Forced Axisymmectric Motion of Shallow Spherical Shells

A formal solution is presented for the dynamic response of a shallow spherical shell under axisymmetric but otherwise arbitrarily distributed, time-dependent surface tractions, for arbitrary initial conditions and (admissible) homogeneous boundary conditions. The solution is obtained in terms of the eigen-functions associated with the free vibration of the shell, and appropriate orthogonality and normalization conditions are formulated. The free vibration problem for a clamped shell is solved, and an example of shell response to a transient loading condition is presented. The theoretical development and its application are carried out within the framework of a theory which accounts for the effect of shear deformation and rotatory inertia. A comparison with the theory which neglects these effects is presented. Significant differences in the predictions of the two theories are noted.