Vibration Analysis of the Structure Exposed to Multidimensional Base Excitation

本研究探讨了基激结构动力特性的方向性。结构通常在任意方向上受到基础激励，即地震或环境激励。了解响应如何随输入方向变化以及响应在哪个方向达到最大值是很重要的。本文首先研究了结构模态响应的方向性。引入模态主轴（MPA），给出了模态响应最大化的方向。将自然模态视为具有一定方向的SDOF系统，称为MPA。当基底随MPA受激时，响应最大。如果碱的激励法向于MPA，响应趋于零。证明了在自然模式下，重心沿MP轴运动。其次，引入了响应主轴，给出了给定输入下结构总响应的最大方向。除了输入频率与固有模态谐振频率重合的情况外，结构的响应一般由几个模态响应的叠加给出。如果输入信号的功率谱是给定的，则由响应主轴检测最大总响应的输入方向。第三，研究了梁结构的方向性。利用三轴振动台对基本固有模态对应的MPAs进行了实验检测。假设输入为任意正弦波，也可以确定RPA。结果表明，所提出的方法对基础激励下结构的设计是有效的。

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.