Three-dimensional analysis of an antiparallel piezoelectric bimorph

Summary Three-dimensional electromechanical responses of a piezoelectric bimorph are studied. The bimorph is antiparallel in the sense that it consists of two identical, plate-like piezoelectric elements with opposite poling directions. Both the top and bottom surfaces of the bimorph are fully covered with negligibly thin conductive electrodes. By introducing a small parameter and using the transfer matrix method it is shown that a three-dimensional solution of the problem can be readily constructed, provided the solution to a set of two-dimensional equations very similar to those in the classic plate theory is obtainable. The three-dimensional solution satisfies all the field equations as well as the boundary conditions on the major surfaces and at the interface between the two piezoelectric plates. In many special cases, the electric edge condition can be fulfilled point by point, and thus the solution is exact in Saint-Venant's sense. The formulation and new analytical results for a strip-shaped cantilever bimorph under the action of applied voltage and end moment are presented.     

Flexural strength and cracking behavior of hybrid strength concrete beams

The flexural and cracking behavior of hybrid strength concrete beams cast with two concrete compressive strengths of 20 and 70 MPa were compared with 20 MPa normal and 70 MPa high strength beams. The hybrid beams showed an improvement in the load carrying capacity at cracking, yielding and ultimate loading as compared to normal strength beams. The increase in load carrying capacity was (1.80–70.8%) higher than normal strength beams and only (3.3–9.8%) lower than corresponding high compressive strength beams. Also from experimental results the crack spacing of hybrid beams were between those of normal strength and high strength beams, but the crack width in the hybrid beams were narrower than both types of beams at all loading stages. At service and ultimate loading stages, the crack width in the hybrid beams were 19.5–26.0% narrower than those of corresponding normal strength beams, and 9.2–15.1% narrower than high strength beams.     

Flexural behavior of reinforced concrete beams with cementitious repair materials

There is an urgent need to develop efficient methods for the repairs and rehabilitation of currently existing structures, they are being deteriorated over time, and also the magnitude of loadings keeps rapidly increasing for such structures. Possibly one of the most challenging taks in the rehabilitation processes is to upgrade the overall capacity of deteriorated concrete structures. Recently, considerable efforts are being directed toward developing new construction materials. This paper presents the experimental study for the flexural behavior of reinforced concrete beams repaired by Polymer Cement Mortar (PCM) and Ordinary Portland Cement Mortar (OPCM) in the tension region. Tests were performed for eight reinforced concrete beams with varying reinforcement ratios, repair materials and repair lengths. Emphasis is given to overall bending capacity, deflection, ductility index, failure mode and crack development of repaired beams. The results are compared with those from the control beam.

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Résumé Il est urgent de développer une méthode efficace pour le renforcement et la réparation afin de remettre en état la structure dont le fonctionnement est dégradé en raison de l'accroissement de la charge ou de l'écoulement du temps. Au cours du processus de renforcement, un des paramètres les plus importants est d'améliorer la performance globale des structures en béton endommagées. La tendance d'aujourd'hui est de développer un nouveau matériau. Dans cet article sont menées des études expérimentales sur la flexion de poutres en béton armé réparées ou renforcées avec du mortier de ciment polymère (MCP) et du mortier de ciment portland ordinaire (MCPO) repectivement. Pour des essais, 8 échantillons d'essais ont été fabriqués en variant le rapport d'armature, le matériau de réparation, ainsi que la longueur à réparer, avant de faire les essais. Les résultats confirment: la capacité de la flexion, une flèche, un indice de la ductilité, une rupture apparente, la forme de la fissure des poutres réparées. Et ces résultats ont été comparés avec celui de l'échantillon de référence.

