In this study, an efficient and flexible hybrid method is presented for the free vibration analysis of thin plates, aiming to enhance the accuracy in regions with complex geometries while significantly reducing the computational cost in the remaining parts of the domain. In the proposed approach, the meshfree Galerkin method employing the Improved Moving Least Squares (IMLS) approximation is seamlessly combined with the classical Finite Strip Method (FSM). In regions with irregular geometries, complex boundaries, or steep gradients, the meshfree method is employed due to its superior capability to model complex geometries and impose boundary conditions without the need for explicit meshing. In contrast, the Finite Strip Method is used in regular rectangular regions because of its simple computational structure and high efficiency. This integration enables a large portion of the computational domain to be modeled using only a limited number of finite strips, while the complex regions are analyzed using the meshfree method. As a result, compared with the meshfree method alone, the overall computational time can be reduced by up to 50% without compromising accuracy. Moreover, by combining the accuracy of the meshfree approach with the computational efficiency of the Finite Strip Method, the proposed hybrid method provides a robust, efficient, and reliable framework for the free vibration analysis of thin plates, particularly those with complex geometries and demanding computational requirements.
