Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method

Dynamics of a double curvature honeycomb sandwich shell with simply supported boundaries are studied in this paper. The nonlinear governing equations of the double curvature honeycomb sandwich shell subjected to transverse excitations are derived by using Hamilton's principle and Reddy's third-order shear deformation theory. Based on the homotopy analysis method, the average equations of the primary resonance and harmonic resonance are obtained. The influence of structural parameters, the transverse exciting force amplitude and transverse damping to the double curvature honeycomb sandwich shell are discussed by using the analytic approximation method. The amplitude-frequency response curves demonstrate softening nonlinearity in primary resonance (no internal resonance), hardening nonlinearity in 3 order superharmonic resonance and no jump phenomenon in 1/3 subharmonic resonance. The variation of nonlinear strength, multivalued jump point and multivalued region are detailed and discussed.