Modal and harmonic response analysis of composite laminated plates based on the absolute nodal coordinate formulation

To overcome the limitations of traditional finite element modal analysis methods in dealing with the vibration problems of composite laminated plates, such as excessive dependence on mesh accuracy, difficulties in handling nonlinear problems, and neglect of modal coupling effects, this article proposes a method for modal and harmonic response analysis of composite laminated plates based on the Absolute Nodal Coordinate Formulation (ANCF). A 36-degree-of-freedom (DOF) reduced-order shell element model is established, and the motion and deformation of the structure are described using the gradient and Green-Lagrange strain. The gradient vector is used to replace the generalized nodal coordinates in traditional finite element methods. The analytical expressions for the mass matrix, generalized external force matrix, and generalized elastic force, along with the Jacobian matrix, are derived. The dynamic equations for the composite laminated plate are established and solved. The composite laminated plate model is constructed based on ANCF, and static analysis is performed to verify the convergence of the model. Modal analysis is conducted to determine the natural frequencies and vibration modes, and harmonic response analysis is used to assess displacement responses under external excitation. The effects of different boundary conditions on the natural frequencies are studied, revealing the relationships between boundary conditions, width-to-thickness ratio, damping ratio, and the vibration response of composite laminated plates. Comparisons with traditional finite element methods confirm the effectiveness and accuracy of the ANCF method in the vibration analysis of composite laminated plates. This study provides an efficient and accurate computational method for the vibration analysis of composite laminated plates.