Dynamic continuum modeling of truss-type space structures using spectral elements

Abstract

A new continuum modeling approach is developed by utilizing the spectral element method to represent a large periodic truss-type beam as an equivalent continuum extended Timoshenko beam model. First, the transfer matrix for a representative truss cell of the periodic truss-type beam is numerically derived by condensing the global dynamic stiffness matrix by use of the continuum degrees of freedom introduced. The global dynamic stiffness matrix is obtained by assembling the spectrally formulated dynamic stiffness matrices for the structural elements within the truss cell. Next, the transfer matrix for an equivalent continuum beam element is analytically derived so that the unknown equivalent structural properties are contained in the transfer matrix. The two transfer matrices are then forced to be equal to each other to determine the equivalent structural properties of the continuum beam model. The equivalent structural properties and vibration characteristics of a continuum beam model by the present continuum method are compared with those by other continuum methods to prove that the present continuum method can give a very reliable continuum model.