In this study, a set of governing equations of the shallow spherical shell under the uniform membrane stresses is derived using Reissner's version of the Love's theory and their solutions are obtained as Bessel functions coupled by two eigen values, where the stresses of shell under a certain static load has been approximated by uniform membrane stresses.
It is found that the smaller the curvature of the shell becomes, the more the influences of the stresses on its natural frequencies are.
To investigate the dynamic characteristics of the system with clamped boundary conditions under time-harmonic uniform loads and point loads, the nondimensional compliance and admittance are worked out, and its values decrease with increase in the membrane stresses.
