Analysis of the stability of stochastic viscoelastic systems

✍ Scribed by V.D Potapov

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 444 KB
• Volume: 61
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(97)00035-x

✦ Synopsis

The RMS stability of viscoelastic systems, subject to parametric loads, with respect to a perturbation of the initial conditions is considered. These loads, as well as the external damping characteristics, are assumed to be random, steady-state, broadband processes. An expansion of the required displacements in a series in the eigenfunctions of the elastic system is used to solve the functional equations wkich describe the motion of such systems. The integro-differential equations in generalized displacements are solved using the method of stochastic averaging (an asymptotic method) under the asannption that the measure of the relaxation of the material and the mean value of the external damping are small quantities compared with unity and that the random fluctuations of the processes under consideration are small in the mean square. It is shown that the critical value of the system parameter may turn out to be least when the form of the perturbations of the initial conditions differs f~m the first form of the natural vibrations.