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Dynamic behavior of cross-ply laminated beams with piezoelectric layers

The dynamic behavior of cross-ply non-symmetric composite beams, having uniform piezoelectric layers is analysed. A first-order Timoshenko type analysis is applied to obtain the equations of motion, which include shear deformation, rotary inertia, bending-stretching coupling terms and induced axial strains caused by the piezoelectric material. Using the principle of virtual work, the coupled equations of motion and the relevant boundary conditions are obtained. For a laminated beam having uniform piezoelectric layers the induced strains appear only in the boundary conditions yielding time dependent ones. Therefore, a special procedure involving orthogonality of the coupled Timoshenko type natural vibrational modes of the beam is applied to help understanding of the dynamic behavior of the non-symmetric laminated beam and to investigate the influence of the induced strains (by the piezoelectric layers) on the dynamic behavior while keeping an ‘open-loop’ control. Typical types of laminates and piezoelectric materials are used to calculate natural frequencies and mode shapes. Numerical results for various parameters of laminated beams are presented to stress the better applicability and suitability of the present approach to the analysis of dynamic behavior of laminated composite beams with piezoelectric layers.     

Flexural vibration of a lithium niobate piezoelectric plate with a ferroelectric inversion layer

Abstract

Two-dimensional equations for flexural motions of a lithium niobate piezoelectric plate are derived from three-dimensional equations. The plate has a ferroelectric inversion layer where the piezoelectric constants reverse signs. The equations show an unconventional behavior that a uniform electric field along the plate thickness can produce bending. This offers many possibilities for new designs of devices. Waves in unbounded plates are examined for the accuracy of the equations. A piezoelectric energy harvester based on such a plate is analyzed as an example of the application of the equations derived in vibrations of finite plates.     

Flexural behavior of reinforced recycled aggregate concrete beams under short-term loading

Recycling of waste concrete is one of the sustainable solutions for the growing waste disposal crisis and depletion of natural aggregate sources. As a result, recycled concrete aggregate (RCA) is produced, and so far it has mostly been used in low-value applications such as for the pavement base. But, from the standpoint of promoting resource and energy savings and environmental preservation, it is essential to study whether a concrete made of recycled aggregates—recycled aggregate concrete (RAC) can be effectively used as a structural material. The experimental research presented in this paper is performed in order to investigate the flexural behavior of RAC beams when compared to the behavior of natural aggregate concrete (NAC) beams under short-term loading and consequently the possibility of using RAC in structural concrete elements. Three different percentages of coarse RCA in total mass of coarse aggregate in concrete mixtures (0 %—NAC, 50 %—RAC50, and 100 %—RAC100), and three different reinforcement ratios (0.28, 1.46, and 2.54 %) were the governing parameters in this investigation. Full-scale tests were performed on nine simply supported beams until the failure load had been reached. Comparison of load-deflection behavior, crack patterns, service deflections, failure modes and ultimate flexural capacity of NAC and RAC beams was made based on our own and other researchers’ test results. The results of conducted analysis showed that the flexural behavior of RAC beams is satisfactory comparing to the behavior of NAC beams, for both the service and ultimate loading. It is concluded that, within the limits of this research, the use of RAC in reinforced concrete beams is technically feasible.     

氯盐环境下锈蚀预应力混凝土梁抗弯性能试验

为探讨氯盐环境下锈蚀预应力混凝土梁的抗弯性能,制作了5根先张预应力混凝土梁,采用电化学法分别对其进行了0 d、7 d、14 d、28 d及42 d的快速腐蚀,随后进行了四点弯曲试验。研究了不同锈蚀程度对预应力混凝土梁自振频率、钢绞线滑移、结构变形、弯曲开裂、破坏模式及极限承载力等性能的影响。结果表明:氯盐环境下锈蚀对预应力混凝土梁高阶频率影响较小,导致一阶频率逐渐增大,28 d后锈蚀裂缝较大且局部混凝土脱落,一阶频率迅速减小;轻微腐蚀对预应力混凝土梁的抗弯性能影响较小,腐蚀程度增大,抗弯性能明显降低,腐蚀42 d后,极限挠度减小了18.7%,抗弯承载力减小了17.3%,延性降低了19%;锈蚀钢绞线与混凝土间滑移速率增大,极限滑移值由5 μm增加至11.4 μm;钢筋锈蚀对弯曲裂缝高度发展的影响不大,但促进了裂缝宽度的扩展,结构屈服后,底部裂缝开裂速率由0.0062 mm/kN增加至0.0252 mm/kN。在试验研究基础上,采用有限元软件ANSYS对各锈蚀梁的受载全过程进行了有限元模拟计算,极限荷载和钢绞线滑移量的模拟值与实测值误差分别小于5%和10%,吻合较好。      

