A Combined Static/Dynamic Technique for Damage Detection of Laminated Composite Plates

There is a growing demand to develop viable techniques for effective damage detection of composite structures, and the dynamics-based approach has been broadly used in structural health monitoring. A new combined static/dynamic technique for improved damage detection of laminated composite plates is presented. The promise of the technique is that under the sustaining static load, the abnormality of dynamic response due to damage may become more pronounced and easy to be detected. The experimental program consists of testing an E-glass/epoxy composite plate with an embedded delamination under a pre-set static compressive force, and the dynamic response of laminated composite plates is measured using two different actuator–sensor systems: (1) PZT (lead–zirconate–titanate) actuators and scanning laser vibrometer (SLV) sensing system (PZT–SLV), and (2) PZT actuators and Polyvinylidenefluoride (PVDF) sensors (PZT–PVDF). The influence of sustaining static forces to dynamic response of delaminated composite plates is evaluated. The numerical finite element (FE) analysis is also conducted to verify the effectiveness of this technique. The experimental and numerical mode shapes are used to detect the presence, location, and size of the delamination and to study the effect of static load on dynamic response. Two relatively new damage detection algorithms (i.e., Simplified Gapped Smoothing Method (GSM) and Generalized Fractal Dimension (GFD)) are employed to analyze the Uniform Load Surface (ULS) calculated from the experimental and numerical data. From the dynamic response and analysis results using the damage detection algorithms, it is observed that as the sustaining static load increases, the delamination is much easier to be identified through the enlarged damage parameters. The present combined static/dynamic technique is capable of magnifying the effect of damage, thus improving the effectiveness of damage detection.     

A Motion Amplifier Using an Axially Driven Buckling Beam: I. Design and Experiments

For active materials such as piezoelectric stacks, which produce large force and small displacement, motion amplification mechanisms are often necessary – not simply to trade force for displacement, but to increase the output work transferred through a compliant structure. Here, a new concept for obtaining large rotations from small linear displacements produced by a piezoelectric stack is proposed and analyzed. The concept uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. The optimal design of the buckling beam end conditions was determined from a static analysis of the system using Euler's elastica theory. This analysis was verified experimentally. A stack-driven, buckling beam prototype actuator consisting of a pre-compressed PZT stack (140 mm long, 10 mm diameter) and a thin steel beam (60 mm× 12 mm× 0.508 mm) was constructed. The buckling beam served as the motion amplifier, while the PZT stack provided the actuation. The experimental setup, measuring instrumentation and method, the beam pre-loading condition, and the excitation are fully described in the paper. Frequency responses of the system for three pre-loading levels and three stack driving amplitudes were obtained. A maximum 16^∘ peak-to-peak rotation was measured when the stack was driven at an amplitude of 325 V and frequency of 39 Hz. The effects of beam pre-load were also studied.     

Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method

The literature regarding the free vibration analysis of Bernoulli–Euler and Timoshenko beams under various supporting conditions is plenty, but the free vibration analysis of Reddy–Bickford beams with variable cross-section on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded and semi-rigid connected Reddy–Bickford beam with variable cross-section on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton’s principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of semi-rigid connected Reddy–Bickford beam with variable cross-section on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed.     

The pre-stack migration imaging technique for damages identification in concrete structures

Pre-stack migration imaging (PMI) method, which is used in geophysical exploration by the performance of single side detection and visually display, can be used to identify the location, orientation, and severity of damages in concrete structure. In particular, this letter focuses on the experimental study by using a finite number of sensors for further practical applications. A concrete structure with a surface-mounted linear PZT transducers array is illustrated. Three types of damages, horizontal, dipping and V-shaped crack damage, have been studied. A pre-stack reverse time migration technique is used to back-propagate the scattering waves and to image damages in concrete structure. The migration results from the scattering waves of an artificial damage are presented. It is shown that the existence of the damage in concrete structure is correctly revealed through migration process.     

