Thermally induced vibrations of viscoelastic shallow shells

A method for the study of thermally induced vibrations of viscoelastic shallow shells of arbitrary shaped plane-form is proposed. It is shown that the time behaviour can be found by assuming a normal mode expansion in tems of the eigenfunctions of the associated elastic shallow shell problem and the deflection is obtained with the aid of the correspondence principle. The response of a shallow shell with rectangular as well as elliptical base to the sudden application of a temperature distribution on the surface of the shell is discussed. For rapidly applied heat inputs, an approximate analysis for its rapid estimation is also presented. All details are illustrated by graphs.