Performance improvement of a piezoelectric bimorph actuator by tailoring geometry

This article illustrates performance improvement of a piezo-bimorph actuator by tailoring its geometry. We have analytically presented that a piezo-bimorph actuator with a tapered surface provides superior performance for out-of-plane bending compared to a rectangular surface while having equal mass and equal primary capacitance. Equal capacitance ensures equal input electrical energy and bandwidth for both the cases below its first resonant frequency. We have analytically derived performance measuring attributes of such an actuator considering high electric field, and shown the performance improvement quantitatively. We have also presented finite element solutions to compare with the analytical solutions. Some results are validated with the earlier published experimental results.     

Vibrations and static responses of asymmetric bimorph disks of piezoelectric ceramics

In an earlier article, the flexural vibrations in bimorph disks and extensional vibrations in homogeneous disks of piezoelectric ceramics were studied. In the present paper, the coupled flexural and extensional vibrations and static responses in an asymmetric bimorph disk, which is formed by bonding together two piezoelectric ceramic disks of unequal thickness and opposite polarization, are investigated. Governing equations of coupled motions for asymmetric bimorphs are deduced from the recently derived 2-D, first-order equations for piezoelectric crystal plates with thickness-graded material properties. Then, closed form solutions of these equations for circular disks are obtained for free vibrations, piezoelectrically forced vibrations, and responses under static voltage difference. Resonance frequencies, distribution of displacements and surface charges, impedances, and static responses are calculated for asymmetric bimorph disks of various thickness ratios and diameter-to-thickness ratios. Experimental data on resonances and impedances are obtained for asymmetric bimorph disks of PZT-857 for different thickness ratios. Comparisons of predicted and measured results show that the agreements are close.     

Flexural behavior of plain concrete beams strengthened with ultra high toughness cementitious composites layer

Ultra high toughness cementitious composites (UHTCC), which has metal-like deformation and crack width restricting ability, is expected to be utilized as retrofit materials. For this application, much attention needs to be paid to the working performance of structure members composed of UHTCC and existing concrete. This paper presents an investigation on the flexural behavior of plain concrete beams strengthened with UHTCC layer in tension face. The effect of UHTCC layer thicknesses on first crack load, ultimate flexural load, crack width, and load–deflection relationship is examined. The experimental results indicate that the use of UHTCC layer significantly increases the first crack load and ultimate flexural load. The first crack load and ultimate flexural load of composites beams increased with the increase of the UHTCC layer thickness. Considerable reduction in crack width was observed for composite specimens, as UHTCC layer restricted the cracks in upper concrete and dispersed them into multiple fine cracks effectively. Moreover, in comparison to plain concrete beam, composite beams could sustain the loading at a larger deflection without failure. Based on the plane section assumption, etc., a calculation method to predict the flexural capacity of composite beam was proposed. Good agreement between predictions and experiments had been obtained.     

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.     

Flexural performance of FRP reinforced concrete beams

A numerical method for estimating the curvature, deflection and moment capacity of FRP reinforced concrete beams is developed. Force equilibrium and strain compatibility equations for a beam section divided into a number of segments are numerically solved due to the non-linear behaviour of concrete. The deflection is then obtained from the flexural rigidity at mid-span section using the deflection formula for various load cases. A proposed modification to the mid-span flexural rigidity is also introduced to account for the experimentally observed wide cracks over the intermediate support of continuous FRP reinforced concrete beams.     

