VARIATIONAL DERIVATION OF THE DYNAMIC EQUILIBRIUM EQUATIONS OF NONPRISMATIC THIN-WALLED-BEAMS DEFINED ON AN ARBITRARY COORDINATE SYSTEM

In this paper, Hamilton's principle is used to derive the dynamic equi librium equations of thin-walled beams of generic section. The displac ements are defined on an arbitrarily selected coordinate system. For H amilton's principle, the dynamic behavior of thin-walled nonprismatic beams is characterized by two energy functions: a kinetic energy and a potential energy. The formulation uses the procedure of variational o perations. The obtained dynamic equilibrium equations and natural boun dary conditions are highly coupled. Though it is difficult or impossib le to find the closed-form solution of the derived differential equati on system, certain inverse or numerical methods can be used to solve i t.