Artykuły w czasopismach: „Piezoceramic layers”

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Tikhonov A., Chugunov S., and Shishkovsky I.V. "Determination of the polymerization depths of lead-free piezoceramic pastes for UV 3D printing." Optics and Spectroscopy 130, no. 10 (2022): 1297. http://dx.doi.org/10.21883/eos.2022.10.54866.3825-22.

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In present study, the polymerization depths for the implementation of the laser stereolithography process in the system (oligomer - piezoceramics) on the wavelengths of 445-465 nm UV range were determined in the original BTO, KNN and NBT lead-free piezoceramic pastes. It was shown that powder pastes, which provide a polymerization depth more than 150 μm, are promising for using in 3D printing. Such depth was chosen to guarantee a sufficient overlap of neighboring layers during polymerization, at the laser beam velocity speed from 1 m/s and the distance between the laser paths of 50 μm. For NBT pastes, successful photo polymerization was carried out for the first time, and for KNN paste the process performance was significantly increased. Keywords: lead-free piezoceramics, stereolitography (SLA) - based ceramics 3D printing, UV- curing and bandwidths

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Wang, Jianjun, Lei Qin, Weijie Li, and Weibin Song. "Parametric Analysis and Optimization of Radially Layered Cylindrical Piezoceramic/Epoxy Composite Transducers." Micromachines 9, no. 11 (2018): 585. http://dx.doi.org/10.3390/mi9110585.

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Radially layered cylindrical piezoceramic/epoxy composite transducers have been designed by integrating the excellent performance of piezoelectric/polymer composites and the radial radiation ability of cylindrical configurations, which are promising in developing novel ultrasonic and underwater sound techniques. Our previous study has explored the effects of the external resistance on the electromechanical characteristics of the transducer, and obtained some valuable findings. To clearly understand the electromechanical characteristics of the transducer and to guide the device design, in this paper, parametric analysis was performed to reveal the effects of multiple key factors on the electromechanical characteristics. These factors include material parameters of epoxy layers, piezoceramic material types, and locations of piezoceramic rings. In order to better analyze the influence of these factors, a modified theoretical model, in which every layer has different geometric and material parameters, was developed based on the model given in the previous work. Furthermore, the reliability of the model was validated by the ANSYS simulation results and the experimental results. The present investigation provides some helpful guidelines to design and optimize the radially layered cylindrical piezoceramic/epoxy composite transducers.

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Shah, D. K., S. P. Joshi, and W. S. Chan. "Static structural response of plates with piezoceramic layers." Smart Materials and Structures 2, no. 3 (1993): 172–80. http://dx.doi.org/10.1088/0964-1726/2/3/005.

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Тихонов, А., С. Чугунов та И. Шишковский. "Определение глубин полимеризации бессвинцовых пьезокерамических паст для УФ 3D печати". Оптика и спектроскопия 130, № 10 (2022): 1555. http://dx.doi.org/10.21883/os.2022.10.53625.3825-22.

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In present study, the polymerization depths for the implementation of the laser stereolithography process in the system (oligomer - piezoceramics) on the wavelengths of 445–465 nm UV range were determined in the original BTO, KNN and NBT lead-free piezoceramic pastes. It was shown that powder pastes, which provide a polymerization depth more than 150 µm, are promising for using in 3D printing. Such depth was chosen to guarantee a sufficient overlap of neighboring layers during polymerization, at the laser beam velocity speed from 1 m/s and the distance between the laser paths of 50 µm. For NBT pastes, successful photo polymerization was carried out for the first time, and for KNN paste the process performance was significantly increased.

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Burdin, Dmitri A., Dmitri V. Chashin, Nikolai A. Ekonomov, Leonid Y. Fetisov, Vladimir L. Preobrazhensky, and Yuri K. Fetisov. "Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric." Sensors 23, no. 13 (2023): 5901. http://dx.doi.org/10.3390/s23135901.

