Design sensitivity analysis for transient response of non-viscously damped systems based on direct differentiate method.

Highlights • The first and second derivatives for the transient response of non-viscously damped systems are calculated. • The direct differentiate method is adopted. • The sensitivities are derived by using a modified precise integration method. • The computational considerations of the methods are investigated and compared. • Two numerical examples are given to show the performances of the method. Abstract Calculation of the first and second derivatives of transient response with respect to design variables is a prerequisite when gradient-based methods are adopted for optimization design in time-domain. In this paper, a design sensitivity analysis (DSA) method for calculating the first and second derivatives of the transient response for non-viscously damped systems is developed. The assumed damping forces depend on the past history of motion via convolution integrals over some kernel functions. The direct differentiate method (DDM) is selected to derive the DSA method. By introducing a generalized damping model in expression of fraction formula, the equations of motion of the non-viscously damped system are transformed into a state-space form without the convolution integral terms. Then, the first and second derivatives of the transient response are formulated based on a modified precise integration method using the DDM. The numerical stability, accuracy and implementation effort of the DDM are discussed. Two numerical examples are comparatively demonstrated using the DDM, the discretize-then-differentiate adjoint variable method (AVM) and the differentiate-then-discretize AVM. The results indicate that, by considering all the computational considerations, the proposed DDM is more suitable than the other two methods for the sensitivity analysis of transient response for non-viscously damped systems. Besides, it is also the only existing method to capture the second-order derivatives of transient response for the non-viscously damped systems. [ABSTRACT FROM AUTHOR]