Sensitivity analysis of frames with unspecified dynamic load and joint parameters accounting for damping - Pozorski, Zbigniew (Computer Assisted Methods in Engineering and Science, 2022)
The paper is concerned with a class of generalized structural optimization problems, in which geometrical nonlinearities play an important role in a response of dynamically loaded structure. Forced, steady-state periodic vibrations of linear elastic frame and beam structures are considered. Both, viscous and complex modulus damping models are used. Using the adjoint variable method, sensitivity operators with respect to variation of stiffness, damping and mass parameters, as well as loading and support conditions are derived. The loading corresponds to an excitation induced by a rotational machine founded on vibroisolation. The forms of response functionals expressed in displacements are discussed. Numerical examples of frame structures illustrate the theory and demonstrate the accuracy of the derived sensitivity operators.