Favorable locations for piezo actuators in plates with good control effectiveness and minimal change in system dynamics

Abstract

Placement and sizing of piezo actuators is normally based on control effectiveness. However, retrofitting of piezoelectric actuators alters the inherent stiffness/mass properties of the parent structure. In rotating structures, the additional mass due to piezo patches contributes to the centrifugal stiffening force. The parent structure is originally designed to have a certain natural frequency spectrum in relation to the disturbance excitation. In the event of failure of the active system, the dynamics of the structure with piezos (now rendered passive) will therefore become significant. Thus it will be helpful to determine locations for mounting piezo patches based on minimal natural frequency change yet with good control authority. In this study, a finite element based procedure for plate structures is presented. Favorable locations for mounting piezos based on minimal natural frequency changes are iteratively evolved from an initial configuration wherein the whole plate is covered with piezos. A modal controllability approach has been used for finding piezo mounting locations from a good controllability perspective. The procedure is demonstrated for simply supported square, swept-back, circular and rotating rectangular plates considering the first four modes.

Optimal piezoelectric control of a plate subject to time-dependent boundary moments and forcing function for vibration damping

“…(41) into Eq. (19), multiplying both sides with Φ n (x), Υ m (y) and integrating on S lead to the following lumped parameter system (LPS) in timë…”

“…The adjoint variable v(x, y, t) satisfies the following equation (19) subject to the boundary conditions…”

“…(40), we need to evaluate v • (x, y, t) in Eq. (19) that requires the solution of the optimal state function w • of Eqs. (12)- (16) subject to the mixed terminal conditions Eq.…”

“…In these studies several aspects of piezoelectric control have been studied including feedback control [14], constraints on control voltage [15], and open-loop control [17]. Optimal placement of patch actuators to improve control has been the subject of [18][19][20]. Numerical solutions of the active piezoelectric control problems have been obtained using finite element formulations in [21][22][23].…”

“…-(16) and the adjoint variable v • (x, y, t) = v(x, y, t; V • e ) satisfies Eq (19),. boundary conditions Eq (20).…”