Nonlinear Vibration Analysis of Shallow Shells - a New Approach

The application of constant deflection contour method is justified in this book and appears to be simpler than existing methods. The present method offers a new approach to deal with problems involving large amplitude vibrations of plates and shallow shells. The significance of this method lies in the fact that the basic governing equations reduce to a set of ordinary differential equations. The present method can be applied to study static as well as dynamic behavior of plates and shells having arbitrary shaped boundaries for which other methods may fail. The present method relies heavily with the assumed form of the contour close to the correct equation. However, in most practical cases of interest they are defined. The application of polynomial expressions for the deflection and the stress functions in conjunction with the Galerkin procedure appears to produce excellent results in all cases, sometimes better than those obtained from other methods. The use of Conformal mapping technique has also been introduced in this book for analyzing the nonlinear response of complex structures. It may become a simple tool for future researchers to use this method for further analyses