SENSITIVITY ANALYSIS FOR THE STEADY-STATE RESPONSE OF DAMPED LINEAR ELASTODYNAMIC SYSTEMS SUBJECT TO PERIODIC LOADS

Adjoint and direct differentiation methods are used to formulate desig n sensitivities for the steady-state response of damped linear elastod ynamic systems that are subject to period loads. Variations of a gener al response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple t he equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity exp ressions. This eliminates the need to separately evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over tim e, thus they are quickly computed. The methodology is valid for proble ms with proportional as well as nonproportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crank shaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. B oth the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are a lso calculated to validate the explicit sensitivity results.