Global-local approach to the design of dynamic vibration absorber for damped structures

The dynamic vibration absorber (DVA) has attracted attention since its invention. This paper deals with the optimization problems of the standard DVA and two other models of DVA called three-element DVA and non-traditional DVA for damped primary structures. Unlike the standard configuration, the three-element DVA contains two spring elements in which one is connected to a dashpot in a series and the other is placed in parallel. Meanwhile the non-traditional DVA has a linear viscous damper connecting the absorber mass directly to the ground. There have been some studies on the design of three-element and non-traditional dynamic vibration absorbers in the case of undamped primary structures. These studies have shown that both three-element and non-traditional DVAs perform better than the standard DVA. When the primary structure is damped, there are very few studies on the three-element and non-traditional DVAs in the literature. This article proposes a global-local approach to give approximate analytical solutions of the H ∞ optimization for all standard, three-element and non-traditional DVAs attached to damped primary structures. The main idea of the study is based on the global-local criterion of the equivalent linearization method in order to replace approximately the original damped structure by an equivalent undamped one. Afterwards, the already derived expressions of the optimal parameters for the undamped primary system case are used with the equivalent undamped structure that was just obtained. The numerical simulations are carried out to verify the effectiveness of the obtained results. Additionally, design aids, which show the variation of the optimal design quantities for various DVA mass ratios and inherent structural damping ratios are also provided.

[1]  Yozo Fujino,et al.  Design formulas for tuned mass dampers based on a perturbation technique , 1993 .

[2]  S. E. Randall,et al.  Optimum Vibration Absorbers for Linear Damped Systems , 1981 .

[3]  Biswajit Basu,et al.  A closed‐form optimal tuning criterion for TMD in damped structures , 2007 .

[4]  A. Baz,et al.  Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems , 2002 .

[5]  P E.,et al.  AN APPLICATION OF CHEBYSHEV’S MIN-MAX CRITERION TO THE OPTIMAL DESIGN OF A DAMPED DYNAMIC VIBRATION ABSORBER , 1997 .

[6]  Omer F. Tigli.  Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads , 2012 .

[7]  G. B. Warburton,et al.  Optimum absorber parameters for various combinations of response and excitation parameters , 1982 .

[8]  Osamu Nishihara,et al.  H2 optimization of three-element type dynamic vibration absorbers , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[9]  Toshihiko Asami,et al.  Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model , 1999 .

[10]  Tarunraj Singh,et al.  Minimax design of vibration absorbers for linear damped systems , 2011 .

[11]  Nd Anh,et al.  Design of non-traditional dynamic vibration absorber for damped linear structures , 2014 .

[12]  T K Gaughey.  Response of Van Der Pol ' s Oscillator to Random Excitation , .

[13]  Liang Liao,et al.  APPLICATION OF A TUNABLE ELECTROMAGNETIC DAMPER IN SUPPRESSION OF STRUCTURAL VIBRATION , 2006 .

[14]  Waion Wong,et al.  Optimal design of a damped dynamic vibration absorber for vibration control of structure excited by ground motion , 2008 .

[15]  Kefu Liu,et al.  The damped dynamic vibration absorbers: revisited and new result , 2005 .

[16]  Thomas K. Caughey,et al.  Random Excitation of a System With Bilinear Hysteresis , 1960 .

[17]  Y. Cheung,et al.  Design of a non-traditional dynamic vibration absorber. , 2009, The Journal of the Acoustical Society of America.

[18]  Hideya Yamaguchi,et al.  Damping of transient vibration by a dynamic absorber. , 1988 .

[19]  W. D. Mark,et al.  Random Vibration in Mechanical Systems , 1963 .

[20]  Waion Wong,et al.  H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results , 2011 .

[21]  T. Asami,et al.  H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers , 2002 .

[22]  Waion Wong,et al.  H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation , 2011 .

[23]  A. G. Thompson,et al.  Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system , 1981 .

[24]  Nguyen Dong Anh,et al.  Dual approach to local mean square error criterion for stochastic equivalent linearization , 2013 .

[25]  Nicolai Minorsky,et al.  Introduction to non-linear mechanics : topological methods, analytical methods, nonlinear resonance, relaxation oscillations , 1947 .

[26]  Toshihiko Asami,et al.  Optimum Design of Dynamic Absorbers for a System Subjected to Random Excitation , 1991 .

[27]  Toshihiro Ioi,et al.  On the Dynamic Vibration Damped Absorber of the Vibration System , 1977 .

[28]  Ettore Pennestrì.  AN APPLICATION OF CHEBYSHEV'S MIN–MAX CRITERION TO THE OPTIMAL DESIGN OF A DAMPED DYNAMIC VIBRATION ABSORBER , 1998 .

[29]  Kefu Liu,et al.  OPTIMAL DESIGN OF DAMPED DYNAMIC VIBRATION ABSORBER FOR DAMPED PRIMARY SYSTEMS , 2010 .

[30]  N. D. Anh,et al.  Design of three-element dynamic vibration absorber for damped linear structures , 2013 .

[31]  N. D. Anh,et al.  Extension of equivalent linearization method to design of TMD for linear damped systems , 2012 .

[32]  M. Ren.  A VARIANT DESIGN OF THE DYNAMIC VIBRATION ABSORBER , 2001 .

[33]  J. Ormondroyd.  Theory of the Dynamic Vibration Absorber , 1928 .

[34]  S. Choura,et al.  Vibration confinement and energy harvesting in flexible structures using collocated absorbers and piezoelectric devices , 2010 .

[35]  Toshihiko Asami,et al.  Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors) , 2002 .