Vibration characteristics of cracked FG-GRC plates in thermal environments based on phase field theory and meshless method

Stiffness degradation resulting from matrix cracking has a great impact on the vibrational behaviors of composite laminates. However, the vibration frequencies of functionally graded graphene-reinforced composite (FG-GRC) plates with crack defects remain largely unexplored. In this paper, the variational phase field theory is implemented to investigate the vibration characteristics of cracked FG-GRC plates subjected to thermal conditions. The effective elastic constants depending on the temperature of FG-GRC plates are characterized by the extended Halpin-Tsai model. The first-order shear deformation theory (FSDT) is employed to describe the displacement fields of the cracked FG-GRC plates. The meshfree kernel particle method is engaged to discretize governing equations over the computational domain and then the obtained governing eigen-equations are calculated using the Ritz methodology. The numerical results illustrate the influences of crack length, crack number, the strength of foundations, graphene distribution, temperature variation and geometric values on the vibration fundamental frequencies of the FG-GRC plates. The present work not only provides an alternative and feasible approach for solving the interaction problems between cracking and vibration, but also makes significant advances to characterize the vibrational behaviors of cracked functionally graded materials for engineering applications.