Vibration Mode Localization in Two-Dimensional Systems

AIAA Journal ◽  
10.2514/2.5 ◽  
1997 ◽  
Vol 35 (10) ◽  
pp. 1653-1659 ◽  
Author(s):  
Wei-Chau Xie ◽  
Xing Wang
Keyword(s):  
Vibration Mode ◽  
Two Dimensional ◽  
Mode Localization

Vibration mode localization in two-dimensional systems

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1653-1659 ◽  
Author(s):  
Wei-Chau Xie ◽  
Xing Wang
Keyword(s):  
Vibration Mode ◽  
Two Dimensional ◽  
Mode Localization

Vibration Mode Localization in Randomly Disordered Weakly Coupled Two-Dimensional Systems

1997 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Eigenvalue Problems ◽  
Vibration Mode ◽  
Numerical Approach ◽  
Logarithmic Scale ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Exponential Rates ◽  
Rates Of Decay

Abstract In this paper, a general method of regular perturbation for linear eigenvalue problems is presented, in which the orders of perturbation terms are extended to infinity. The method of regular perturbation is applied to study vibration mode localization in randomly disordered weakly coupled two-dimensional cantilever-spring arrays. Localization factors, which characterize the average exponential rates of decay or growth of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factors are obtained using a combined analytical-numerical approach. For the systems under consideration, the direction in which vibration is originated corresponds to the smallest localization factor; whereas the “diagonal” directions correspond to the largest rate of decay or growth of the amplitudes of vibration. When plotted in the logarithmic scale, the vibration modes are of a hill shape with the amplitudes of vibration decaying linearly away from the cantilever at which vibration is originated.

A New Mistuning Form in Periodic Structure - Force Mistuning

2012 ◽  
Vol 562-564 ◽  
pp. 2092-2096 ◽  
Author(s):  
Guo Hui Yang ◽  
Ai Lun Wang ◽  
Xu Hui Cao
Keyword(s):  
Periodic Structure ◽  
Vibration Mode ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
Engineering Practice ◽  
Characteristic Vibration ◽  
Natural Parameter ◽  
Mode Localization ◽  
Vibration Localization ◽  
Natural Characteristic

The mistuning of periodic structure was generally considered to be natural parameter mistuning, such as stiffness mistuning, damping mistuning and mass mistuning. However, in engineering practice, there was another kind of mistuning——force mistuning, which has not been studied yet. Based on a typical concentrated parameter model of periodic structure, the vibration characteristics, such as natural characteristic, vibration mode and vibration localization of periodic structure with different mistuning forms, were compared and analyzed. The results show that, as a new mistuning form, force mistuning won’t bring mode localization, while it could lead to vibration response localization

A New Mistuning Form Existed in Periodic Structure-Force Mistuning

2012 ◽  
Vol 229-231 ◽  
pp. 377-381
Author(s):  
Ai Lun Wang ◽  
Jie Chen ◽  
Qian Jin Wang
Keyword(s):  
Periodic Structure ◽  
Vibration Mode ◽  
Structure Design ◽  
Engineering Practice ◽  
Characteristic Vibration ◽  
Natural Parameter ◽  
Mode Localization ◽  
Vibration Localization ◽  
Natural Characteristic ◽  
Design And Manufacture

The mistuning of periodic structure was generally considered to be natural parameter mistuning, such as stiffness mistuning, damping mistuning and mass mistuning. However, in engineering practice, there was another kind of mistuning—force mistuning. Based on a typical concentrated parameter model of periodic structure, the vibration characteristics, such as natural characteristic, vibration mode and vibration localization of periodic structure with different mistuning forms, were compared and analyzed. The results show that, as a new mistuning form, force mistuning won’t bring mode localization, while it could lead to vibration response localization. The results are very important for periodic structure design and manufacture.

A Two-Dimensional Ultrasonically Assisted Grinding Technique for High Efficiency Machining of Sapphire Substrate

2009 ◽  
Vol 626-627 ◽  
pp. 35-40 ◽  
Author(s):  
Z. Liang ◽  
Yong Bo Wu ◽  
Xin Bing Wang ◽  
Y. Peng ◽  
Wei Xing Xu ◽  
...  
Keyword(s):  
Ultrasonic Vibration ◽  
Sapphire Substrate ◽  
High Efficiency ◽  
Vibration Mode ◽  
Two Dimensional ◽  
Grinding Forces ◽  
Work Surface ◽  
Conventional Grinding ◽  
Grinding Technique ◽  
Ultrasonic Vibration Assisted Grinding

This paper discusses the feasibility of improving machining efficiency of sapphire substrate by using two-dimensional (2D) ultrasonic vibration assisted grinding. An elliptic ultrasonic vibrator is designed and produced by bonding a piezoelectric ceramic device (PZT) on a metal elastic body (stainless steel, SUS304). The sapphire substrate is fixed onto the top face of the vibrator and ultrasonically vibrates in 2D vibration mode when the PZT is excited by two alternating current voltages with a phase difference. A grinding apparatus mainly composed of the ultrasonic vibrator is constructed, and experiments are performed with lateral modulation of elliptic ultrasonic vibration vertical to the grinding direction. Both the grinding forces and the ground work surface are measured and examined. Experimental results show that the grinding force decreases significantly and the resulted surface is improved in certain degree with the ultrasonic vibration compared to those of conventional grinding without ultrasonication. This indicates that the high efficiency grinding for sapphire substrate can be performed with the two-dimensional vibration grinding technique presented in this paper.

Mode Localization Phenomena in Nearly Periodic Systems

1995 ◽  
Vol 62 (1) ◽  
pp. 141-149 ◽  
Author(s):  
C. W. Cai ◽  
Y. K. Cheung ◽  
H. C. Chan
Keyword(s):  
Normal Mode ◽  
Three Dimensional ◽  
Degree Of Freedom ◽  
Three Dimensions ◽  
Periodic Systems ◽  
Two Dimensional ◽  
Transformation Technique ◽  
Mode Localization

The normal mode localization in nearly periodic systems with one-degree-of-freedom subsystems and a single subsystem departing from the regularity in one, two, and three dimensions has been studied. The closed-frequency equations may be derived by using the U-transformation technique. It is shown that in one- and two-dimensional problems any amount of simple disorder (for stiffness or mass), however small, is sufficient to localize one mode and in three-dimensional systems, a finite threshold of disorder is needed in order to localize one mode. These conclusions are in agreement with those predicted by Hodges.

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