Transient vibrations of an isotropic elastic sphere

Summary An attempt is made to study the dynamic response of a thick, homogeneous isotropic elastic sphere under the action of uniformly distributed internal and external pressure distributions which vary sinusoidally with time. An exact solution of the problem is obtained with the aid of the Laplace transform method and the theory of residues. Some main properties of the radial vibration field are examined. The frequency equation for the free vibration is derived explicitly. Several limiting cases of interest are recovered.