多板結構耦合系統的振動特性與暫態波傳之理論解析及數值計算

Theoretical Analysis and Numerical Calculation on Vibration Characteristics and Transient Wave Propagation of Structure for Multiple Plate Coupled System

顏貞卿(Chen-Chin Yan)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202202685

摘要

本研究結合理論分析和有限元素數值計算分析等向性矩形薄板、L型薄板與長方體薄殼腔體之穩態振動與暫態波傳問題。
自由振動分析以古典薄板理論為基礎，由能量的觀點以哈密頓原理與變分法推導出薄板的運動方程式及邊界條件，並以矩形薄板運動特性將振動行為區分為彎曲振動與伸展振動為主導之振動問題。首先透過疊加法分別求解薄板彎曲振動與伸展振動之共振頻率與模態振型，進而針對多板耦合振動問題作解析，利用耦合條件連接兩組相互垂直的矩形薄板，考慮不同平板間面內與面外物理場量之交互影響，以疊加法求解L型薄板與長方體薄殼腔體之自由振動問題，探討不同邊界情況下L型薄板三維模態振型並分析其主導特性，以及分析不同長度之長方體薄殼腔體對於振動特性之影響。
結構件承受動態負載的暫態分析，則以模態疊加法將結構的暫態位移以時間函數與模態形狀之空間函數的組合來呈現，以此連接結構之穩態振動問題與暫態波傳問題，使得問題的解析更具物理意義。本文考慮結構承受動態負載以面外單點撞擊與面外單點週期外力激振的強迫振動兩大類，分別用於解析結構暫態波傳與強迫振動問題，並採用疊加法求得的穩態振動模態振型對L型薄板與長方體薄殼腔體之暫態問題進行解析，探討動態負載施加於不同位置對多板耦合結構動態特性之影響。

關鍵字

暫態波傳 ； 振動 ； L型薄板 ； 薄殼腔體 ； 疊加法 ； 模態展開法

並列摘要

This study uses theoretical analysis and finite element method to analyze the vibration and transient behavior of an isotropic rectangular plate, an L-joint, and a thin-walled container.
The Kirchhoff-Love assumption and Hamilton's principle are used to derive the equations of motion and boundary conditions for free vibration problem. The problem is solved analytically using the superposition method for free vibation of a rectangular plate. The solution to the free vibration issue of the rectangular plate provides flexural and extensional dominated vibrations. The continuity conditions at the common edge of the plates are explored to investigate the resonant frequencies and associated mode shapes of the L-joint and thin-walled container. The superposition method is used to provide solutions for L-joints with different boundary conditions and thin-walled containers with varying lengths.
The normal mode method is performed as a method for calculating the transient response of an L-joint and a thin-walled container. The transient displacement solution is a product of the time function and mode shape. The superposition method is used to derive the modes and associated natural frequencies of the plate assembly. The dynamic point load is considered for imapct force and periodic force in order to analyze the wave propagation and forced vibration problem.

並列關鍵字

wave propagation ； vibration ； L-joint ； thin-walled container ； superposition method ； normal mode expansion

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