Torsional Vibrations of Homogeneous and Sandwich Spherical Caps and Circular Plates

摘要

Torsional vibrations of spherical caps are investigated on the basis of equations including thickness-shear deformation. Secondary transverse shear effect on extensional motion and secondary inertia effect are explicitly shown to be negligibly small for both homogeneous and sandwich caps. When these secondary effects (but not the primary transverse shear effect) are neglected, the curvature effect also drops out, and the problem becomes coincident with that of torsional vibrations of circular plates. A degenerate solution of the equations of motion further leads to an interesting torsional thickness-shear mode, which is particularly important for sandwich caps and plates with free edges. In general, frequencies of torsional vibrations of spherical caps and circular plates are found to start at a much higher level than those of axisymmetric vibrations. (Author)