Dynamics of shallow shells taking into account physical non-linearities

In this paper the author, has presented a solution to the problem of dynamics of shallow shell taking into account physical non-linearities. The shell is made of non-linear material obeying a cubic stress–strain law, and energy dissipation has been included in the formulation of the problem. Solutions for cylindrical and spherical shells and numerical results for these cases are based on approximate shape functions consisting of a single term in each. Some curves of amplitude–frequency relationships are given for cylindrical and spherical shells in the case of soft-type physical non-linearity.