Showing papers on "Multiple-scale analysis published in 1973"

Nonlinear transverse vibrations of beams with properties that vary along the length

Abstract: The method of multiple scales is used to analyze the nonlinear transverse vibrations of inhomogeneous beams including the effects of transverse shear and rotary inertia. First‐order uniform perturbation expansions are derived for the displacements, shear force, and frequency in terms of the ratios of maximum transverse displacement to cross‐sectional radius of gyration and cross‐sectional radius of gyration to wave length.

Nonlinear stability of a liquid film adjacent to a supersonic stream

Abstract: The nonlinear stability of a liquid film adjacent to a supersonic gas stream is investigated. The gas is assumed to exert a mean shear stress at the liquid/gas interface which in turn establishes a linear mean velocity profile in the liquid. The analysis takes into account the pressure perturbation exerted by the gas on the liquid assuming the disturbed gas motion to be inviscid and the mean gas velocity profile to be uniform. The problem is formulated within the long wave approximation, and solutions are obtained for finite amplitude waves by using the method of multiple scales. The results predict the existence of finite amplitude periodic waves, in qualitative agreement with recent experimental observations.

Acoustic propagation in ducts with varying cross sections and sheared mean flow.

Abstract: An analysis is presented of the wave propagation and attenuation in two-dimensional ducts with slowly varying cross sections which carry sheared mean flow. A uniformly valid asymptotic expansion of the acoustic waves is obtained in terms of the maximum slope of the wall by using the method of multiple scales. The result is a first-order differential equation describing the amplitude variation with the axial distance. This equation is used to evaluate the effects of variations of the duct cross section and growing boundary layers on the different acoustic modes.