An analytical investigation of the active control of the transmission of sound through plates
An analytical investigation of the active control of the transmission of sound through plates
复制标题
板声传播主动控制的分析研究
DOI：
10.1006/jsvi.1995.0155
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发表时间：
1995
影响因子：
4.7
通讯作者：
S. J. Elliott
中科院分区：
文献类型：
--
作者：
D. Thomas;P. Nelson;R. Pinnington;S. J. Elliott
摘要利用振动板的分析模型，探讨了通过对板的振动进行主动控制来减少谐声传播的控制机理。板振动的一般模型(以前由Berrite al.)将板的边界条件模拟为板边缘的可变转动和平移弹性约束。给出了问题的变分形式，并用Rayleigh-Ritz方法导出了板的运动方程。同时考虑了边固定的弹性板和边自由的刚性板。对于刚性壁板，如果使用三个控制致动器(每个刚体模式一个)，或者将壁板的运动限制为沿垂直于壁板的轴的活塞式平移，则可以获得较大的传声衰减。对于弹性板，观察到两种控制机制：“振型控制”和“振型重排”，“振型控制”是指控制声辐射的那些振型的幅值减小；“振型重排”是指调整板振型的相对幅值和相位，以产生低辐射效率的振动分布。后一种机制被证明是微妙的(通常涉及很小的振型幅度变化和板的整体振动幅度的很小变化)和非常有效的(在大多数频率下占辐射声衰减的很大比例)。对于感兴趣的频率范围(0.92小于2.75)，如果二次力的数目和位置选择正确，则传输的声音总是可以实现较大的衰减。模拟还证实了“溢出”现象，即在引入控制后，低效率的辐射板模式被强烈激励，从而导致板振动的整体增加。
Abstract An analytical model of a vibrating plate is used to explore the mechanisms of control involved in the reduction of harmonic sound transmission through the active control of plate vibration. A general model of the plate vibrations (previously used by Berryet al.) is presented, with the boundary conditions of the plate being modelled as variable rotational and translational elastic restraints at the edges of the plate. A variational formulation of the problem is presented and the equation of motion of the plate is derived by using a Rayleigh-Ritz method. Both an elastic plate with clamped edges and a rigid panel with free edges are considered. For the rigid panel it is found that large attenuations in transmitted sound can be obtained if either three control actuators are used (one for each rigid body mode) or the motion of the panel is restricted to piston type translation along an axis perpendicular to the panel. For the elastic plate two mechanisms of control are observed: “modal control” where the amplitudes of those modes which dominate sound radiation are reduced, and “modal rearrangement” where the relative amplitudes and phases of plate modes are adjusted to produce a vibration distribution of low radiation efficiency. The latter mechanism is shown to be both subtle (often involving little change in mode amplitudes and little change in the overall vibration amplitude of the plate) and very effective (accounting for a large proportion of the attenuations in radiated sound at most frequencies). For the frequency range of interest (0.92 less thankaless than 2.75) large attenuations in the transmitted sound could always be achieved if the number and positioning of the secondary forces is correctly chosen. The simulations also demonstrate the phenomenon of “spill-over”, where inefficiently radiating plate modes are strongly excited with the introduction of control often resulting in an overall increase in the plate vibration.