Analytical Solution to Single Degree of Freedom Bi-Linear Spring Mass Systems Transient Vibration

Abstract

Conventional approach to solution of linear systems under transient vibration has been through Convolution integral or Duhamel integral method which employs the method of superposition of linear solutions to obtain the total solution. Principle of superposition is not possible for non-linear systems and hence transient vibration solution cannot be obtained through classical methods. Nevertheless, the solution to transient vibration for each domain can be obtained as a sum of homogeneous solution and particular integral. The solutions for each domain within each cycle as well as between adjacent cycles are related through displacement and velocity continuity equations for mechanical systems. Displacement-time as well as velocity-time plots are presented for different types of standard excitations like quadratic and exponential. Harmonic excitation is treated as one of the cases of transient excitation and system behavior under resonance is presented in detail. The solution methodology developed is validated against finite element transient simulations as well.

Keywords: Bi-linear spring, transient vibration, harmonic, resonance

Cite this Article: Prasanth Gopi Nair, Sundaresan Poovalingam. Analytical Solution to Single Degree of Freedom Bi-Linear Spring Mass Systems Transient Vibration. Journal of Aerospace Engineering & Technology. 2018; 8(2): 7–18p.