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 equilibrium equations of thin-walled beams of generic section. The displacements are defined on an arbitrarily selected coordinate system. For Hamilton'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 operations. The obtained dynamic equilibrium equations and natural boundary conditions are highly coupled. Though it is difficult or impossible to find the closed-form solution of the derived differential equation system, certain inverse or numerical methods can be used to solve it.