压电式模态传感器的研究

Design and implementation of piezoelectric modal sensors for active noise and vibration control (ANVC) system has been a subject of intense interest for many years.There are two broad ways to design piezoelectric modal sensors: (a) continuous shaped sensor and (b) array of piezoelectric patch. Using piezoelectric modal sensors in active control improves the stability of the closed-loop system and reduces the problem of control spillover. However, most current published research on piezoelectric modal sensors has been limited to those involving simple structures with classical boundary conditions and relies on precise knowledge of the boundary conditions of the structures. The main objective of this project is to find an asymptotic solution to the problem of the design of piezoelectric modal sensor for general structures under arbitrary boundary conditions by combining a theoretical analytical approach with an experimental approach. The output signal of the designed modal sensor can measure either the response of the selected structural mode for active vibration control (AVC) system or the radiation mode for active structural acoustic control (ASAC) system and filter out the responses of the other modes. .The main research work and the key issues of this project are as follows: First, a relatively new mathematical approach called the Adomian decomposition method (ADM) is introduced to establish a general theoretical model to accurately describe the behaviour of piezoelectric modal sensors. The perforance of the proposed piezoelectric modal sensor will be analyzed and discussed in detail. Second, using a distributed piezoelectric array, the curvature mode properties of the vibrating structure is directly determined based on an experimental methodology. Then a general expression for designing of the piezoelectric modal sensor will be derived without any structural boundary condition information by imposing pseudo-inverse method and using measured curvature mode shape. Third, based on modal filtering approach, an online and real-time sensor self-diagnostics method is proposed to monitor sensor faults for piezoelectric array modal sensor. Final, the proposed piezoelectric modal sensors will be demonstrated on the beam-like, plate-like and double plate structures, respectively.

压电式模态传感器（包括特定形状的模态传感器和阵列式模态传感器）的设计是当前噪声与振动主动控制领域的研究热点。通过压电式模态传感器可以有效防止控制溢出、提高控制系统的稳定性。针对目前研究主要集中在经典边界条件下的简单结构、需要预知精确的边界条件等不足。本项目拟通过解析法结合实验方法建立一般工程结构在任意边界条件下压电式模态传感器的通用设计模型，并分别设计用于振动控制的结构模态传感器和用于结构声控制的声辐射模态传感器。主要研究内容：1通过现代数学方法Adomian分解法建立压电式模态传感器的理论模型，并对模态传感器物理参数进行性能分析；2通过压电传感阵列基于实验方法直接提取结构的曲率模态信息，并结合伪逆方法建立未知边界条件下模态传感器的设计理论；3基于模态滤波方法，探讨阵列式压电式模态传感器在线实时自我诊断功能的实现；4通过梁、平板、双层板结构设计压电式模态传感器的试验模型，进行验证试验。

噪声与振动主动控制技术（Active Noise and Vibration Control, ANVC）是声学与振动领域长期研究的课题。ANVC系统中的一个基本问题就是设计恰当的传感器输出误差信号，压电式模态传感器（包括特定形状的模态传感器和阵列式模态传感器）的设计是当前噪声与振动主动控制领域的研究热点。通过压电式模态传感器可以有效防止控制溢出、提高控制系统的稳定性。项目以此为背景，分别通过Adomian分解法、伪逆方法结合实验方法建立一般工程结构在任意边界条件下压电式模态传感器的通用设计模型。并分别设计用于振动控制的结构模态传感器和用于结构声控制的声辐射模态传感器。开展研究包括：.（1）通过Adomian分解法建立压电式模态传感器的理论模型。该模型可用于变截面梁在任意边界条件下的模态传感器设计。并对Adomian分解法提出了一种修正方法，并对该修正方法在不同振动和声学问题上的适用性进行了深入分析，并研究其收敛性和计算精度等问题。通过数值计算可以发现，Adomian修正方法具有计算方法简便、快捷，具有良好的收敛性。并且在求解过程中不需要进行离散化。.（2）建立了基于伪逆方法结合Tikhonov正则化方法的阵列式PVDF压电模态传感器设计理论，该方法的主要优点在于不需要预先获知结构模态信息和边界条件，并可用于任意梁、板结构。并通过数值分析和实验验证了该方法的可行性和有效性，同时发现其测量结果对于结构边界条件的微小扰动具有一定的稳定性。.（3）为了进一步简化模态传感器的设计，提出一种新的阵列式压电传感器的设计方法，即直接将利用PVDF阵列进行实验模态分析得到的曲率模态作为加权系数，对振动结构进行模态滤波。实验研究结果表明：该方法操作简单，模态滤波效果良好。.（4）压电薄膜反复变形出现的连接不牢或损伤等因素都会造成传感器输出信号出现较大偏差，所以，本项目对阵列式压电模态传感器的故障诊断问题也进行了研究，基于模态滤波理论，引入平均误差向量曲率的平方作为诊断参数，数值计算和实验结果表明：该方法不仅可以对故障进行有效定位识别，而且直接通过时域信号进行模态传感器的故障诊断，可用于在线实时检测。.通过上述研究工作，进一步拓展了模态传感器的设计理论，为任意边界条件下梁板结构模态传感器的设计提供了一种有效的分析设计手段，所得研究结果有助于进一步设计更加简单高效的ANVC系统。