Analytical Solution to Bi-Linear Spring Mass Systems Free Vibration

Abstract

Dynamic systems are generally categorized as linear and non-linear systems based on the analysis approaches developed. Bi-linear spring mass systems form an intermediate category which possesses characteristics of both linear and non-linear systems. Analytical solutions to bi-linear systems cannot in general be reduced to a single equation covering the entire motion domain as in the case of linear systems. Nevertheless, the step-wise linear solutions can be obtained within each domain and the solutions can be related to one other from displacement and velocity continuity requirement for mechanical systems. Detailed analytical solution to single degree of freedom bi-linear spring mass system free vibration is presented in this paper towards deriving equations for time period as well as logarithmic decrement. Displacement versus time as well as velocity versus time plots is generated to demonstrate bi-linear system behavior against the linear system behavior. The solution developed is validated against numerical results obtained from finite element analysis. The methodology shall be extended for higher degree of systems with increased complexity compared to linear system solutions which are already well developed. To demonstrate this, two degree of freedom bi-linear spring mass system solutions are also presented. Keywords: Bi-Linear spring, free vibration, frequency, logarithmic decrement Cite this Article Prasanth Gopi Nair, Sundaresan Poovalingam. Analytical Solution to Bi-Linear Spring Mass Systems Free Vibration. Journal of Aerospace Engineering & Technology . 2018; 8(1): 21–35p.