Study On The Electro-mechanical Characteristics Of The Piezoelectric-actuated Non-cracked And Cracked Beams

The existence and the growing of cracks in structures will undoubtedly affect the structural safety in use. It is necessary to take the structural health monitoring, especially for the important structures. Piezoelectric materials can be used as the active sensors for the online health monitoring of structures by means of their piezoelectric properities. However, the effect of cracks on the electric impedance of the active sensors is unclear at present. Therefore, it is valuable that the further studies on the electro-mechanical coupling behaviors between piezoelectric elements and non-cracked or cracked structures should be done. In this dissertation, the electro-mechanical characteristics of piezoelectric-driven non-cracked or cracked beams are systematically investigated by using proposed analytical approach, FEM and experimental method. The achievements of the present study are as follows:(1)Based on the impedance method and the equivalent electric circuit method, an analytical method called finite impedance elements method is proposed to analyze the dynamics of a straight beam actuated simultaneously by the piezoelectric stacks and the piezoelectric patches. Three types of beam segments including piezoelectric sandwich segments, elastic beam segments and the piezoelectric stacks are all regarded as different impedance elements, these impedance elements are used to analyze the composite beam. The physical fields can be obtained by solving the linear impedance equations of all impedance elements in the system. The results on the dynamical response of these smart structures are compared with the results calculated by impedance method or FEM. The comparisons show the developed method is efficient to analyze the electro-mechanical behaviors of these structures. The method improves the impedance method and the equivalent circuit method on the scopes of their application.(2)For a piezoelectric sandwich with nonconductive middle elastic layer, a 5×5 equivalent impedance matrix representing the dynamics of the sandwich is derived. Then, an electric impedance function of a cracked beam with piezoelectric actuators is built. The effect of the open cracks and other system parameters on the electric impedance of the system may be analyzed by using the impedance function. Further, the experiment on the electric impedance of the cracked beam system is conducted, the different depth and location of the crack and the different types of the crack are considered. Some important characteristics shown from both the theoretical results and the experimental results are as follows: for a single-edge or double-edge crack, as the crack is located at the node point the displacement mode of the undamaged beam, the frequency of the system corresponding to the mode almost keeps unchanged as the crack depth increases, other mode frequencies decrease gradually. However, as a crack is located at the anti-node point of the displacement mode, the descent amplitude of the corresponding mode frequency is bigger than that of the closest two modes. These characteristics may be taken as the reference of the crack detection in straight beam by using active piezoelectric sensors.(3)Based on the small curvature beam theory and the equivalent single-layer approach, the governing equation of a circular piezoelectric sandwich beam is derived. Consequently, a 7×7 equivalent impedance matrix representing the dynamics of the sandwich is given. Based on finite impedance elements method, the electro-mechanical behaviors of the piezoelectric-driven circular ring or beam is analyze analytically by using the sandwich impedance elements and the elastic impedance elements. In numerical examples, the results of the dynamical responses of different types of smart structures are compared with the results obtained from FEM or the known experimental results. The agreement among these results shows that the developed approach well describes the dynamics of the piezoelectric-driven beam or ring. Compared with the impedance method and the static approach, both the effect of the inertia, the rigidity and the curvature of the piezoelectric elements and the different types of smart curved beam may be considered by the present approach.(4)The static responses of piezo-driven circular beam are studied in the dissertation. Firstly, the static governing equations of circular unimorph beam and bimorph beam are derived. Then, the explicit expressions of the displacement responses are given for the cantilever sandwich beam and the cantilever segmented beam with distribute actuators. The present results of the displacement responses are validated by the results obtained from FEM. The agreement between these results shows the accuracy of the modeling and these explicit expressions. In the parameters studies of the segmented beam, it is found that the change trends of the radial displacement responses seriously depend on the central angles representing the actuator location and the beam length. In the study of the displacement control by using piezoelectric elements, as the radial displacement response at the free end of a cantilever sandwich is controlled to zero, it is found that the peak control voltage and the negative control voltage will occur with the changes of the load location and the beam length. The developed method and the obtained analytical expressions may be directly used as the reference of the design and the control of curved smart structures.(5)For a cracked circular beam with symmetric actuators, the continuous conditions at the interface of the open crack are derived. Based on the dynamics of the piezoelectric-driven beam, the electric impedance function of the damaged system is built by using the similar process to analyze of the cracked straight beam with actuators. The effect of the depth and the location of the crack on the electric impedance is investigated by the present method and the FEM. The following important characteristics are obtained by the present analysis: as the crack is located at the node point of the displacement mode of the undamaged beam, the frequency of the damaged system changes little as the crack depth increases, other mode frequencies decrease; Howerer, as the crack is located at the anti-node of the mode, the corresponding mode frequency seriously decreases. For the given crack depth, as the crack is close gradually to the anti-node point of the mode, the descent amplitude of the corresponding frequency increases; As the crack is close gradually to the node point of the mode, the descent amplitude of the corresponding frequency decreases. These characteristics may be taken as the reference of crack detection in curved beam by active piezoelectric sensors.