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Magnetic field sensors using magnetoelectric (ME) effects in planar ferromagnetic-piezoelectric heterostructures convert a magnetic field into an output voltage. The parameters of ME sensors are determined by characteristics of the magnetic constituent. In this work, the low-frequency ME effects in heterostructures comprising a layer of antiferromagnetic hematite α-Fe2O3 crystal with easy-plane anisotropy and a piezoelectric layer are studied. The effects arise due to a combination of magnetostriction and piezoelectricity because of mechanical coupling of the layers. The field dependences of magnetization and magnetostriction of the hematite crystal are measured. The resonant ME effects in the hematite-piezopolymer and hematite-piezoceramic structures are studied. The strong coupling between magnetic and acoustic subsystems of hematite results in a tuning of the acoustic resonance frequency by the magnetic field. For the hematite layer, the frequency tuning was found to be ~37% with an increase in the bias field up to 600 Oe. For the hematite-PVDF heterostructure, the frequency tuning reached ~24% and the ME coefficient was 58 mV/(Oe∙cm). For the hematite-piezoceramic heterostructure, the frequency tuning was ~4.4% and the ME coefficient 4.8 V/(Oe∙cm). Efficient generation of the second voltage harmonic in the hematite-piezoceramic heterostructure was observed.

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Grigoryeva, Ludmila. "Transient responses in Piezoceramic Multilayer Actuators Taking into Account External Viscoelastic Layer." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 255–66. http://dx.doi.org/10.32347/2410-2547.2020.105.255-266.

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The work develops a generalized approach to the study of thickness (radial) vibrations arising in the piezoceramic plates, cylinders, spheres under electrical loads. The state of the problem and the main approaches, used in the problems of studying the oscillations of electroelastic bodies, are described. The use of multilayer elements with electroded interface surfaces and variable direction of polarization of the layers increases the conversion efficiency of electrical energy into mechanical energy, so multilayer piezoceramic plates, cylinders, spheres with changing polarization directions with electroded interfaces are considered. Because of piezoelectric elements are often embedded in the housing and supplemented with matching layers to protect against mechanical damage, it is necessary to study their effect on the oscillations of the element. The proposed approach makes it possible to study the vibrations of plane, cylindrical and spherical bodies with layers made of various electroelastic and elastic materials. Numerical implementation is carried out using finite differences. Nonstationary oscillations of PZT-4 ceramic elements at zero initial conditions are investigated. Oscillations of multilayer plates, cylinders and spheres with and without an external elastic or viscoelastic reinforcing layer under impulse and harmonic unsteady loads are investigated and compared. There are found own frequencies for 5-layer bodies of different geometry with and without an external layer. The first natural frequency for cylinder and sphere corresponds to the radial mode of oscillations, while the second natural frequency for cylinders and spheres and the first for flat bodies are almost equal and correspond to thickness mode. The transient processes in the elements under impulse loads and the influence of the outer elastic layer (housing or matching layer) are studied, taking into account the Rayleigh attenuation. It is established that for a flat layer the outer layer increases the amplitude and the period of free vibrations after removing the load, and for cylinders and spheres it decreases. The presence of an elastic layer enhances the third and dampens the fourth natural frequency of the transducer, thereby expanding the frequency range of its operation.

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Wang, H. R., X. Xie, Y. T. Hu, and J. Wang. "Weakly Nonlinear Characteristics of a Three-Layer Circular Piezoelectric Plate-Like Power Harvester Near Resonance." Journal of Mechanics 30, no. 1 (2013): 97–102. http://dx.doi.org/10.1017/jmech.2013.64.

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ABSTRACTThe nonlinear characteristics of a simply-supported three-layer circular piezoelectric plate-like power harvester near resonance are examined in the paper, where the energy-scavenging structure consists of two properly poled piezoceramic layers separated by a central metallic layer. The structure is subjected to a uniform harmonic pressure on the upper surface. Nonlinear effects of large deflection near resonance to induce the incidental in-plane extension are considered. Results on output powers are presented, which exhibit multi-valuedness and jump phenomena.

