任意边界板结构的声辐射模态误差传感器的设计

获取声辐射模态伴随系数是基于声辐射模态理论进行主动结构声控制(ASAC)的重要环节。以往PVDF分布式传感器的设计难点是振速展开受边界条件的限制,其设计过程往往是针对特定边界条件展开的。本文在声辐射模态理论和两维分布式传感器的压电方程的基础上,将板表面振速分布用Legendre多项式展开,给出了两维板结构的PVDF传感器形状与边界条件无关的设计方法。这样设计得到的传感器能应用于任意边界条件和任意振速分布的两维板结构,且实时性好,拓宽了其应用范围。本文还分别以固定边界条件板及在该板中任取一小区域两种情况为例,证明了该设计方法的可行性。

Design of a radiation-mode error sensor for plate with arbitrary boundary condition

To obtain the adjoint coefficients of the radiation modes is an important step in ASAC system which is based on the theory of radiation modes. Previous difficulty in designing PVDF sensors was that the velocity expression is restricted by the boundary conditions, and that the sesors were designed under the special boundary conditions. This paper presents a new method, which is based on the theories of radiation modes and the piezoelectric equations, using Legendre polynomials to express the velocity distribution, to design the PVDF sensor for two-dimensional structure. The PVDF sensor designed by this method can be used to measure the adjoint coefficients of radiation modes for two-dimensional plate structures with arbitrary boundary conditions, and has good real-time quality. For either a clamped plate or part of a clamped plate, the first adjoint coefficients of radiation modes can be measured. By numerical calculation, the outputs of the PVDF sensor are compared with the theoretical values, and the results demonstrate the feasibility of this method.