Axisymmetric vibrations of composite annular sandwich plates of quadratically varying thickness by harmonic differential quadrature method

作者：Lal Roshan; Rani Rashmi^*

来源：Acta Mechanica, 2015, 226(6): 1993-2012.

DOI：10.1007/s00707-014-1284-0

In the present paper, axisymmetric vibrations of annular sandwich plates with isotropic core and orthotropic face sheets have been studied using the harmonic differential quadrature (HDQ) method. The thickness of the core is assumed to vary quadratically in the radial direction, and the face sheets are treated as membranes of constant thickness. The effect of shear deformation and rotatory inertia in the core has been taken into account, and the mathematical analysis of the model is based upon first-order shear deformation theory. The governing differential equations of motion have been obtained using Hamilton's energy principle. In the resulting equations, the HDQ method is employed to obtain the frequency equations for the three edge conditions, namely CC, i.e., clamped at both the inner and outer edges, CS, i.e., clamped at the inner edge and simply supported at the outer edge, and CF, i.e., clamped at the inner edge and free at the outer edge. The lowest three roots of these equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, core thickness at the center, facing thickness and radii ratio on the natural frequencies has been studied. Three-dimensional mode shapes for the specified plates have been illustrated. To check the validity of the present considerations and the technique, a frequency parameter has been compared in particular cases.

• 出版日期2015-6