Engineering Science and Materials Commons^™

Exact Solution Of Time History Response For Dynamic Systems With Coupled Damping Using Complex Mode Superposition, Manoj Kumar Chinnakonda

All Theses

An exact solution method for general, non-proportional damping time history response for piece-wise linear loading proposed by Dickens is generalized to piece-wise quadratic loading. Comparisons are made to Trapezoidal and Simpson's quadrature rules for approximating the time integral of the weighted generalized forcing function in the exact solution to the decoupled modal equations arising from state-space modal analysis of linear dynamic systems. The time integral of the forcing function is recognized as a weighted integral with complex exponential and the general update formulas are derived using polynomial interpolation to the forcing function. Closed-form expressions for the weighting parameters in the …