A Nonlinear Theory for the Bending, Buckling, and Vibrations of Conical Shells
Equations of motion and associated boundary conditions are developed for the general nonlinear vibrational behavior of thin conical shells. The theory is based upon nonlinear strain-displacement relations deduced for a conical shell from those derived by Sanders for thin shells of compound curvature. Equations for the bending, buckling, and postbuckling of conical shells under arbitrary loads are also developed and are shown to reduce to equations based on more simplified theories for both conical and circular cylindrical shells and circular flat plates. Various solution approaches to the nonlinear conical shell vibration problem are examined, and a new numerical method of solution is proposed and discussed. (Author-PL).