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Transfer Matrix Method for 2-Dimension System

机译:二维系统的传递矩阵法

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摘要

Classical Transfer Matrix Method (TMM) for 1-dimension system is widely used in many science and technology fields and has been expanded to the study of mutibody system dynamics. In order to solve the dynamics problems of 2-dimension system, such as, vibration characteristics of thin plate, the transfer matrix method for 2-dimension system has been developed by expanding the classical Transfer Matrix Method for 1 -dimension system in this paper. A 2-dimension system, such as, a thin plate is modelled to a network structure composed by lumped mass and massless beam. By means of the transfer matrices of lumped mass and massless beam, the transfer matrix of sub-structure which is arranged in column has been easily developed. The overall transfer equation of the plate is obtained. By solving the overall transfer equation and the element equations of the thin plate with various kind of boundary condition, the vibration characteristics of the system can been obtained easily. Numerical examples shown that the new method has following characteristic: simple calculating process, high compute efficiency and good universality. Comparing with Finite Element Method (FEM) or Finite Element Transfer Matrix Method (FETMM), this method's calculating process is simpler. This method can straight be used to study other complex dynamics problems of two dimension system. The idea of this method can be used to develop transfer matrix method for three-dimensional systems.
机译:一维系统的经典转移矩阵方法(TMM)已在许多科学和技术领域中广泛使用,并已扩展到多体系统动力学的研究中。为了解决二维系统的动力学问题,例如薄板的振动特性,通过扩展经典的一维系统传递矩阵方法,发展了二维系统的传递矩阵方法。将二维系统(例如薄板)建模为由集总质量和无质量梁组成的网络结构。借助于集总质量和无质量束的传递矩阵,可以很容易地开发布置在列中的子结构的传递矩阵。获得了板的整体传递方程。通过求解具有各种边界条件的薄板的整体传递方程和单元方程,可以轻松获得系统的振动特性。数值算例表明,该方法具有计算过程简单,计算效率高,通用性好的特点。与有限元法(FEM)或有限元传递矩阵法(FETMM)相比,该方法的计算过程更为简单。该方法可直接用于研究二维系统的其他复杂动力学问题。该方法的思想可用于开发三维系统的传递矩阵方法。

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