Second‐order design sensitivity analysis of mechanical system dynamics

Dependence of dynamic response of nonlinear mechanical systems on design variables is analysed. An adjoint variable method is used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. A computational algorithm is presented for numerical calculation of first and second design derivatives. A simple oscillator example is solved analytically and by the adjoint variable method, with identical results. A burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically. It is shown that quadratic appriximations of dynamic response, using results of second-order design sensitivity analysis, can be substantially better than conventional linear approximations.