New Eigenvalue Criteria for Structural Optimization For Harmonic Loading

题目：New Eigenvalue Criteria for Structural Optimization For  Harmonic Loading

报告人：Bo Ping Wang教授

美国德州大学艾灵顿分校机械与航空工程系（Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, USA）

时间： 2018年6月21日，上午 10:00                            

地点：综合1号实验楼602 

摘要：

In structural dynamics, it is well known that resonance frequencies in forced harmonic response of an undamped structure are related to the eigenvalue for free vibration problem. These resonance frequencies are the peaks in the frequency response plots. In a recent  paper, it is shown that the frequencies for the valleys (lowest points in vibration amplitude) in the frequency response plot can also be computed by solving eigenvalue problems associated with the forced harmonic response of the system.  When the minimum response is zero, the corresponding frequencies are the well-known antiresonsnt frequencies. Otherwise, these are minimum response frequency between two resonances.  Using the eigenvalue formulation, the sensitivities of the antiresonant or minimum response frequency can be readily computed using eigenvalue sensitivity results for general non-symmetrical matrices. In this paper, these new eigenvalues will be used in the objective or constraints in structural optimization under harmonic loading. This is achieved by tailoring the structure so that minimum response or antiresonsnt frequencyoccurs at the specified forcing frequency. Detailed formulations will be presented in the paper. Several beam problem will be use to illustrate the general formulations.