On The Analytical Solution Of A Cubic Nonlinear Structure Controlled By Linear Tuned Mass Damper

Abstract

Nonlinear structural systems when are subjected to unpleasant excitations can be controlled by linking tuned mass dampers to the structure. Tuned mass dampers have successfully been used to control the response of tall buildings cable stayed bridges, and offshore structures. This paper studies the analytical solution for the forced vibration response due to harmonic loading for a cubic nonlinear structure coupled with a linear tuned mass damper. The analytical solution is obtained using first order perturbation analysis by the method of multiple scales. The analytical results are compared with the numerical solution which is obtained using Runge-Kutta algorithm. There were some discrepancies between the analytical and numerical results attributed mainly to not using second order perturbation analysis which is very lengthy process. However, the first order perturbation analysis could give the qualitative behaviour of the controlled structure at various forced frequencies. The advantage of using linear tuned mass damper to control cubic nonlinear structures is pointed out.