Abstract: A set of formulas calculating higher-order updates and gradient for dynamic responses is derived by setting up the mapping relationship between the design variables space and the re-analysis variables space, hence, higher-order directional derivatives of dynamic response and the Taylor-series representation of dynamic reponse updates considered in the re-analysis variables space. and the technique of modal analysis is utilized. What is significantly noteworthy is that the computational effort needed in obtaining the expression of the convergent series is based entirely on the first-order information. The formulas are suitable to the dynamic response optimal design of large scale structures where the modal truncation can be employed to reduce the computational costs. Numerical examples are provided to illustrate accuracy and efficiency of the proposed procedures.

Key words: dynamic response optimal design, response update, sensitivity calculation