HYBRID ANALYTICAL TECHNIQUE FOR EVALUATING THE SENSITIVITY OF THE NONLINEAR VIBRATIONAL RESPONSE OF BEAMS

A three-step hybrid analytical technique is presented for evaluating t he nonlinear vibrational response as well as the first-order sensitivi ty coefficients of thin-walled beams (derivatives of the nonlinear fre quency with respect to material and geometric parameters of the beam). The first step involves the generation of various-order perturbation functions, and their derivatives with respect to the material and geom etric parameters of the beam, using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functio ns as coordinate (or approximation) functions and then computing the a mplitudes of these functions and the nonlinear frequency via a direct variational procedure. The third step consists of using the perturbati on functions, and their derivatives, as coordinate functions and compu ting the sensitivity coefficients of the nonlinear frequency via a sec ond application of the direct variational procedure. The analytical fo rmulation is based on a form of the geometrically nonlinear beam theor y with the effects of in-plane inertia, rotatory inertia, transverse s hear deformation, and cross-sectional warping included. The effectiven ess of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section.