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Supancic, Peter, Z. Wang, Walter Harrer, K. Reichmann, and Robert Danzer. "Strength and Fractography of Piezoceramic Multilayer Stacks." Key Engineering Materials 290 (July 2005): 46–53. http://dx.doi.org/10.4028/www.scientific.net/kem.290.46.

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Modern low-voltage piezoelectric actuators consist of a stack of piezoceramic layers (PZT) with metallic electrodes in between. Due to the use of these parts in automotive applications, a big but sensitive market is opened. During application mechanical stresses are an inherent loading of these electro-mechanical converter components. Therefore some strength of the actuators is necessary to guarantee a demanded life time. Bending and tensile tests were performed on commercial components to measure the strength in axial direction. Fracture surfaces were investigated with the methods of fractography to get information about the weakest links in the microstructure.

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Shah, D. K., W. S. Chan, and S. P. Joshi. "Delamination detection and suppression in a composite laminate using piezoceramic layers." Smart Materials and Structures 3, no. 3 (1994): 293–301. http://dx.doi.org/10.1088/0964-1726/3/3/005.

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Grigorenko, A. Ya, and I. A. Loza. "Axisymmetric waves in layered hollow cylinders with axially polarized piezoceramic layers." International Applied Mechanics 47, no. 6 (2011): 707–13. http://dx.doi.org/10.1007/s10778-011-0495-5.

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Grigorenko, A. Ya, and I. A. Loza. "Nonaxisymmetric Waves in Layered Hollow Cylinders with Radially Polarized Piezoceramic Layers." International Applied Mechanics 49, no. 6 (2013): 641–49. http://dx.doi.org/10.1007/s10778-013-0597-3.

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Grigorenko, A. Ya, and I. A. Loza. "Nonaxisymmetric Waves in Layered Hollow Cylinders with Axially Polarized Piezoceramic Layers." International Applied Mechanics 50, no. 2 (2014): 150–58. http://dx.doi.org/10.1007/s10778-014-0619-9.

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VELI, Yelda, Claudia SĂVESCU, Alexandru-Mihail MOREGA, and Daniel COMEAGĂ. "NUMERICAL ANALYSES ON THE RESPONSES OF UNIMORPH AND BIMORPH PIEZOELECTRIC HARVESTERS IN TIME DOMAIN." ACTUALITĂŢI ŞI PERSPECTIVE ÎN DOMENIUL MAŞINILOR ELECTRICE (ELECTRIC MACHINES, MATERIALS AND DRIVES - PRESENT AND TRENDS) 2022, no. 1 (2023): 1–7. http://dx.doi.org/10.36801/apme.2022.1.14.

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The paper presents the assessment of the electric output rendered by a unimorph and a bimorph piezoelectric harvester, with one and two active piezoceramic wafers, using numerical simulations. Expected sinusoidal voltages were obtained in a time-dependent study, with a time step corresponding to the eigenfrequency found after conducting an Eigenfrequency study. The terminal voltages obtained agree with the Euler-Bernoulli beam theory and with the distance of the piezoelectric layers from the neutral fiber. By adding an electric circuit node to the electric field problem to form a closed internal circuit, a single unified sinusoidal voltage response should be obtained, coinciding with the input vibration signal. The independent voltages of the layers of a piezoelectric structure with more than one layer (usually two or four) cannot be observed experimentally, as a harvester has only two terminals that pick the overall electric response from all the layers, giving a single alternating voltage output.

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Feng, Zhangbin, Ke Wang, Yukang Liu, Biao Han, and Deng-Guang Yu. "Piezoelectric Enhancement of Piezoceramic Nanoparticle-Doped PVDF/PCL Core-Sheath Fibers." Nanomaterials 13, no. 7 (2023): 1243. http://dx.doi.org/10.3390/nano13071243.

