An enhanced reverberation-ray matrix approach for transient response analysis of composite laminated shallow shells with general boundary conditions

In this work, an enhanced reverberation-ray matrix (ERRM) approach is presented to develop an exact and unified solution for the transient response analysis of composite laminated shallow shells with general boundary conditions. The Hamilton's principle and Laplace transforms are employed to deduce the theoretical formulations based on the first-order shear deformation shallow shell theory (FSDSST) and the classical shallow shell theory (CSST). Each of the wave solutions is derived from the exact solutions of governing equations. Under the present framework, the artificial spring boundary technique is introduced to achieve the general boundary conditions. Accordingly, the scattering matrix is modified in unified and compact forms to enable the ERRM approach to deal with all kinds of boundary conditions including the classical cases, elastic restraints and their combinations. Then, the transient responses can be readily calculated by the Neumann series expansion and Fast-Fourier transform (FFT) algorithm. The excellent accuracy, reliability and efficiency of the current approach are validated by several numerical examples. Simultaneously, a comprehensive parametric investigation concerning the effects of elastic restraint parameters, shear deformation and rotary inertia, shallowness, material properties and lamination schemes is performed. Furthermore, the sensitivity of composite laminated shallow shells under different impact loads is also analyzed.