Flexural behaviour of strengthened reinforced concrete beams

A large experimental research programme has investigated the flexural strength of simply supported reinforced concrete beams. The beams were first damaged so that they could be strengthened by means of jackets (cast-in-place shotcrete or pre-packed special mortar plus additional new reinforcement). This paper analyses the flexural strength of these beams. The behaviour in service and ultimate state as well as the bond characteristics are studied.

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Résumé Au cours d'un vaste programme expérimental, on a étudié la résistance en flexion de poutres en béton armé à appui simple. Ces poutres ont d'abord été endommagées, pour ensuite être renforcées par du béton projeté ou par du mortier spécial préconditionné, avec l'adjonction de nouvelles armatures. Cet article discute de la résistance en flexion de ces poutres. Le comportement en service et à l'état limite ultime, ainsi que les caractéristiques d'adhérence, sont étudiés.

     

Shear piezoelectric vibration pickups

On the basis of unified theoretical considerations an analysis is made of basic construction diagrams with annular, sectioned, and doubled sensitive piezoelectric elements of shearing vibration pickups, which are being used more and more. The most favorable operating conditions are indicated for bringing out the qualities of these pickups. This paper was read at the International Scientific and Practical Conference on Piezoelectric Actuators and Pickups, Obninsk. January 14–15, 1993.Translated from Izmeritel'naya Tekhnika, No. 12, pp. 33–36, December, 1993.     

Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator

A laminated piezoelectric bimorph actuator with a graded compositional distribution of PZT and Pt was fabricated, and its deflection characteristics were evaluated. Using experimentally determined compositional dependency of elastic and piezoelectric properties in the PZT/Pt composites, the modified classical lamination theory and the finite element method were applied to find the optimum compositional profile that will give a larger deflection and smaller stress, simultaneously. The miniature bimorph-type graded actuator that consists of a composite internal-electrode (PZT/30 vol% Pt) and three piezoelectric layers of different compositions (PZT/0–20 vol% Pt) were fabricated by powder stacking and sintering. The deflection of the actuator was measured using electric strain gages mounted on the top and bottom surfaces of the actuator. The deflection was found to strongly depend on the composition distribution profile. Under an applied electric field of 100 V m^–1, the actuator with an optimum composition profile exhibited a curvature of up to 0.03 m^–1, which is a satisfactory performance for this kind of actuators. The stress generated on actuation was estimated to be as low as 0.4 MPa, which is much smaller than those of conventional directly bonded actuators and will assure a long actuation life.     

Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator

A laminated piezoelectric bimorph actuator with a graded compositional distribution of PZT and Pt was fabricated, and its deflection characteristics were evaluated. Using experimentally determined compositional dependency of elastic and piezoelectric properties in the PZT/Pt composites, the modified classical lamination theory and the finite element method were applied to find the optimum compositional profile that will give a larger deflection and smaller stress, simultaneously. The miniature bimorph-type graded actuator that consists of a composite internal-electrode (PZT/30 vol% Pt) and three piezoelectric layers of different compositions (PZT/0–20 vol% Pt) were fabricated by powder stacking and sintering. The deflection of the actuator was measured using electric strain gages mounted on the top and bottom surfaces of the actuator. The deflection was found to strongly depend on the composition distribution profile. Under an applied electric field of 100 V m⁻¹, the actuator with an optimum composition profile exhibited a curvature of up to 0.03 m⁻¹, which is a satisfactory performance for this kind of actuators. The stress generated on actuation was estimated to be as low as 0.4 MPa, which is much smaller than those of conventional directly bonded actuators and will assure a long actuation life.     

