Free vibration anlysis of point supported beams, plates and circular cylindrical shells by the Ritz method

ABSTRACT Science of engineering mechanics has an important place especially in civil engineering. Improvements and advantages of computer technology make it possible to find solutions to most complex and difficult problems. In this study, by using these advantages, eigenvalues and mode shapes of, point supported beams, point supported orthotrop plates and point supported orthotrop circular cylindrical shells are investigated mainly. The classical Ritz method is used for solving the problem. In the study, for applying the Ritz method, the trial function denoting the deflection of the plate is expressed in the polynomial form. By using the Ritz method, the problem is reduced to the solution of a system of algebraic equations. In this study, the results are given for the eigenvalues and mode shapes of the point supported beams. The influence of the mechanical properties on the mode shapes of the point supported rectangular orthotropic plates are investigated numerically for various values of mechanical properties characterizing the anisotropy at the plate material and aspect ration. The eigenvalues are tabulated for various orthotrophy parameters and two aspect rations for four mode families. For each mode family, the eigenvalues are provided for the first three vibration modes. Separately, point supported orthotrop circular cylindrical shells are investigated numerically for various values of mechanical properties characterizing the anisotropy at the shell material. It is believed that the tabulated results will prove useful to designers and provide a reference against which other researchers can compare their results. Keywords: Point support, orthotropy, free vibration, beam, plate, circular cylindrical shell. x