梁振动控制中压电作动器的位置优化准则

Optimal Placement Criterion of the Piezoelectric Actuators for Vibration Control of Beams

以输入的控制信号能量最小为目标,提出了梁结构振动控制中压电作动器的位置优化准则,基于压电片层合简支弹性梁的模态振动方程,给出了反映各压电作动器上控制电压与模态控制力之间关系的控制电压影响系数的表达式;详细推导了控制信号能量的表达式,并根据控制能量最小的准则对压电作动器的位置进行优化.数值分析中,对梁结构的振动控制过程进行系统仿真,比较了相同衰减时间下压电作动器位于梁表面不同位置时系统输入能量的大小.数值模拟所得的最优位置与理论结果非常吻合,验证了该准则的正确性.

Based on the object of minimizing the control energy, a criterion for the optimal placement of piezoelectric actuators patched on beams was proposed. The modal equation of vibration for a simply-supported elastic beam was established and the control voltage coefficient was presented, which reflects the relationship between the control voltage and the modal force in the actuators. Moreover, the expression of the control energy was derived. According to the energy criterion, the locations of the piezoelectric actuators were optimized. In the numerical analysis, the process of the vibration control of beams was simulated. With the same attenuation time and the actuators on various locations of the beams, the magnitudes of the controls energy of the system were compared with each other. The criterion was validated by the consistence of the numerical results and the theoretical ones.