Direct Sensitivity Analysis of Dynamic Responses for Nonlinear Structure

The vibration performance of a nonlinear structure can be assessed by analyzing the effects of change in parameters on nonlinear dynamic responses. A direct sensitivity analysis method for nonlinear dynamic responses is proposed in this paper. By directly differentiating the nonlinear equation of motions, the dynamic response and corresponding sensitivity can be synchronously determined using a forward time integration algorithm. The proposed method is applied to perform sensitivity analysis for different nonlinear vibrations of Duffing oscillator and Duffing-type Ueda oscillator. The accuracy of the proposed method is verified by other numerical approaches. Results show that the proposed method, which avoids the errors caused by the secular term in the computation of long-term responses, can be successfully applied to the sensitivity computation of periodic and quasi-periodic vibrations. The dynamic sensitivity of the quasi-periodic response remains bounded and settles into a regular region. When the structure vibrates in a chaotic region, the proposed method gives a more consistent solution than that obtained by the finite difference method.