Semi-Exact Algebraic Expressions For The Natural Frequencies Of Rectangular Kirchhoff-Love Plates
Semi-exact, closed-form algebraic expressions are developed for the natural frequencies of rectangular
Kirchhoff-Love plates. The approach employs plane waves, their edge reflections, and phase closure considerations. The
semi-exact nature is such that the analysis exactly satisfies plate boundary conditions along each edge when taken in
isolation, but not fully when combined, and thus is approximate near a corner. As frequency increases, the expressions
become increasingly more accurate. For clamped square plates, closed-form expressions are developed in algebraic form for
the first time and it is shown that the expressions for the first twenty non-dimensional natural frequencies are within 0.06%
of their exact values.