摘 要

本研究采用构建连续条件的方法根据轴的轴向振动运动方程，设其方程解并进行简化变换，通过一般求解方法得到含实常数参数的方程完全解，构建矩阵运算求解力的分布变化并研究螺旋桨处激励对于艉轴的振动影响。采用解析波传播和数值搜索的方法对柱壳结构进行分析，比较轴对称激励主要激起的振动。采用幂级数法构建连续条件求解锥壳在不同激励下的振动特性。之后通过三角变换建立轴，锥壳，柱壳耦合的连续条件，对组合体进行振动分析，以求得不同激励下轴系纵向振动对于潜艇振动的影响。以上连续条件的构建主要包含对微元模块两端的位移，斜率，剪力和弯矩。

本研究主要采用解析法，通过数值模拟和矩阵运算，利用matlab软件对耦合结构进行简化分析，为降低潜艇辐射噪声提供理论依据。

关键词：轴壳耦合振动；解析波法；构建矩阵计算

Abstract

In this study, the continuous condition method is used to construct the complete solution of the equation with real constant parameters according to the axially vibrating motion equation of the shaft. The matrix operation is used to solve the force distribution and the influence of the excitation at the propeller on the vibration of the stern shaft.Analytical wave propagation and numerical search methods are used to analyze the cylindrical shell structure, and the main vibration induced by axisymmetric excitation is compared. The power series method is used to construct continuous conditions to solve the vibration characteristics of conical shells under different excitations.Then, the continuous coupling conditions of axle, conical shell and cylindrical shell are established by triangular transformation, and the vibration analysis of the composite body is carried out to obtain the influence of the longitudinal vibration of the shafting system on the submarine vibration under different excitations. The construction of the above continuous conditions mainly includes the displacement, slope, shear force and bending moment at both ends of the micro-element module.

In this study, the analytical method is used to simplify the analysis of the coupled structure through numerical simulation and matrix operation, and the MATLAB software is used to provide theoretical basis for reducing the radiated noise of submarines.

Key Words:Coupled vibration of axle-shell; Method of Analytic wave; Construction Matrix Computing.

目录

第1章绪论.......................................................................................................................................................1

1.1研究意义与背景..................................................................................................................................1

1.1.1研究意义.......................................................................................................................................1

1.1.2研究背景.......................................................................................................................................1

1.2国内外研究现状.........................................................................................................................................2

1.2.1研究现状.......................................................................................................................................2

1.2.2轴的振动分析..............................................................................................................................2

1.2.3圆柱壳的运动分析.....................................................................................................................2

1.2.4轴壳耦合结构的分析................................................................................................................2

第二章轴-旋转壳子系统理论建模研究...................................................................................................4

2.1轴的振动理论.......................................................................................................................................4

2.1.1轴的横向振动...............................................................................................................................4

2.1.2轴的纵向振动...............................................................................................................................6

2.2柱壳的振动...................................................... .....................................................................................8

2.3锥壳的振动..........................................................................................................................................10

2.4耦合振动...............................................................................................................................................14

2.4.1锥柱组合壳的耦合....................................................................................................................14

2.4.2轴与组合壳的横向耦合...........................................................................................................15

2.4.3轴与组合壳的纵向耦合...........................................................................................................16

第三章轴-旋转壳耦合系统理论建模计算.............................................................................................17

3.1模型构建及参数确定........................................................................................................................17

3.2连续条件，边界条件及激励.............................................................................................................18

3.2.1轴的工况分析.............................................................................................................................18

3.2.2壳的工况分析.............................................................................................................................19

3.3矩阵构建...............................................................................................................................................22

3.3.1轴的矩阵......................................................................................................................................22