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Electrospinning is considered to be an efficient method to prepare piezoelectric thin films because of its ability to transform the phase of the polymers. A core-sheath structure can endow fibers with more functions and properties. In this study, fibers with a core-sheath structure were prepared using polyvinylidene fluoride (PVDF) included with nanoparticles (NPs) as the shell layer and polycaprolactone (PCL) as the core layer. Their mechanical and piezoelectric properties were studied in detail. During the course of the electrospinning process, PVDF was demonstrated to increase the amount of its polar phase, with the help of nanoparticles acting as a nucleating agent to facilitate the change. PCL was chosen as a core material because of its good mechanical properties and its compatibility with PVDF. Transmission electron microscope (TEM) assessments revealed that the fibers have a core-sheath structure, and shell layers were loaded with nanoparticles. Mechanical testing showed that the core layer can significantly improve mechanical properties. The XRD patterns of the core-sheath structure fibers indicated the β phase domain the main component. Piezoelectric testing showed that the doped nanoparticles were able to enhance piezoelectric performances. The increases of mechanical and piezoelectric properties of core-sheath structure fibers provide a feasible application for wearable electronics, which require flexibility and good mechanical properties.

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Shalimov, V. V., and P. N. Yakushev. "Metallic conduction in the nanoporous silicon layers on the PZT-ceramics surface." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 9 (2022): 122–25. http://dx.doi.org/10.17223/00213411/65/9/122.

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Nanoporous silicon and ceramics based on lead zirconate titanate (PZT-ceramics) have unique properties in themselves. It is shown that their mechanochemical interaction makes it possible to create compositions with a metallic type of conductivity. The formation of conductive paths occurs when silicon particles wedged into microcracks, creating unique highly sensitive layers of piezoceramic compounds, incl. intercalates. Silicon atoms embedded deform the elementary cells of crystals and redistribute charges in them. The connection with the lattice is formed due to the transition of electrons to the boundary layers or the space between them. In the transition layers at T < 260 K, chains with electrical conductivity of the metallic type appear, shunting the piezodielectric.

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Abramovich, H. "Deflection control of laminated composite beams with piezoceramic layers — closed form solutions." Composite Structures 43, no. 3 (1998): 217–31. http://dx.doi.org/10.1016/s0263-8223(98)00104-4.

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Deü, Jean-François, and Ayech Benjeddou. "Free-vibration analysis of laminated plates with embedded shear-mode piezoceramic layers." International Journal of Solids and Structures 42, no. 7 (2005): 2059–88. http://dx.doi.org/10.1016/j.ijsolstr.2004.09.003.

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Kusculuoglu, Ziya K., and Thomas J. Royston. "Nonlinear modeling of composite plates with piezoceramic layers using finite element analysis." Journal of Sound and Vibration 315, no. 4-5 (2008): 911–26. http://dx.doi.org/10.1016/j.jsv.2007.06.081.

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Shah, D. K., S. P. Joshi, and W. S. Chan. "Stress concentration reduction in a plate with a hole using piezoceramic layers." Smart Materials and Structures 3, no. 3 (1994): 302–8. http://dx.doi.org/10.1088/0964-1726/3/3/006.

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Bardzokas, D. I., L. A. Filshtinskii, and L. V. Shramko. "Homogeneous solutions of the electroelasticity equations for piezoceramic layers in R 3." Acta Mechanica 209, no. 1-2 (2009): 27–41. http://dx.doi.org/10.1007/s00707-009-0155-6.

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Koszewnik, Andrzej. "Analytical Modeling and Experimental Validation of an Energy Harvesting System for the Smart Plate with an Integrated Piezo-Harvester." Sensors 19, no. 4 (2019): 812. http://dx.doi.org/10.3390/s19040812.

