Steady state periodic response of truncated conical shell undergoing large amplitude vibration

The large amplitude steady state periodic response of truncated conical shell panels under the influence of transverse harmonic excitation is analyzed by considering the nonlinear strain displacement relations. The finite element analysis is based on the kinematics of first-order shear deformation theory and the constrained strain terms have been interpolated using field-consistent modified shape functions to avoid shear locking. The governing equation of motion has been obtained using Hamilton's principle, which has been solved using the Modified shooting method and continuation schemes to yield the complete frequency response. The influence of boundary conditions, the amplitude of the forcing function and curvature on the periodic response was investigated. The hardening or softening nonlinear behavior has been obtained depending upon boundary conditions, geometry and forcing function amplitude. The combined influence of geometric nonlinearity and varying curvature of the truncated conical shell leads to significantly greater negative half-cycle amplitude. The peculiar nature of the restoring force dynamics with increased inward deflection causes the restoring forces to act in a destabilizing sense leading to increase in negative half-cycle amplitude. The periodic stress variation reveals multiple stress reversals during a loading cycle and is very critical for the fatigue design of such components. The multiple slope changes/bifurcations in the frequency response have been examined using response history, frequency spectra and the phase plane plots where it is revealed that for some cases the higher harmonic contributions are even greater than the fundamental harmonic. The deformed configuration at various instants during the periodic cycle reveals modal interaction between first and higher modes. Moreover, the nonlinear frequency response curves depict softening nonlinear behavior for deeper shells which gradually transforms into hardening behavior for shallow shell panels.