Torsional vibrations of circular poroelastic plates

Abstract

Torsional vibrations of annular poroelastic circular plates are studied in the framework of Biot's theory of wave propagation in porous solids. The frequency equation of torsional vibrations is same for pervious and impervious surfaces. The frequency equation of torsional vibrations is obtained by using the traction free boundaries and edges of the annular circular plate. Non-dimensional frequency of annular plate is computed as a function of aspect ratio. The frequency equation is discussed for first two modes. Frequency equation of torsional vibrations of uniform circular poroelastic plate is obtained as a particular case of the annular plate. Resonant frequency of infinite poroelastic plate is obtained as a limiting case of annular plate. The expressions for phase velocity and attenuation are obtained and these are computed for two different poroelastic materials as a function of frequency in presence of dissipation. Phase velocity is almost same for the considered poroelastic materials and dissipations. Results of previous study are obtained as a particular case of the present investigation.