Spectrally formulated element for wave propagation in 3-D frame structures

A spectral formulation of the dynamics of frame structures suitable for a computer matrix method implementation is presented. The analysis is based on a spectral frame element that is assembled to give the exact frequency dependent stiffness matrix for the complete structure. The frequency domain response is converted to the time domain response using the fast Fourier transform algorithm. The formulation is verified by comparison with conventional finite element techniques. It is found that the spectral method can be less costly from a computational standpoint than the conventional finite element method. This is especially true for events involving high frequencies such as impact. The most significant strength of the spectral method, however, lies in its ability to go directly to the heart of dynamics problems; namely, the system frequency response function. Some of the implications of this are discussed.