Comparison of several approximate modal methods for computing mode shape derivatives

Abstract Five approximate modal methods for computing mode shape (eigenvector) derivatives with respect to design parameters are compared in terms of their computational accuracy and efficiency. These five methods are the truncated modal method, Wang's explicit method, Wang's implicit method, and two methods presented by Liu et al. Nelson's method is adopted to give the exact eigenvector derivative for defining a scalar error measure of the approximate solution. All the above methods are implemented in a general-purpose commercial structural analysis program and applied to the calculation of the mode shape derivatives of three structures—a cantilever beam, a truss tower and a beam-shell structure—each with respect to two design variables. The results show that Wang's implicit method and the second method by Liu are the most efficient ones among the five approximate methods.