Analysis of Loosely Clamped Plates

One of the few analytical methods available for the analysis of flexure of plates with large deflections is the perturbation method, the main feature of which is the representation of a dependent variable as a power series in a constant (perturbation) parameter. In the geometrically nonlinear theory of axisymmetric circular plates, the central deflection, edge rotation, load and (1-ν), where ν is Poisson's ratio, all have been used in the role of the perturbation parameter. The asymptotic solutions thus obtained indicate the (1-ν²) is a suitable perturbation parameter for the analysis of loosely clamped circular plates with finite axisymmetric deflections. In order to demonstrate the utility of this new parameter, an analysis of a unifromly loaded circular plate with movable clamped edge is carried out. Furthermore, deviating from the usual practice of obtaining the necessary linearized equations from the nonlinear differential equations of Kirchoff's theory, the derivations make use of the energy integrals. The first two differential equations of the linear infinite system coincide with Berger's equations.