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 同心环支
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 Flexural Vibration of Mindlin Moderately Thick Annular Plates on Multiple Concentric Ring Supports 域内同心环支Mindlin中厚环板的弯曲振动 短句来源 The Transfer Matrix Solution of Transverse Vibration of Circular Plates with Arbitrary Number of Concentric Ring Supports 受任意个同心环支圆板横振特性的传递矩阵法 短句来源 This paper deduces the analytical solution of transverse vibration of circular plates with arbitrary number of concentric ring supports at all kinds of boundary conditions by the use of transfer matrix method. The frequency equations are described by the multiplication of a series of two order matrices. The eigen -frequencies can be obtained by the searching root method of non-linear algebra equation. 本文用传递矩阵法推导了各种边界条件下受任意个同心环支圆板(包括实心圆板和圆环板)横向振动频率方程的精确解析式,频率方程是以一系列二阶矩阵的乘积表示的,利用非线性代数方程搜根法数值求解固有频率,方法具有公式简单、分析统一以及计算量小和计算精度高的特点,本文最后给出了两个算例. 短句来源 The method proposed herein is applicable to free vibration of annular plates continuous over ring supports or internal point supports. 域内环支条件则通过拉氏乘子法予以处理，适于具有同心环支及点支环板的振动分析。 短句来源
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 The Transfer Matrix Solution of Transverse Vibration of Circular Plates with Arbitrary Number of Concentric Ring Supports 受任意个同心环支圆板横振特性的传递矩阵法 短句来源 Flexural Vibration of Mindlin Moderately Thick Annular Plates on Multiple Concentric Ring Supports 域内同心环支Mindlin中厚环板的弯曲振动 短句来源 An Analysis of the Flow in Cocentric Flluld Ring Transportation 液环同心输送的流动分析 短句来源 A NEW ANALYTICAL SOLUTION TO FREE TRANSVERSE VIBRATIONOF CIRCULAR PLATES WITH CONCENTRIC ELASTIC RING SUPPORTS 受任意个同心弹性环支圆板横向自由振动的一个新的解析解法 短句来源 Buckling of Axisymmetric Concentric Ring 轴对称同心环支承厚圆板的屈曲 短句来源

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 This paper deduces the analytical solution of transverse vibration of circular plates with arbitrary number of concentric ring supports at all kinds of boundary conditions by the use of transfer matrix method. The frequency equations are described by the multiplication of a series of two order matrices. The eigen -frequencies can be obtained by the searching root method of non-linear algebra equation. The method has some special advantages that the formulae are unified. easily programed, less the amount of calculation... This paper deduces the analytical solution of transverse vibration of circular plates with arbitrary number of concentric ring supports at all kinds of boundary conditions by the use of transfer matrix method. The frequency equations are described by the multiplication of a series of two order matrices. The eigen -frequencies can be obtained by the searching root method of non-linear algebra equation. The method has some special advantages that the formulae are unified. easily programed, less the amount of calculation and good accuracy. Finally, two examples are given. 本文用传递矩阵法推导了各种边界条件下受任意个同心环支圆板(包括实心圆板和圆环板)横向振动频率方程的精确解析式,频率方程是以一系列二阶矩阵的乘积表示的,利用非线性代数方程搜根法数值求解固有频率,方法具有公式简单、分析统一以及计算量小和计算精度高的特点,本文最后给出了两个算例. This paper presents a new analytical solution to free transverse vibration ofcircular plates with arbitrary number of concentric ring supports。The analytical solution ofdynamic response of the circular plate is obtained by regarding the reaction forces of thering supports as the unknown external forces acted on the plate。The integral constants aredecided by the boundary conditions of the plate,The reaction forces of ring supports aredecided by the condition of zero displacements at the ring supports。 The frequency... This paper presents a new analytical solution to free transverse vibration ofcircular plates with arbitrary number of concentric ring supports。The analytical solution ofdynamic response of the circular plate is obtained by regarding the reaction forces of thering supports as the unknown external forces acted on the plate。The integral constants aredecided by the boundary conditions of the plate,The reaction forces of ring supports aredecided by the condition of zero displacements at the ring supports。 The frequency equationis a determinant whose order is equal to the number of ring supports。 The eigenfrequencies of the plate can be given numerically. And the mode shape function is describedby an analytical representation。 该文给出了受任意个同心环支圆板横振特性的一个新的解析解法，将环支反力视为作用于板上的待定外力，在求得板受迫振动的解析解后，由边界条件确定积分常数，利用环支处板位移为零条件决定环支反力，所得频率方程是一阶数等于环支个数的行列式，可数值计算出固有频率，而振型函数用一解析式表示。 Based on Mindlin plate theory, a flexural vibration analysis of moderately thick annular plates on multiple concentric ring supports is presented in this paper. The admissible displacement functions take the form of power series with supplementary terms, and the Lagrangian multiplier technique is employed to deal with displacement conditions on ring supports.The method proposed herein is applicable to free vibration of annular plates continuous over ring supports or internal point supports. 本文基于Ｍｉｎｄｌｉｎ中厚板理论，给出了域内设有多道同心环向支承时中厚环板弯曲振动分析的一种有效方法。位移函数采用带补充项的幂级数，并以环板内外边界广义位移作为基本未知量。域内环支条件则通过拉氏乘子法予以处理，适于具有同心环支及点支环板的振动分析。
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