Vibrations suppression of fractionally damped plates using multiple optimal dynamic vibration absorbers

ABSTRACT

The vibration suppression of fractionally damped thin rectangular plates is studied. The plate has simply supported edges and is subjected to a concentrated harmonic loading. The vibration suppression is accomplished by attaching multiple fractionally damped absorbers in order to minimize the plate deflection at the natural frequencies of the plate. First, the governing equations are derived and solved analytically in Laplace domain. Next, the solution in time domain is derived analytically by contour integration and also numerically via Fixed-Talbot method and are compared with each other. The formulation of the problem is capable of optimizing the $L_2$ norm of the plate deflection at the wide frequency band with respect to mass, stiffness, and fractional damping parameters.

KEYWORDS:

• Dynamic vibration absorber
• L_2· norm
• contour integration
• fixed-Talbot method

2010 AMS SUBJECT CLASSIFICATIONS:

• 70Q05
• 70J35
• 35Q74
• 26A33
• 34A08

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The third author was supported by the US AFOSR Young Investigator Award FA9550-17-1-0150 and partially by the US MURI/ARO award W911NF-15-1-0562.