Vibration Analysis of the Structure Exposed to Multidimensional Base Excitation

本研究探讨基底激振结构动力特性的方向性。结构经常在任意方向上经受基础激励，即，地震或环境激励。重要的是要知道如何响应的变化取决于输入方向，在哪个方向上的响应最大。首先，本研究调查的方向特性的模态响应的结构。引入了模态主轴（MPA），它给出了使模态响应最大化的方向。将固有模态视为单自由度系统具有一定方向的MPA，当基底沿着MPA方向受激时，系统响应达到最大。如果基地是正常的MPA兴奋，响应为零。证明了在自然模态下，结构的重心沿着MP轴移动。其次，引入响应主轴，给出了在给定输入下，结构总响应最大的方向。结构的响应通常由几个模态响应的叠加给出，除了当输入频率与固有模态的共振频率一致时的情况。在已知输入信号功率谱的情况下，通过响应主轴确定使总响应最大的输入方向。再次，研究了梁结构的方向特性。利用三轴振动台对结构的基本模态进行了实验检测。假设输入为任意正弦波，也可以确定RPA。计算结果表明，本文所提出的方法对基底激励下的结构设计是有效的。

This study explores the directional property of dynamic characteristics of the base-excited structures. Structures often undergoes the base excitation in an arbitrary direction, i.e., earthquakes or ambient excitations. It is important to know how the response changes depending on the input direction and in which direction the response goes to maximum.Firstly this study investigates the directional properties of modal response of the structure. Modal Principal Axis (MPA) is introduced which gives the direction maximizing the modal response. The natural mode is regarded as the SDOF system having a certain direction called MPA.If the base is excited along with MPA, the response goes to maximum. And if the base is excited normal to MPA, the response goes to zero. It is proved that the Center of Gravity moves along with the MP axis at the natura1 mode.Secondly Response Principal Axis is introduced which gives the direction maximizing the total response of the structure for the given input. The response of the structure is generally given by superposition of several modal responses except the case when the input frequency coincides the resonant frequency of a natural mode. If the power spectrum of the input signal is given, the input direction maximizing the total response is detected by the response principal axis.Thirdly the directional properties of a beam structure is investigated. The MPAs corresponding to the fundamental natural modes are detected experimentally by using the three axial vibration table. The RPA is also determined assuming the input as an arbitrary sinusoidal wave. It is confirmed that the presented approaches are effective to design the structures exposed to the base excitation.