Design and fabrication of bimorph transducer for optimal vibration energy harvesting

High energy density piezoelectric composition corresponding to 0.9Pb(Zr0.56Ti0.44)O3–0.1Pb[(Zn0.8/3Ni0.2/3) Nb2/3]O3 + 2 mol% MnO2 (PZTZNN) and 0.8[Pb(Zr0.52Ti0.48) O3]-0.2[Pb(Zn1/3Nb2/3)O3] (PZTPZN) were synthesized by conventional ceramic processing technique using three different sintering profiles. Plates of the sintered samples were used to fabricate the piezoelectric bimorphs with optimized dimensions to exhibit resonance in the loaded condition in the range of ~200 Hz. An analytical model for energy harvesting from bimorph transducer was developed which was confirmed by experimental measurements. The results of this study clearly show that power density of bimorph transducer can be enhanced by increasing the magnitude of product (d ? g), where d is the piezoelectric strain constant and g is the piezoelectric voltage constant.     

Flexural vibration of a pyrocomposite hollow cylinder

Flexural vibration of an infinite pyrocomposite circular hollow cylinder composed of an inner and outer pyroelectric layer of class 6 bonded together by a linear elastic material with voids (LEMV) is studied. The exact frequency equation is obtained for traction-free surfaces with continuity conditions at the interfaces. Numerical results in the form of data and dispersion curves for the first and second modes of the flexural vibration of the cylinder ceramic-1/Adhesive/ceramic-2 by taking the adherents as BaTio₃ and the adhesive as an existing carbon fibre-reinforced polymer (CFRP) or as a hypothetical LEMV layer with and without voids are compared with that of a single-layered pyroelectric hollow cylinder. The damping is analyzed through the imaginary parts of the complex frequencies.     

Flexural behaviour of glue-laminated fibre composite sandwich beams

This study involved experimental investigation onto the flexural behaviour of glue-laminated fibre composite sandwich beams with a view of using this material for structural beams. Composite sandwich beams with 1, 2, 3, and 4 composite sandwich panels glued together were subjected to 4-point static bending test in the flatwise and edgewise positions to evaluate their stiffness and strength properties. The results showed that the composite sandwich beams in the edgewise position failed with 25% higher bending strength but have 7% lower bending stiffness than beams in the flatwise position. The results however indicated that the bending stiffness of flatwise specimens converges to that of the edgewise specimens with increasing laminations. More importantly, the specimens in the edgewise position failed with greater ductility due to progressive failure of the fibre composite skins while the specimens in the flatwise position failed in a brittle manner due to debonding between the skin and core. Wrapping the glue-laminated sandwich beams with one layer of tri-axial glass fibres did not prove to be effective. Overall, it has been demonstrated that the glue-laminated sandwich beams exhibited better performance than the individual composite sandwich beams.     

Benchmark analysis of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates

This paper is concerned with the derivation of exact solutions for the responses of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates. An electro-elastic finite element model is also developed based on the layer wise first order shear deformation theory for computing the responses of the bimorphs under general boundary and loading conditions. Both series and parallel connections of the piezoelectric layers of the bimorphs are considered. The responses computed by the finite element model excellently match with that obtained by the exact solutions. The induced electric potential in case of the bimorph in which the piezoelectric layers are connected in series is significantly larger than that in case of the bimorph with piezoelectric layers connected in parallel. If the thickness of the piezoelectric layers and the substrate remain same, the piezoelectric bimorph composed of antisymmetric angle-ply substrate beam is capable of inducing more electric potential than the bimorphs with cross-ply substrate beams. Also, if the bimorph is cantilever, it induces significantly more electric potential than when it is simply supported. Optimum thickness of the piezoelectric layers of the bimorph and unimorph harvesters has been determined. Most importantly, it is found that the bimorph with its piezoelectric layers connected in series performs significantly better than the unimorph if the mass and volume of the piezoelectric layers and the substrates remain same. The results presented here may serve as the benchmark results for verifying experimental and numerical models.