Affiliations: Department of Mechanical Engineering, Shijiazhuang
Tiedao University, Shijiazhuang, Hebei, China | Center for Vehicle Systems and Safety, Department of
Mechanical Engineering, Virginia Polytechnic Institute and State University,
Blacksburg, VA, USA
Note: [] Corresponding author: Yongjun Shen, Department of Mechanical
Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, Hebei, China.
E-mail: shenyongjun@126.com
Abstract: In this paper four semi-active dynamic vibration absorbers (DVAs)
are analytically studied, where the time delay induced by measurement and
execution in control procedure is included in the system. The first-order
approximate analytical solutions of the four semi-active DVAs are established
by the averaging method, based on the illustrated phase difference of the
motion parameters. The comparisons between the analytical and the numerical
solutions are carried out, which verify the correctness and satisfactory
precision of the approximate analytical solutions. Then the effects of the time
delay on the dynamical responses are analyzed, and it is found that the
stability conditions for the steady-state responses of the primary systems are
all periodic functions of time delay, with the same period as the excitation
one. At last the effects of time delay on control performance are discussed.
Keywords: Dynamic vibration absorber, averaging method, time delay, nonlinear dynamics
