A novel method is proposed to obtain the optimum configuration of dynamic vibration absorber (i.e., DVA) attached to an undamped or damped primary structure. The performance index, i.e., the quadratic integration, includes two types of controls, i.e., velocity and displacement controls of the primary mass. Based on the Lyapunov equation, the performance indices are simplified into matrix quadratic forms. With the help of the Kronecker product and matrix column expansion, the closed-form solutions of optimum parameters for undamped primary structure are finally presented. Moreover, in some cases, the method can produce perturbation solutions in simple forms for damped primary structure. Especially, from these solutions, the classical optimum designs under external force or base acceleration excitation can be derived out.
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October 2008
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Analytical Solutions for DVA Optimization Based on the Lyapunov Equation
Dong Du
Dong Du
251 HuaNing Road,
e-mail: wideface@sjtu.edu.cn, doodon@163.com
MinHang District
, Shanghai City, People's Republic of China
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Dong Du
251 HuaNing Road,
MinHang District
, Shanghai City, People's Republic of Chinae-mail: wideface@sjtu.edu.cn, doodon@163.com
J. Vib. Acoust. Oct 2008, 130(5): 054501 (10 pages)
Published Online: August 12, 2008
Article history
Received:
June 27, 2006
Revised:
April 13, 2008
Published:
August 12, 2008
Citation
Du, D. (August 12, 2008). "Analytical Solutions for DVA Optimization Based on the Lyapunov Equation." ASME. J. Vib. Acoust. October 2008; 130(5): 054501. https://doi.org/10.1115/1.2948373
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