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The literature on piezoelectric energy harvesting (PEH) is strongly focused on structures, like cantilever beams with piezoceramic layers, due to the fact that they are easily modelled and implemented. As compared to the number of studies dealing with the aforementioned case, research on 2D structures with an attached piezoceramic patch harvester is very limited. Thus, an analytical modeling and experimental validations of a piezo harvester structurally integrated on a thin plate with SFSF (Simply supported-Free-Simply supported-Free) boundary conditions is presented in this paper. The distributed parameter electroelastic model of a harvester bonded to an aluminum plate with both piezo-patch actuators is developed on the basis of the Kirchhoff plate theory and the modal analysis for physical and modal coordinates. This allows to estimate the steady-state value output voltage for each odd mode in the frequency range of 10–300 Hz. Finally, the obtained results for the electroelastic analytical model is experimentally verified on a laboratory stand.

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Kusculuoglu, Z. Koray, and Thomas J. Royston. "Finite element formulation for composite plates with piezoceramic layers for optimal vibration control applications." Smart Materials and Structures 14, no. 6 (2005): 1139–53. http://dx.doi.org/10.1088/0964-1726/14/6/007.

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Khazaee, Majid, Alireza Rezaniakolaei, and Lasse Rosendahl. "An Experimental Study on Macro Piezoceramic Fiber Composites for Energy Harvesting." Materials Science Forum 951 (April 2019): 3–8. http://dx.doi.org/10.4028/www.scientific.net/msf.951.3.

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During the last decades, composite materials are being widely used in a variety of applications. Recently, a type of composite materials with piezoelectric fibers has been introduced for energy harvesting. This study presents an experimental study about composite materials with Piezoceramic fibers for energy harvesting. For this purpose, Macro Fiber Composite (MFC) layers were attached to the surface of metal substrates to form a unimorph harvester. In addition, to investigate the effect of substrate geometrical imperfection on output power, unimorph harvester with notched corners are studied. The output voltage and power were measured during different base excitations. Voltage frequency spectrum and output power as a function of load resistance are analyzed. Results show that the power density for the MFC harvester is 10.37 [μW/cm3.g2] when vibrating on its fundamental natural frequency with current of 50 [μA], which are relatively higher than previous studies.

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Micu, Lavinia Madalina, Iosif Lazar, Adrian Circiumaru, Ilare Bordeasu, Liviu Daniel Pirvulescu, and mihai Hluscu. "New Results Regarding Cavitation Behavior of Polymers Modified with Anorganic Substances Coated on Bronze Surfaces." Materiale Plastice 55, no. 3 (2018): 460–63. http://dx.doi.org/10.37358/mp.18.3.5051.

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Due to mechanical resistance characteristics, chemical corrosion and abrasive erosion resistance, the polymers are more widely used in equipments and installations that are exploited in different fluid hydrodynamic conditions. Among these applications there is the protection of surfaces of hydromechanic organs stressed by cavitation, like in hydraulic machines rotors and valves. Consequently, the research aimes the extension of using these and protection of other components surfacess hardly streesed by cavitation. The research in this paper points toward the behavior of modified polymer layer, coated on surfaces of bronze used in casting the propellers of maritim and river ships. The tests were performed in standard piezoceramic crystal vibrating equipment within Cavitation Laboratory of Politehnica University of Timisoara. The damaging intensity of equipment is much greater than any cavitational vortex, created by ship propeller, hydraulic turbine or centrifugal pump. The obtained results, compared to both recorded on uncovered surfaces with polymer layer and recorded on surfaces covered with HVOF composite materials layers, show an increased resistance that implies the increased exploiting duration of those surfaces.

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Machů, Zdeněk, Oldřich Ševeček, Zdeněk Hadaš, and Michal Kotoul. "Modeling of electromechanical response and fracture resistance of multilayer piezoelectric energy harvester with residual stresses." Journal of Intelligent Material Systems and Structures 31, no. 19 (2020): 2261–87. http://dx.doi.org/10.1177/1045389x20942832.

