FREE-VIBRATION ANALYSIS AND OPTIMIZATION OF AXISYMMETRICAL PLATES ANDSHELLS .1. FINITE-ELEMENT FORMULATION

This paper deals with the free vibration analysis of shells of revolut ion using the finite element method. A family of variable thickness, c urved C(0) Mindlin-Reissner axisymmetric finite elements is presented which include shear deformation and rotatory inertia effects. The accu racy, convergence and efficiency of these newly developed elements are explored through a series of free vibration analyses of axisymmetric shell structures and the results are compared with those obtained by o ther analytical and numerical methods. The comparisons show that the m ethod yields very good results with a relatively small number of eleme nts and that estimates for the higher modes can be obtained without an y difficulties. A companion paper will consider the structural optimis ation of axisymmetric shells undergoing free vibrations.