A non-linear dynamic lumped-parameter model of a rectangular plate

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Kármán large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.