TY - RPRT

T1 - Nontrivial effects of high-frequency excitation for strongly damped mechanical systems

AU - Fidlin, Alexander

AU - Thomsen, Jon Juel

PY - 2007

Y1 - 2007

N2 - Some nontrivial effects are investigated, which can occur if strongly damped mechanical systems are subjected to strong high-frequency (HF) excitation. The main result is a theoretical prediction, supported by numerical simulation, that for such systems the (quasi-)equilibrium states can change substantially with the level of damping. For example, a strongly damped pendulum, with a hinge vibrated at high frequency along an elliptical path with horizontal or vertical axis, will line up along a line offset from the vertical; the offset vanishes for very light or very strong damping, attaining a maximum that can be substantial (depending on the strength of the HF excitation) for finite values of the damping. The analysis is focused on the differences between the classic results for weakly damped systems, and new effects for which the strong damping terms are responsible. The analysis is based on a slightly modified averaging technique, and includes an elementary example of an elliptically excited pendulum for illustration, alongside with a generalization to a broader class of strongly damped dynamical systems with HF excitation. As an application example, the nontrivial behavior of a classical optimally controlled nonlinear system is investigated, illustrating how HF excitation may cause the controller to leave the system in an unexpected equilibrium state, quite different from the setpoint. The effects can be interesting for specialists in control of mechanical systems and structures. However the obtained results are more general. Similar effects could be expected first of all for microsystems where damping forces are typically dominating over inertia forces.

AB - Some nontrivial effects are investigated, which can occur if strongly damped mechanical systems are subjected to strong high-frequency (HF) excitation. The main result is a theoretical prediction, supported by numerical simulation, that for such systems the (quasi-)equilibrium states can change substantially with the level of damping. For example, a strongly damped pendulum, with a hinge vibrated at high frequency along an elliptical path with horizontal or vertical axis, will line up along a line offset from the vertical; the offset vanishes for very light or very strong damping, attaining a maximum that can be substantial (depending on the strength of the HF excitation) for finite values of the damping. The analysis is focused on the differences between the classic results for weakly damped systems, and new effects for which the strong damping terms are responsible. The analysis is based on a slightly modified averaging technique, and includes an elementary example of an elliptically excited pendulum for illustration, alongside with a generalization to a broader class of strongly damped dynamical systems with HF excitation. As an application example, the nontrivial behavior of a classical optimally controlled nonlinear system is investigated, illustrating how HF excitation may cause the controller to leave the system in an unexpected equilibrium state, quite different from the setpoint. The effects can be interesting for specialists in control of mechanical systems and structures. However the obtained results are more general. Similar effects could be expected first of all for microsystems where damping forces are typically dominating over inertia forces.

KW - control

KW - vibrations

KW - effective properties

KW - high-frequency

M3 - Report

T3 - DCAMM Report

BT - Nontrivial effects of high-frequency excitation for strongly damped mechanical systems

PB - Technical University of Denmark

CY - Kgs. Lyngby, Copenhagen

ER -