In-plane Free Vibration Analysis For Functionally Graded Material Annular Sector Plates

This paper is based on theory of Two-Dimensional Elastic Classic.the differential equations of equilibrium and the geometrical relation are given in this paper,then established the governing differential equations of motion and the corresponding boundary conditions for the free vibration of annular sector plates which are made of traditional materials and functionally graded materials,Last,we use the differential quadrature method to study the free vibration of circular plates with traditional materials and functionally graded materials.The specific research contents as follows:Firstly,we introduce the research status of all the theoretical foundation and the annular sector plate used to this paper,which comes to the main background and application status of annular sector plates;concrete origin of functionally graded materials,the physical properties of functionally graded materials;the basic concepts of differential quadrature method and the optimal method of its interpolation function and node selection.Secondly,we studied the free vibration of annular sector plate of the traditional materials,the research is based on the two-dimensional linear elastic theory,draw the corresponding control motion differential equations for in-plane free vibration of annular sector plate,then discrete equations with the differential quadrature method,and wo got the numerical solution of dimensionless frequency for annular sector plate,finally,The numerical results confirm with recently published results,part of the data are compared with the commercial software ANSYS calculation results,which showing the differential quadrature method are widely,precisely and conveniently.In the process of analysis,we consider three kinds of common boundary conditions,in order to analyze the influence of different parameters on the dimensionless frequency which under the different conditions.Thirdly,we studied the free vibration of annular sector plates with functionally graded materials in-plane,we initially set the physical parameters of functionally graded materials along the radial annular sector plate in accordance with the power function distribution,then use classic two-dimensional linear elastic theory,deducing and simplifying the free vibration of its motion control differential equation for functionally gradient materials annular sector plate which we needed,and then using the differential quadrature method to disperse the differential motion equations,finally calculate the eigenvalues and the dimensionless frequency.Part of the data are compared with the numerical results which are given by commercial software ANSYS are further proof of the accuracy of the method.In the analysis process,we considered three kinds of common boundary conditions,in order to analyze the influence for the dimensionless frequency of annular sector plates,we used different conditions of the inner and outer radius ratio,fan angle and gradient index.Finally,we summarize the research results and some follow-up prospects,the results show that: in the three kinds of common boundary conditions,whether it is homogeneous materials or functionally graded materials of the in-plane free vibration of annular sector plate,the final dimensionless frequency obtained will increase with the radius ratio increase,on the anther hand it will decrease with angles increasing.Therefore,these numerical results and analytical methods of this problem can be provided as a reference for future assumptions and research designs.