Three-dimensional vibration analysis of a finite cylinder using the generalised differential quadrature method

Using the Navier's equations of the motion in cylindrical coordinate, vibration analysis of a finite cylinder is accomplished. These equations are transformed into the dimensionless forms in terms of non-dimensional displacements and time. The different boundary conditions are considered for this problem which the former analytical and semi-analytical methods could not treat them. Two ends boundary condition namely fixed-fixed and fixed-free are examined. The dimensionless governing equations of the motions in conjunction with the boundary condition are discretised making use of the generalised differential quadrature (GDQ) method. The ensuing system of algebraic equations in terms of displacement components leads to an eigenvalue problem to find the natural frequencies of the problem. The comparison of the results with some earlier works validates the methodology and formulation of the problem.