三維剛架結構之迴傳波射動力分析

Abstract

本文承襲Pao、Howard和Keh等人的研究成果，以彈性波理論為基礎，分析結構構件中的軸向波、扭轉波和撓曲波等三種應力波，依應力波之傳播、折射和反射追蹤計算波形之變化，將到達觀測點之所有波形疊加，求出結構之動態反應，稱為迴傳波射法。文中特別針對結構構件各種邊界條件之處理加以說明，並詳述計算三維空間構架動態歷時反應之數值方法。此外，並由就物理上的觀點，探討入射波和出射波之因果關係，並修正了理論公式的誤差。目前迴傳波射法的理論發展已臻完整，此一概念若應用於結構靜力分析時，則稱之為迴傳矩陣靜力分析，其逐次疊加之過程即相當於彎矩分配法。

This study follows the previous research of Pao, Howard and Keh, to analyze the stress waves of axial, torsional, and bending waves propagating in structural members, based on the theory of elastic waves. The overall transient response of the structure at any observing point can be obtained by superposing the arriving waves via scattering, refraction and reflection traced in time. This process is referred to as the method of reverberation-ray. In this thesis, treatments of various boundary conditions of the structural members are presented in details, along with the numerical procedure for dynamic analysis of 3-D space frame. Moreover, the causality between the arrival and departure waves is explored, and the previous derived formula is modified accordingly for improved accuracy. Theoretical development of the method of reverberation-ray has been completed. Similar technique has been developed for static analysis of structures and referred to as the method of reverberation matrix. The process of summing the solutions term by term is physically equivalent to the classical moment distribution method.