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, a closed-loop non-linear control strategy to reduce the flexural vibrations of a hinged-hinged initially imperfect beam is investigated, where the beam is subjected to a harmonic transverse excitation involved in a primary resonance of the first antisymmetric mode.
27 citations
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01 Jan 1980TL;DR: In this paper, a comparison of perturbation methods for nonlinear hyperbolic wave propagating in thermoviscous fluids is presented. But the authors do not consider the nonlinear acoustic wave propagation.
Abstract: Publisher Summary This chapter discusses the comparison of perturbation methods for nonlinear hyperbolic waves. It discusses five numbers of perturbation methods including the method of renormalization, the method of strained coordinates, the analytic method of characteristics, the method of multiple scales, and the Krylov–Bogoliubov–Mitropolsky method. These techniques are applied to nonlinear acoustic waves propagating in thermoviscous fluids. For lossless, oppositely traveling, one-dimensional waves, a first-order uniformly valid expansion can be obtained by using any of these techniques provided the waves do not mutually interact in the body of the medium. This is so if the waves are periodic or pulses. If the mutual-interaction terms are not negligible, only the method of renormalization, strained coordinates, and characteristics can be used. For dissipative media, it is not clear how one can use the method of renormalization, strained coordinates, and characteristics to determine an approximate solution when the dissipation term is the same order as the nonlinear term. For conservative multidimensional waves, a combination of the methods of renormalization and matched asymptotic expansions appear to be the most powerful. In applying the analytic method of characteristics to multi-dimensional waves, one can obtain uniformly valid expansions only if the characteristic surfaces are chosen appropriately. For waves that are short compared with the radii of curvature of the wave fronts, choosing the appropriate characteristics does not present any difficulty because the linear solution displays the role of the characteristic and geometric rays.
27 citations
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TL;DR: In this article, a nonlinear analytical model for vibration analysis of partially cracked thin orthotropic plate as affected by the fibre orientation and arbitrary position of a partial crack is presented, which is based on the classical plate theory and the effect of microstructure is incorporated using the modified couple stress theory.
27 citations
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TL;DR: In this paper, a composite laminated circular cylindrical shell under the combined action of radial harmonic excitation, compressive in-plane force and aerodynamic pressure is studied.
27 citations
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TL;DR: In this article, the free vibration and primary resonances of an inextensional spinning beam with six general boundary conditions are studied, and the results of the analysis are verified by numerical simulations.
27 citations