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The article focuses on a modeling and subsequent optimization of a novel layered architecture of the vibration piezoceramic energy harvester composed of ZrO2/Al2O3/BaTiO3 layers and containing thermal residual stresses. The developed analytical/numerical model allows to determine the complete electromechanical response and the apparent fracture toughness of the multilayer vibration energy harvester, upon consideration of thermal residual stresses and time-harmonic kinematic excitation. The derived model uses the Euler–Bernoulli beam theory, Hamilton’s variational principle, and a classical laminate theory to determine the first natural frequency, steady-state electromechanical response of the beam upon harmonic vibrations, and also the mechanical stresses within particular layers of the harvester. The laminate apparent fracture toughness is computed by means of the weight function approach. A crucial point is the further optimization of the layered architecture from both the electromechanical response and the fracture resistance point of view. Maximal allowable excitation acceleration of the harvester upon which the piezoelectric layer will not fail is determined. It makes possible to better use the harvester’s capabilities in a given application and simultaneously guarantee its safe operation. Outputs of the derived analytical model were validated with finite element method simulations and available experimental results, and a good agreement between all approaches was obtained.

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YAMASHITA, Yuji, Fumihiro ASHIDA, and Seiichiro SAKATA. "K-0613 Control of Transient Thermoelastic Displacement in a Two-Layer Composite Disk Consisting of Transversely Isotropic and Piezoceramic Layers." Proceedings of the JSME annual meeting I.01.1 (2001): 221–22. http://dx.doi.org/10.1299/jsmemecjo.i.01.1.0_221.

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Nasedkin, A. V., A. A. Nasedkina, and M. E. Nassar. "FINITE ELEMENT CALCULATION OF DISK TRANSDUCER WITH CYMBAL-SHAPED END-CAPS AND ACTIVE ELEMENT FROM POROUS PIEZOCERAMICS WITH EXTREME CONDUCTIVITY OF PORE SURFACES." Problems of Strength and Plasticity 85, no. 1 (2023): 63–76. http://dx.doi.org/10.32326/1814-9146-2023-85-1-63-76.

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The paper presents a finite element analysis of a disk-shaped piezoelectric transducer with end-cap patches, which is usually called as Cymbal transducer. The efficiency of such a transducer is determined both by its geometric dimensions and by the values of the longitudinal and transverse piezoelectric moduli (piezoelectric charge coefficients) of the piezoceramic disc material. As was recently found, for porous piezoceramics with completely metallized pore surfaces, the effective transverse piezoelectric modulus does not decrease in absolute value with increasing porosity, as in conventional porous piezoceramics, but, on the contrary, increases, as does the longitudinal piezoelectric modulus. These unusual properties of porous piezoceramics with pore surface metallization are determined by the extreme properties of the phases that make up the piezocomposite material, and, in particular, the extremely high conductivity of the pore surface material inside the dielectric composite medium. In this regard, the main task was to study the efficiency of the Cymbal transducer depending on the type of porous piezoelectric disc material. Comparisons were made for solid piezoceramics, for ordinary porous piezoceramics, for porous piezoceramics with a very thin metal coating of the pores, and for porous piezoceramics with a relatively thick metallization layer on the surface of the pores with different porosities. In the ANSYS finite element package, steady-state oscillations of the cymbal transducer were calculated under nonresonant operating modes and near the first electrically active frequencies, which corresponds to the use of the transducer as a device for energy harvester and as a piezoelectric emitter of acoustic waves. In both cases, the results of computational experiments showed the promise of using new types of porous piezoceramic materials for the considered configurations of a disk piezoelectric transducer with end-cap cymbal patches. In this case, the best results were obtained for a porous piezoceramic material with a very thin metal coating of the pores.

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Yumaryanto, Abdul A., Jae Bum An, and Li Li Xin. "A Piezoelectrically Actuated Biomimetic Walking Robot." Key Engineering Materials 326-328 (December 2006): 1435–38. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1435.

