VIBRATION STUDIES ON MODERATELY THICK DOUBLY-CURVED ELLIPTIC SHALLOW SHELLS

Based on a refined first-order shear deformation theory, the vibratory characteristics of doubly-curved shallow shells of elliptical planfor m are investigated. Integral expressions incorporating the effects of shear deformation and rotary inertia for the strain and kinetic energi es are derived. The transverse shear strain components are obtained as linear functions of thickness in contrast to constant strains availab le in the current literature. With the use of the extremum energy prin ciple, a governing eigen-matrix equation is formulated which is subseq uently solved to extract the frequencies and mode shapes. The shallow shells considered here are the spherical, cylindrical and hyperbolic p araboloidal shells. The effects of various geometric parameters and bo undary constraints on the resonant frequencies and mode shapes are exa mined. The solution method employs displacement functions comprising o f a set of two-dimensional orthogonal polynomials and a basic function for each degree of freedom: three orthogonal displacement components and two rotations. The convergence of eigenvalues is examined. The val idity of the present results is verified by comparing, if possible, wi th the values from the literature.