Abstract
The algebraic equations for the forced, damped, periodic, axisymmetric motion of circular plates, solid and annular, are derived directly through the application of Hamilton's law of varying action. The simplicity, for many problems, of direct analytical solutions by means of Hamilton's law has previously been demonstrated. The method is called the Hamilton-Ritz method. In this paper, direct analytical solutions from Hamilton's law are shown to be exactly the same as direct analytical solutions from the ancient and fundamental principle of virtual work. The Hamilton-Ritz formulation is compared to the Galerkin formulation. Results from one- and two-term solutions by direct virtual work (Hamilton-Ritz) are compared to results from the exact solution and to results from the Galerkin method.
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