocities, and depths have destabilizing effects, and the electric field has a dual role in the stability of the system. In the nonlinear analysis, it is found that the electric field has a...

Analytical Investigation of Hydrodynamic Cavitation Control by Ultrasonics

Abstract: In recent experimental work, Chatterjee and Arakeri have demonstrated that an imposed acoustic field of sufficiently high strength and frequency can suppress or control cavitation. In this paper, we analytically study the equation governing the dynamics of a single bubble in a time-varying pressure field, for parameter ranges representative of those experimental conditions. The governing equation is strongly nonlinear and intractable in general; however, for the parameter ranges of interest, we are able to nondimensionalize and scale the governing equation into a form that, though still strongly nonlinear, is amenable to analysis using the method of multiple scales (MMS) based on an arbitrarily chosen “small” parameter ∊. Removal of secular terms, a key step in the MMS, raises an interesting issue which we discuss. Second order MMS gives the slow average evolution of the bubble radius. Numerical solutions of the original equation match the MMS approximation well on time scales of \(\cal O\)(1/∊). The MMS approximation also provides insight into the roles played by relevant physical parameters in the system. Our results provide theoretical support for the abovementioned experimental results.

A perturbation method for nonlinear forced vibration of orthotropic rectangular plates with in-plane loads

Abstract: The method of multiple scales in conjunction with Galerkin's method is used to analyze the nonlinear f orced and damped response of a rectangular orthotropic plate subjected to a uniformly distributed transverse l oading. The effects of damping and in-plane l oads are considered. The analysis considers simplysupported as well as clamped panels. For each case, both movable and immovable edge conditions are considered. By using the method of rnultiplescales, all the the possible resonances such as primary, subharmonic and superharmonic resonances are also studied. For the undamped response without in-plane l oading, comparisons of the present results with those obtained by finiteelement technique show excel lent agreement. Moreover, we present the results f or the damped response with and without in-plane l oading.

Primary Resonance of the Current-Carrying Beam in Thermal-Magneto-Elasticity Field

Abstract: On base of the electro-magneto-elastic theory and the theory of the bending vibration of the electric beam, nonlinear vibration equation of current-carrying beam subjected to thermal-magneto-elasticity field is studied The Lorentz force and thermal force on the beam are derived According to the method of multiple scales for nonlinear vibrations the approximation solution of the primary resonance of the system is obtained Numerical analysis results show that the amplitude changed with the system parameters With the decrease of magnetic intensity, the amplitude increases rapidly The response curve occurs bending phenomenon and soft features is increased gradually Increasing current, the amplitudes increase With the decrease of temperature, the peak of response curves decrease With the increase of temperature, natural frequency decreased It is useful in practical engineering