压电激励的无损及裂纹梁系统的力电特性研究
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摘要
结构中裂纹的存在及其不断的扩展,对结构安全性构成了重大的威胁。利用主动式压电传感器的力电转换特性,将其集成在结构中,可以进行结构在线健康监测。然而,结构中的裂纹对压电传感器的电阻抗的影响规律尚不十分清楚。因此,开展压电单元激励的完整或含裂纹结构的力电特性的深入研究,具有重要的理论和实际应用价值。本文主要采用解析的分析方法,并结合有限元方法和实验研究方法,系统研究压电单元与无损梁或裂纹梁的相互作用,分析梁系统的力电特性。获得的主要研究成果有:
(1)在阻抗法和等效电路法的基础上,提出有限阻抗单元法,将其应用于梁形压电智能结构的解析分析。用本文方法计算智能梁的动态响应,并将计算结果与用阻抗法得到的结果或有限元结果比较,表明了本文方法可以有效描述压电片和压电柱激励的直梁系统的力电动态特性,拓展了阻抗法和等效电路法的应用范围。
(2)基于有限阻抗单元法和裂纹的等效弹簧模型,导出了压电激励的含裂纹的梁系统的压电阻抗函数,并据此分析了裂纹及其他参数对系统电阻抗的影响。然后,通过实验研究了不同裂纹深度、不同裂纹位置以及不同的裂纹形式等对梁系统的电阻抗的影响规律。分析与实验结果均表明:对于单边或双边对称裂纹,当裂纹位于梁的某阶位移模态节点上时,尽管裂纹深度不断增加,这阶模态的频率并不发生变化,而其他阶数的模态的频率会逐渐减小;当裂纹位于梁的某阶位移模态反节点上时,随着裂纹深度的增加,比较于前后相邻的两个模态的频率,此阶模态的频率明显减少。以上研究为利用主动式压电传感器进行直梁结构损伤监测提供了理论参考。
(3)基于小曲率曲梁理论和等效单层方式,建立了压电层对称布置的夹层圆形曲梁的动态控制方程,得到了代表夹层梁动态特性的7×7等效阻抗矩阵。将智能直梁中的有限阻抗单元法拓展到智能曲梁中,用有限个夹层梁阻抗单元和弹性梁阻抗单元来分析压电驱动的圆形曲梁或圆环的动态力电特性。用本文方法计算圆形曲梁或圆环智能结构的动态响应,并将计算结果与有限元结果或已有的实验结果进行比较,表明了本文方法可以有效分析对称压电单元驱动的圆形曲梁或圆环的动态特性。比较于早期的两种解析方法-阻抗法和静态模型,此方法不仅可以考虑压电单元惯性、刚度和曲率,而且可以分析多种智能曲梁结构。
(4)针对压电片的单面非对称和双面对称两种布置方式,提出用于分析压电单元激励的圆形曲梁的静态响应的解析方法。首先建立了相应的压电夹层梁的静态控制方程,然后导出夹层悬臂梁和带分布式压电单元的节式悬臂梁径向位移响应的解析表达式。采用本文方法计算出的智能梁的移移响应与有限元结果吻合,表明了本文提出的方法的合理性和导出的解析表达式的正确性。以圆形曲梁静态响应分析为基础,进一步进行了参数研究和位移控制研究。对压电单元相关参数的研究显示:对于节式悬臂梁,自由端径向位移响应与梁长所对应的圆心角和标识激励器位置的圆心角密切相关。梁的圆心角的临界值仅取决于给定的激励器的圆心角大小。对悬臂式夹层梁位移控制研究表明:当控制悬臂夹层梁的自由端径向位移响应为零时,随着集中力载荷的位置变化和梁长的变化,最优控制电压将出现峰值和反号。以上研究为智能曲结构设计和控制提供了直接的参考。
(5)基于压电驱动的圆形曲梁的动态分析,导出了压电激励的含裂纹的曲梁系统的电阻抗函数,并据此分析了不同裂纹深度以及不同裂纹位置对系统电阻抗的影响,得到与前述含裂纹直梁基本一致的规律。以上研究为利用主动式压电传感器进行曲梁结构损伤监测提供了的理论参考。
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.
(1)在阻抗法和等效电路法的基础上,提出有限阻抗单元法,将其应用于梁形压电智能结构的解析分析。用本文方法计算智能梁的动态响应,并将计算结果与用阻抗法得到的结果或有限元结果比较,表明了本文方法可以有效描述压电片和压电柱激励的直梁系统的力电动态特性,拓展了阻抗法和等效电路法的应用范围。
(2)基于有限阻抗单元法和裂纹的等效弹簧模型,导出了压电激励的含裂纹的梁系统的压电阻抗函数,并据此分析了裂纹及其他参数对系统电阻抗的影响。然后,通过实验研究了不同裂纹深度、不同裂纹位置以及不同的裂纹形式等对梁系统的电阻抗的影响规律。分析与实验结果均表明:对于单边或双边对称裂纹,当裂纹位于梁的某阶位移模态节点上时,尽管裂纹深度不断增加,这阶模态的频率并不发生变化,而其他阶数的模态的频率会逐渐减小;当裂纹位于梁的某阶位移模态反节点上时,随着裂纹深度的增加,比较于前后相邻的两个模态的频率,此阶模态的频率明显减少。以上研究为利用主动式压电传感器进行直梁结构损伤监测提供了理论参考。
(3)基于小曲率曲梁理论和等效单层方式,建立了压电层对称布置的夹层圆形曲梁的动态控制方程,得到了代表夹层梁动态特性的7×7等效阻抗矩阵。将智能直梁中的有限阻抗单元法拓展到智能曲梁中,用有限个夹层梁阻抗单元和弹性梁阻抗单元来分析压电驱动的圆形曲梁或圆环的动态力电特性。用本文方法计算圆形曲梁或圆环智能结构的动态响应,并将计算结果与有限元结果或已有的实验结果进行比较,表明了本文方法可以有效分析对称压电单元驱动的圆形曲梁或圆环的动态特性。比较于早期的两种解析方法-阻抗法和静态模型,此方法不仅可以考虑压电单元惯性、刚度和曲率,而且可以分析多种智能曲梁结构。
(4)针对压电片的单面非对称和双面对称两种布置方式,提出用于分析压电单元激励的圆形曲梁的静态响应的解析方法。首先建立了相应的压电夹层梁的静态控制方程,然后导出夹层悬臂梁和带分布式压电单元的节式悬臂梁径向位移响应的解析表达式。采用本文方法计算出的智能梁的移移响应与有限元结果吻合,表明了本文提出的方法的合理性和导出的解析表达式的正确性。以圆形曲梁静态响应分析为基础,进一步进行了参数研究和位移控制研究。对压电单元相关参数的研究显示:对于节式悬臂梁,自由端径向位移响应与梁长所对应的圆心角和标识激励器位置的圆心角密切相关。梁的圆心角的临界值仅取决于给定的激励器的圆心角大小。对悬臂式夹层梁位移控制研究表明:当控制悬臂夹层梁的自由端径向位移响应为零时,随着集中力载荷的位置变化和梁长的变化,最优控制电压将出现峰值和反号。以上研究为智能曲结构设计和控制提供了直接的参考。
(5)基于压电驱动的圆形曲梁的动态分析,导出了压电激励的含裂纹的曲梁系统的电阻抗函数,并据此分析了不同裂纹深度以及不同裂纹位置对系统电阻抗的影响,得到与前述含裂纹直梁基本一致的规律。以上研究为利用主动式压电传感器进行曲梁结构损伤监测提供了的理论参考。
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.
引文
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