AMPLITUDE BOUNDS OF LINEAR FORCED VIBRATIONS

For reasons of safety and reliability, the maximum amplitudes of vibra tion responses must be taken into account in engineering. The exact ma ximum amplitudes are available from solving linear differential equati ons. However, for large scale systems, it requires too much computatio n time to be useful. Therefore, simple amplitude bounds are of great i nterest for engineers. Up to now, only for classically damped linear s ystems, some approximate amplitude bounds were presented. In this pape r, amplitude bounds of linear forced vibrations are presented for gene ral damped linear vibrating systems. For transient, harmonic and step excitations, the presented amplitude bounds show simple relations to t he system parameters, and are easy to calculate. The advantage is the possibility to judge the level of vibrations, and to choose appropriat e parameters at design. Compared with the approximate underestimating amplitude bounds available in literature, the presented amplitude boun ds are overestimating the maximum amplitude and, therefore, can be saf ely applied to general damped vibrating systems.