Wave motion and its dispersive properties in a finite element model with distortional elements

Abstract

Solutions are obtained for wave motion in a hybrid-mass distortional finite element model by employing the extended method of lattice dynamics. The dispersion equations of wave motion are also given through the solutions. The dispersive properties of a plane wave and the existential condition of an inhomogeneous wave are studied. The results show that the ability of the hybrid-mass model to resist the distortion of element shape is greater than that of the consistent-mass model but lower than that of the lumped-mass model. The velocities of wave propagation in the lumped-mass model are not always lower than that in the corresponding continuum. When the element shape is highly distorted, the velocities in the lumped-mass model may exceed those in the continuum. The effects of discretization in time domain on wave propagation are also discussed.