阶梯压电层合梁的波动动力学特性

采用行波理论系统地研究了压电阶梯梁的自由振动分析以及强迫响应的分析方法. 基于分布 参数理论研究了压电阶梯梁的波传播特性，忽略柔性梁横向剪切和转动惯量的影响，给出了 梁的轴向和横向的简谐波解. 将压电阶梯梁离散化为单元，考虑压电片的刚度和质量的影响， 建立了节点散射模型. 应用位移连续和力平衡条件，推导了节点的波反射和波传递矩阵，在 此基础上，引入波循环矩阵的概念，给出波循环矩阵、波传递系数矩阵的确定方法. 应用波 循环矩阵可以有效地计算结构的固有频率. 另外，应用波传递系数研究了压电陶瓷作动器位 置对其驱动能力的影响. 得出两个主要结论：1)作动器靠近悬臂梁固定端将有较强的驱动 能力，悬臂梁边界反射行波产生弯曲消失波有利于增大压电波的模态传递系数；2)模态传 递系数与固有频率的灵敏度密切相关，波传递系数越大, 对应该处固有频率变化灵敏度越大. 另外，数值算例表明了行波方法比有限元方法具有更高的计算精度.     

Generalized-order perturbation with explicit coefficient for damage detection of modular beam

A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed. In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile, for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster to the termination criterion.     

Condition monitoring of bones using piezo-transducers

This paper explores the feasibility of employing piezoelectric ceramic (PZT) patches as bio-medical sensors for monitoring condition of bones, through experimental studies on human and rabbit bones. Conductance signatures of PZT patches bonded to bones are acquired using the electro-mechanical impedance (EMI) technique, while the bones are subjected to varying conditions such as and density changes, occurrence of cracks and fracturing. The changes in the signature correlate fairly well with the changes in the condition of the bones. Finally, the effect of healing process is experimentally simulated on rabbit bones, which showed that the conductance signature of the bones shifted back towards the original state after rejoining. The overall results of the study demonstrate good prospects of using PZT patches as bio-medical sensors.     

Thermal reliability testing of functionally gradient materials using thermal shock method

We found a solution of an unsteady two-dimensional heat conduction equation in a functionally gradient material (FGM) which is subjected to a double thermal shock, namely, a local heating of a specimen by a power laser beam and cooling of a heated surface by a water-air spray. We developed an analytical method whereby a coating is described as a laminated plate composed of n layers with the constant material properties within a layer. Temperature distribution in a nonhomogeneous laminated plate is obtained in a form of series using the Laplace–Hankel integral transforms. In order to extend the model of a laminated plate to describe FGM where thermal physical characteristics are continuous functions of spatial coordinate, we considered the limiting case of the obtained temperature distribution when the thickness of the layer iΔ _i → 0, and the number of layers n→∞. This allowed us to obtain the temperature distribution in an easy-to-use analytical form which can be used for determining thermal stresses in FGM. The dependence of the temperature distribution in FGM on the operating parameters of a double thermal shock method, e.g., a duration of heating, laser beam radius, the rate of a spray cooling, is discussed. Received on 3 May 1999     

An experimental technique to measure projectile deceleration history during normal penetration into plain concrete

The present paper presents a new experimental method to measure the deceleration time history of projectiles penetrating into concrete in full-size test. The experiment can be carried out by using an onboard accelerometer to measure the projectile deceleration history and the data are transmitted to a ground recording system. With this experimental method, a series of tests on hemisphere-nose steel projectiles penetrating normally into plain concrete at the velocity region 150–400 m/s have been executed and the deceleration histories obtained. The high frequency portion in the deceleration data has been investigated and proved to be the structure response of projectile. The characteristics of deceleration history have also been analyzed and discussed.     

A Motion Amplifier Using an Axially Driven Buckling Beam: II. Modeling and Analysis

In this paper, the nonlinear behavior of a motion amplifier used to obtain large rotations from small linear displacements produced by a piezoelectric stack is studied. The motion amplifier uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. Since the amplifier is driving a large rotary inertia at the pinned end and the operational frequency is low compared to the resonant frequencies of the beam, the mass of the buckling beam and the dynamics of the PZT stack are neglected and the system is modeled as a single-degree-of-freedom, nonlinear system. The beam simply behaves as a nonlinear rotational spring having a prescribed displacement on the input end and a moment produced by the inertial mass acting on the output end. The moment applied to the mass is then a function of the beam end displacement and the mass rotation. The system can, thus, be modeled simply as a base-excited, spring–mass oscillator. Results of the response for an ideal beam using this reduced-order model agree with the experimental data to a high degree. Inclusion of loading and geometric imperfections show that the response is not particularly sensitive to these imperfections. Parameter studies for the ideal buckling beam amplifier were conducted to provide guidance for improving the design of the motion amplifier and finding the optimal operating conditions for different applications. An erratum to this article can be found at