Pressure radiation from an infinite two layered plate is studied theoretically. The plate is made of a transversely isotropic material and an elastic or viscoelastic material of uniform thickness. It is bounded by a fluid of infinite extent on one side and the other by a vacuum.
The equation of motion of plate includes the effects of rotary inertias and transverse shear deformations. The solution is obtained by means of Hankel transform with respect to radial coordinate and Laplace transform with respect to time variable. Sommerfeld's technique and the steepest descent method are used to get the inverse Hankel transform for the farfield radiation.
As examples the pressure radiation patterns as functions of $\phi$ are evaluated numerically for the cases of elastic and viscoelastic coating in cases of harmonic excitations with and without damping. The effects of coating layers on the pressure radiation patterns are discussed. The result is applicable to the noise control and pressure wave generation in fluids.