A deep rod finite element for structural dynamics and wave propagation problems

In this paper, a new element for higher order rod (normally referred to as Minlin{Herrman rod) is formulated by introducing lateral contraction e ects. The cross-section is assumed to be rectangular. The sti ness and mass matrices are obtained by using interpolating functions that are exact solution to the governing static equation. The studies using this element for free vibration analysis show that lateral contractional inertia has a pronounced e ect on the natural frequencies of the rod systems. The formulated element is not only able to capture the two propagating spectrums but also the dispersive e ects in a deep rod. The results obtained from this element is compared with the previously formulated exact higher order spectral rod element.