Solution of free harmonic vibration equation of simply supported Kirchhoff plate by Galerkin-Vlasov method
This work studies the dynamic characteristics of simply supported rectangular thin plates undergoing natural transverse vibrations in harmonic motion. The governing partial differential equation for the free transverse vibration of the plate was solved by the Galerkin-Vlasov variational technique. The assumption of free harmonic motions reduced the governing equation to an algebraic eigen value eigenvector problem, which was solved in the space domain to obtain the eigen frequencies and modal shape functions of the vibrating Kirchhoff plate. The eigen frequencies and modal shape functions obtained were found to be identical with the results obtained by the classical methods of Navier and Levy for the same problem.
Keywords: Kirchhoff plate, Galerkin-Vlasov method, harmonic vibration, natural vibrations, eigen frequencies.