Eigen vector buckling based boundary analysis method for free vibration of rectangular thin plates
The main research topic of this paper is the application of the finite element method boundary analysis theory to study the stability of plate in irregular shape. First of all, the basic theory of free vibration of elastic plate and the basic equations of elastodynamics are introduced, and the governing equation of small deflection of free vibration of plate is given. Secondly, the finite element method boundary analysis method is introduced in details, including the basic idea and analysis steps of finite element method boundary analysis, and some element types, so as to lay a theoretical foundation for better understanding of finite element method boundary analysis method and application of it to analyze the stability of plate. At last, finite element method boundary analysis is applied to analyze the stability of plate, among which, the structural analysis types in ANSYS software and its analysis steps are introduced, and buckling (eigenvalues) analysis in ANSYS software is mainly introduced, and the effective performance of algorithm is verified by applying ANSYS software.
Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method
This paper aims at extending the application of two-dimensional differential transform method (2D-DTM) to study the free vibration of thin plates with arbitrarily varying thickness. First, the differential equation of motion governing thin plates with varying thickness is derived using Hamilton’s principle. Afterward, the 2D-DTM, a numerical method which is capable of reducing the size of computational work and can be applied to various types of differential equations, has been applied to derive the natural frequencies of variable thickness thin plates with different boundary conditions. Several numerical examples have been carried out to demonstrate the applicability and accuracy of the present method in free vibration analysis of both uniform plates and plates with variable thickness.
Comments on "Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method"
Tari et al. [A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comput. Appl. Math. 228 (2009) 70-76], presented some fundamental properties of TDTM for the kernel functions in two-dimensional Volterra integral equations. Here, we suggest simple proofs of those fundamental properties by using the basic properties of TDTM. Furthermore, we present some fundamental properties of TDTM for the kernel functions of a quotient type in two-dimensional Volterra integral equations. Numerical illustrations are demonstrated to show the effectiveness of the TDTM for solving two-dimensional Volterra integral equations.