Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels: Fid-Bau Portal

Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels

Singh, Vijay K. / Panda, Subrata K.

Abstract In this present article, large amplitude free vibration behaviour of doubly curved composite shell panels have been analysed using the nonlinear finite element method. The nonlinear mathematical model is derived using Green Lagrange type geometric nonlinearity in the framework of higher order shear deformation theory. In addition to that all the nonlinear higher order terms are included in the mathematical model to achieve more general case. The nonlinear governing equation of free vibrated curved panel is derived based on Hamilton׳s principle and solved numerically by using the direct iterative method. The developed mathematical model has been validated by comparing the responses with those available numerical results. Finally, some new numerical experimentation (orthotropicity ratio, stacking sequence, thickness ratio, amplitude ratio and support conditions) have been carried out to show the significance and the efficacy of the proposed mathematical model.

Highlights • A general nonlinear doubly curved laminated composite shell panel model is developed based on the HSDT mid-plane kinematics to achieve the parabolic distribution of the in-plane/out of plane shear stresses. • The nonlinearity in geometry is taken in Green-Lagrange sense to capture the total flexure (large displacement and rotation) under large amplitude vibration. • The nonlinear vibration behavior is analyzed for single/doubly curved shell panel by deriving the nonlinear stiffness matrices in Green-Lagrange sense including all the nonlinear higher order terms in the mathematical model. • Effect of different geometries and parameters on nonlinear free vibration behavior is analyzed thoroughly.