The evolution of a trapped mode of oscillations in a “string on an elastic foundation-moving inertial inclusion” system

✍ Scribed by S.N. Gavrilov; D.A. Indeitsev

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 645 KB
• Volume: 66
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(02)90013-4

✦ Synopsis

It is shown that natural vibrations, localized around the inclusion, are possible in a system consisting of an "infinite string on an elastic foundation-concentrated inertial inclusion which moves at a constant, subcritical velocity". The evolution of the trapped mode of oscillations is described analytically for the case of a slowly accelerating inclusion, i.e. the dependence of the amplitude of the oscillations on the frequency is found. The solution which is constructed holds in the time interval when the velocity of the inclusion is not close to the critical velocity (the non-resonance case). An approach to the solutions of similar problems, based on the method of multiple scales, is proposed which enables one to reduce the solution of a problem to investigating an ordinary differential equation with slowly varying coefficients.