Study On Modeling Methods For Rectangle Plate With Holes Under Arbitrary Boundary Conditions

A rectangular plate with rectangular holes under arbitrary boundary conditions are widely used in aerospace,marine,automobile and other engineering fields.Due to the existence of holes,the quality and stiffness of the whole structure are changed.As a key factor affecting the vibration characteristics of the plate structure,in-depth study on the plate structure is of great theoretical and engineering significance.However,due to the current research on rectangular thin plate with rectangle holes,it mainly focuses on Vibration Modeling under classical boundary conditions,rarely involving arbitrary elastic boundary conditions,and there is still much room for improvement in solving efficiency.In this paper,an open hole rectangular plate model is established by combining the improved Fourier series method and the Rayleigh-Ritz method,so that it is suitable for arbitrary elastic boundary conditions.On the basis of this,an improved modeling method for independent coordinate coupling is proposed,which not only applies to arbitrary elastic boundary,but also improves the efficiency of solving.Firstly,a model of free vibration of rectangular thin plate with elastic boundary under elastic boundary conditions is established by using improved Fourier series method and Rayleigh-Ritz method in the global coordinate system.The vibration displacement function of both the domain of the hole and the rectangular plate is expressed as a linear combination of the standard two-dimensional Fourier cosine series and the sine series,which overcomes the discontinuity of the traditional Fourier series method on the boundary condition and makes it suitable for any elastic boundary condition.Then,the matrix equation of free vibration of rectangular thin plate with holes is derived by Rayleigh-Ritz method.The natural frequencies and modal shapes are obtained by solving the equations.The correctness and accuracy of the method are verified by comparison with the literature and FEM results,and the location and size of the hole were analyzed parametrically.Then,the method of modeling the hole and plate domain based on the Rayleigh-Ritz method in the global coordinate system is improved,and the modeling method of the rectangular plate with holes under any boundary condition is proposed based on theindependent coordinate coupling method.The independent coordinate system is established for the hole domain and the plate domain.The vibration displacement function of the rectangular plate adopts an improved Fourier series,and the vibration displacement function of the rectangular hole is based on the uniform beam function under the free boundary.Firstly,the independent mass and stiffness matrix is established based on their respective coordinate systems.Then,the relationship between the two independent coordinate systems is established by the continuity integral condition of the vibration displacement function in the hole domain.Then,the overall matrix equation is obtained and the natural frequencies and mode shapes are solved.In addition,the free vibration of rectangular plates with two rectangular holes under different boundary conditions is also analyzed.The correctness of the method is proved by comparison with the results of literature and finite element simulation.Finally,two methods are compared to verify the advantages of the independent coordinate coupling method in solving the efficiency.At last,the modal experimental scheme of rectangular plate with holes under free boundary conditions and clamped boundary conditions was designed and carried out.The vibration data are collected,and the DHDAS software is used to process the data to obtain the natural frequency and modal shape of the opening plate.Compared with the calculation results in this paper,the correctness of the modeling method in this paper is further verified.