FORCED RESPONSE OF STRUCTURAL DYNAMIC SYSTEMS WITH LOCAL TIME-DEPENDENT STIFFNESSES

• Published in: Journal of sound and vibration Vol. 237; no. 5; pp. 761 - 773
• Main Authors: DELTOMBE, R., MORAUX, D., PLESSIS, G., LEVEL, P.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 09.11.2000; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Resonance, damping and dynamic stability; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Dynamic response; Spectral method; Differential equation; Forced vibration; Clamped plate; Dynamical system; Runge Kutta method; Steady state; Beam(mechanics); Spring mass system; Time dependence; Time varying system; Vibration damping; Equations of state; Analysis method; Linear equation; System with one degree of freedom; Structural analysis
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2000.3072

This paper deals with a method which is meant to directly approximate the steady state response of linear differential equations with periodic coefficients under external excitations. The interest lies in the use of particular systems with time-independent characteristics (mass, damping) and with periodically time-varying stiffness. A description of the principle of the method is provided. This method has been successfully tested on a single-degree-of-freedom (s.d.o.f) example and compared to the standard Runge–Kutta method. Moreover, the parameters are assumed to be a modification of initial non-parametric systems and allow us the use of the forced reanalysis methods to improve the direct spectral method (DSM). The description of the reanalysis method is made with its implementation within the direct spectral method. Then, a practical application concerning a clamped/free beam with parametric mounts is presented to demonstrate the ability of the proposed method in the analysis of systems which have many d.o.f.s and localized parameters.