Nonlinear and Random Vibrations

Random differential inequalities and comparison principles for nonlinear hybrid random differential equations

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

Wavelet-based Random Vibrations in Earthquake Engineering

The recent development of wavelet analysis techniques has made it possible to represent the temporal variations of frequency content in an earthquake accelerogram elegantly. These techniques are more versatile than the other time-frequency localizing techniques due to their flexible time-frequency windowing feature. This development has led to the timeand frequency-based characterizations of gr...

Delocalized vibrations in classical random chains.

Normal modes of one-dimensional disordered chains with two couplings, one of them assigned at random to pairs in an otherwise perfect chain, are investigated. We diagonalize the dynamical matrix to And the normal modes and to study their spatial extent. Multifractal analysis is used to discern clearly the localized or delocalized character of vibrations. In constrast to the general viewpoint th...

Forced Vibrations for a Nonlinear Wave Equation

A Brief Introduction to Nonlinear Vibrations

Vibration phenomena that might be modelled well using linear vibration theory include small amplitude vibrations of long, slender objects like long bridges, aeroplane wings, and helicopter blades; small rocking motions of ships in calm waters; the simplest whirling motions of flexible shafts, and so on. However, interactions between bridges and foundations, between wings/blades and air, between...