基于电阻抗单元的含裂纹智能梁的动态特性

Dynamic analysis of impedance element-based smart crack beams actuated by distributed piezoelectric actuators

分析了受一对分布式双压电片激励产生弯曲的含裂纹智能梁的动态特性.智能梁被划分为有限个电阻抗单元,在这些单元中包括双压电晶片梁阻抗单元和弹性梁阻抗单元,分别用一个5×5和4×4的阻抗矩阵表示.基于阻抗单元间和裂纹处的连续条件以及智能梁的边界条件,求解线性阻抗方程,建立起裂纹参数及其他系统参数和压电片输入导纳间的关系,并方便地得到含裂纹智能梁受压电片激励的动态特性.通过数值算例,分别对含单边和双边对称裂纹的智能梁的动态特性进行了讨论,并与已知实验比较,比较的结果说明了分析方法是有效的.

The smart beams, with cracks driven by a pair of distributed bi-piezoelectric actuators, were analyzed dynamically. The beams were divided into finite impedance elements, consisting of two typical impedance elements, impedance elements of bi-piezoelectric crystals and impedance ones of elastic beams expressed by 4 × 4 and 5 ×5 impedance matrix respectively. Considering the continuum conditions between impedance elements, the continuum conditions at the location of cracks represented by massless spring and mechanical boundary conditions, the relation between the input electric admittance of piezoelectric patches and the crack parameters is built by solving these elements＇ linear impedance equations, also the electromechanical dynamic characteristic of cracked smart beam is obtained conveniently. In the numerical examples, the dynamic analysis of smart beam containing single-edge and double-edge open crack is given to illustrate the appllcanon of tins moaelmg metnoa oy assemunng the two different impedance elements. The obtained resonant frequencies of cracked beam agree with the results of other methods and known experiment results. It is found that the dynamic analysis of cracked beam based on impedance elements yields an efficient expression for the vibration of the cracked smart beam.