Dynamic Axisymmetrical Problem of Elastic Theory for a Rigidly Fixed Circular Laminated Plate
A non-stationary axisymmetric problem for a rigidly fixed circular laminated plate under the action of distributed load on the end surface (normal stresses) is considered. This load is an arbitrary function of the radial coordinate and time. For definiteness, a three-layer system is studied. New closed solution has been constructed within the theory of elasticity in three-dimensional statement by means of the consistent use of the method of incomplete separation of variables in the form of finite integral transformations. The Hankel transform is applied consistently with finite limits on the axial coordinate and generalized finite transformation (MRA) on the radial variable. At each stage of the solution, the procedure of standardization is conducted that allows implementing the appropriate algorithm of transformation. The calculated ratio makes it possible to study the character of variations of the stress-strain state of the laminated plate and to make the qualitative and quantitative analysis of mechanical stress fields relatedness in composite laminated structures. In addition, it is possible to analyze the impact of structural and mechanical properties of materials, the order of layers, the ratio of thicknesses of layers in the package, as well as their number on self-axisymmetric frequencies and forms of natural oscillations of structures.