A comparison of several methods for the calculation of vibration mode shape derivatives

Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are reviewed and compared. These methods (finite difference method, Nelson's method, modal method and a modified modal method) are implemented in a general-purpose commercial finite element program and applied to a cantilever beam and a stiffened cylinder with a cutout. A beam tip mass, a beam root height and specific dimensions of the cylinder model comprise the design variables. Data are presented showing the amount of central processor time used to compute the first four eigenvector derivatives for each example problem; errors and rapidity of convergence of the approximate derivative to the exact derivative are taken into account. Nelson's method proved to be most reliable and efficient.