EIGENVALUE SENSITIVITY ANALYSIS OF PLANAR FRAMES WITH VARIABLE JOINT AND SUPPORT LOCATIONS

Various sensitivity equations are developed in this study for eigenvalue sensitivity analysis of planar frames with variable joint and support locations. The emphasis is placed on the derivation of the sensitivity equations by the continuum approach. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed with respect to the local coordinate system. The material derivative of this variational form is then sought to account for the changes in the member's length and orientation resulting from the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). Examples are presented to validate these derived sensitivity equations with analytical solutions as well as numerical results. It is concluded that the sensitivity equation derived by the boundary method is computationally more efficient but less accurate than that of the domain method. Nevertheless, both of them are superior to the conventional discrete analytical method in terms of computational efficiency.