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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01 Sep 2005
TL;DR: In this paper, a generalized non-linear kinematic model is derived to represent the physical system and is solved by the long-wave perturbation method in a two-step procedure.
Abstract: Non-linear stability theories for the characterization of Newtonian film flow down an infinite vertical rotating cylinder is given. A generalized non-linear kinematic model is derived to represent the physical system and is solved by the long-wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviours. In the second step, an elaborated non-linear film flow model is solved by using the method of multiple scales to characterize flow behaviours at various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The modelling results indicate that by increasing the rotation speed, ω, and decreasing the radius of cylinder, R, the film flow becomes less stable, generally.
6 citations
TL;DR: In this article, the transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated, with special attention paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature.
Abstract: The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice.
6 citations
TL;DR: In this article, the response of a single-degree-of-freedom system with quadratic, cubic and quartic nonlinearities subjected to a sinusoidal excitation that involves multiple frequencies is considered.
Abstract: The response of a single-degree-of-freedom system with quadratic, cubic and quartic nonlinearities subjected to a sinusoidal excitation that involves multiple frequencies is considered. The method of multiple scales is used to construct a first order uniform expansion yielding two first-order nonlinear ordinary differential equations that are derived for the evolution of the amplitude and phase. These oscillations involve a subharmonic oscillation of order one-fourth and superharmonic oscillation of order two. Steady state responses and their stability are computed for selected values of the system parameters. The effects of these (quadratic, cubic, and quartic) nonlinearities on these oscillations are specifically investigated. With this study, it has been verified that the qualitative effects of these nonlinearities are different. Regions of hardening (softening) behaviour of the system exist for the case of subharmonic resonance. The response curve is not affected by decreasing the damping factor for the case of superharmonic resonance. It is shown that the response curve contracts or expands as the parameters vary. The multivalued region increases or decreases when some parameters vary.
6 citations
TL;DR: Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading using Reddy's third-order shear deformation theory and von Karman’s nonlinearity.
Abstract: Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading. Using Reddy’s third-order shear deformation theory and von Karman’s nonlinearity, the governing partial differential equations are derived by Hamilton’s principle and then truncated into a set of ordinary differential equations by Galerkin method. The critical speed for flutter is discussed by employing the linear theory. Further, the method of multiple scales is used in the nonlinear dynamical analysis of the truncated system. The Poincare map is numerically calculated to identify dynamical behaviors. The bifurcation diagrams are presented for varying the dimensionless in-plane loading fluctuation amplitude and the Mach number related dimensionless parameter while other parameters are unchanged.
6 citations
TL;DR: In this paper, the authors analyzed the influence of damping on Lamb wave dispersion curves and attenuation coefficients using self-adjointness and the method of multiple scales (MMS), which is a type of perturbation method.
6 citations