In this paper，we propose a general displacement field function method，which consists of the highly freely chosen basic function and a series of undetermined weighted coefficients to study the free vibration characteristics of GPLs/Al composite plate with an array cutouts. This general displacement field function method can solve the boundary constraint dependence when choosing the displacement field function to obtain the analytical solution in classical plate theory. There is a linear correlation between the weight coefficients. The system of linear equations is constructed based on the boundary constraints，thus the fundamental system of solutions can then be determined. By changing the system of linear equations as well as the fundamental system of solutions，the type of boundary constraint can be easily transferred. This proposed semi-analytic method not only solves the problem of assumed field function dependence on boundary constraints in the classical solution，but also has the superiority of fast conversion of boundary conditions. Meanwhile，by introducing the scatter integral method，a much more efficient and robust method is obtained other than the continuous integral method on the study of free vibration for the structure with an array cutouts. In this paper，we study the free vibration of GPLs/Al composite plates with a single and array cutouts. From the natural frequency and modal analysis，it is found that the generalized mass matrix and stiffness matrix of the open structure decrease synchronously when the cutouts distributed uniformly，and its free vibration characteristics tend to that of the complete plate.