On Thermoelastic and Hygrometric Response of Sandwich Beams with Laminate Facings and Honeycomb Cores: Part IV—A Dynamic Theory

Abstract

The systematic development of a dynamic theory for a sandwich beam is presented leading to the governing equations of equilibrium and the natural boundary conditions. Using Timoshenko beam theory [I], a function 1' is introduced in terms of the kinetic and strain energies of the system consisting of both laminate facings and honeycomb core. Reissner's variational theorem is used in conjunction with Hamilton's principle in order to obtain a new set of governing equations of motion, which is accomplished by letting the variation of D vanish. In addition, the natural boundary conditions are obtained in the process of the development of the theory. The constitutive equations for the beam are recovered as an outcome of the variational analysis. The static equations of equilibrium are obtained as a special case.