Modeling of coupled structural systems by an energy spectral element method

Solving approximate energy flow partial differential equations for structural elements can be done analytically (energy flow analysis—EFA) or using finite element approximations (energy finite element method—EFEM). In this paper, energy equations are solved using the spectral element method (SEM). This new approach, which is called the energy spectral element method (ESEM), can be applied to predict the distribution of the energy flow and energy density of built-up structures at high frequencies. Energy spectral element method is a matrix formulation based on the general solution of the partial differential equations for energy density in structural vibrations such as longitudinal and transversal vibrations of frames. A spectral energy element can be shown to be equivalent to an infinite number of energy finite elements. In this work, numerical models involving coupled rods and beams are generated by energy spectral element method, and the results obtained are compared with energy densities computed from the displacement fields predicted by the SEM to solve the conventional boundary value problem.