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, the chaotic dynamics and global bifurcations of the suspended elastic cable under combined parametric and external excitations are investigated and the non-linear equations of motion of the elastic cable to small vibration of one support are derived.
Abstract: The chaotic dynamics and global bifurcations of the suspended elastic cable under combined parametric and external excitations are investigated. The non-linear equations of motion of the elastic cable to small vibration of one support are derived. The averaged equations are obtained by using the method of multiple scales. Based on the averaged equations, the theory of normal form and Maple program are used to obtain the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues. On the basis of the normal form, global bifurcation analysis of the parametrically and externally excited suspended elastic cable is given by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of the elastic cable is also found by numerical simulation.
69 citations
TL;DR: In this paper, a simple mass-spring-damper vibration absorber is employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions, and the effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibration are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.
69 citations
TL;DR: In this article, the nonlinear free vibration of a fractional dynamic model for the viscoelastic pipe conveying fluid is studied and the dynamic equations of coupled planar motion for the pipe are derived by employing the Euler beam theory and the generalized Hamilton principle when considering both the fractional material model and the geometric nonlinearity.
69 citations
TL;DR: In this article, the Gurtin-Murdoch elasticity theory is adopted to the classical beam theory in order to consider the surface Lame constants, surface mass density, and residual surface stress within the differential equations of motion.
69 citations
TL;DR: In this paper, an Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system, and the beam is supported by immovable end conditions, thus leading to stretching during the vibrations.
68 citations