  Efficient and accurate numerical algorithms are developed to solve a
generalized Kirchhoff-Love plate model subject to three common physical
boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. We
solve the model equation by discretizing the spatial derivatives using
second-order finite-difference schemes, and then advancing the semi-discrete
problem in time with either an explicit predictor-corrector or an implicit
Newmark-Beta time-stepping algorithm. Stability analysis is conducted for the
schemes and the results are used to determine stable time steps in practice.
  A series of carefully chosen test problems are solved to demonstrate the
properties and applications of our numerical approaches. The numerical results
confirm the stability and 2nd-order accuracy of the algorithms, and are also
comparable with experiments for similar thin plates. As an application, we
illustrate a strategy to identify the natural frequencies of a plate using our
numerical methods in conjunction with a fast Fourier transformation (FFT) power
spectrum analysis of the computed data. Then we take advantage of one of the
computed natural frequencies to simulate the interesting physical phenomena
known as resonance and beat for a generalized Kirchhoff-Love plate.