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In this paper we present the design and prototype of a six-legged walking robot which uses Lightweight Piezoceramic Composite curved Actuator (LIPCA) as its actuator. LIPCA consists of multiple layers of glass/epoxy and carbon/epoxy that encapsulate a unimorph piezoelectric ceramic actuator. It uses lightweight fiber-reinforced plastic layers, and it is a lighter structure and generates a higher force and a larger displacement than other conventional piezo-composite type actuators. Like most six-legged walking insects including cockroaches, our robot uses the alternating tripod gait where the front and rear legs on the same side move together with the middle leg on the other side for its locomotion. Two LIPCA strips in different phases are used for actuating each tripod so that only one tripod may touch the ground ensuring static stability while walking. All the experiments with the prototype show that LIPCA can be used as an alternative actuator for small and light mobile robots.

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Petrakov, E. V., H. Lotfi Pour, and E. V. Drobny. "ACTIVE DAMPING OF TRANSVERSE VIBRATIONS OF CONSOLE BEAM BY PIEZOELECTRIC LAYER WITH DIFFERENT ELECTRODE SHAPES OF DAMAGED MEDIA." Problems of strenght and plasticity 81, no. 4 (2019): 429–42. http://dx.doi.org/10.32326/1814-9146-2019-81-4-429-442.

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The damping efficiency is considered for a console beam described by a linear viscosity Bernoulli-Euler model. The article presents the methods of damping transverse vibrations implemented by a dynamic damper from a piezoelectric layer distributed symmetrically along the axis of symmetry of the beam. Piezoelectric layers with a triangular and rectangular shape of electrode plates are considered, which affects the nature of mechanical stresses upon application of electrical voltage. The electrode plates are thin layers made of nickel or silver several microns thick and located normal to the polarization axis, that is, along the length of the piezoceramic plate. The control of the piezoelectric layers is realized by changing the potential difference between the electrode plates, while the piezoelectric material uncoated by the electrode plate on both sides is useless to use as an active material. Mathematical models of the effect of piezoelectric elements on the cantilever beam are derived from the Hamilton principle. The Pareto-efficiency of quenching by piezoelectric plates with different electrode shapes is evaluated relative to two criteria: the level of control voltage and the maximum deflection of the beam. To compare the results with the best variant of vibration damping, in this formulation, the result of vibration damping for a beam with piezoelectric layer applied along the entire length is given. The damping efficiency was confirmed in an applied and particular example by means of vibrograms. The synthesis of Pareto-optimal controls is based on the Germeier convolution, and the search for optimal feedback is based on the application of the theory of linear matrix inequalities and effective algorithms for solving them.

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Soloviev, Arkady N., Le Van Duong, P. A. Oganesyan, and E. V. Kirillova. "Modeling Energy Harvesting Devices with Non-Uniformly Polarized Piezoceramic Materials." Applied Mechanics and Materials 889 (March 2019): 322–28. http://dx.doi.org/10.4028/www.scientific.net/amm.889.322.

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Non-uniformly polarized piezoceramic materials can be used in effective energy harvesting devices. Axisymmetric and plane models of electro elastic bodies were studied using applied theory and finite element method (FEM). Applied theory for devices made of parts with longitudinal and transverse polarization was developed. It was based on bending of electro elastic plates models. Numerical experiments for FEM models were performed in ACELAN package. Comparison of applied theory and FEM results showed satisfactory accuracy. First model consists of three parts: transversally polarized part and two parts with opposite longitudinal polarization. It was compared with uniformly polarized model of the same size. Both electro-mechanical coupling coefficient and output voltage produced by forced oscillations were greater in case of non-uniform polarization. Geometrical parameters – such as relative size of parts, electrode positioning and thickness of the device - were varied in series of numerical experiments to determine range of applicability for developed models and to perform initial analyses of most effective set of parameters. Model was analyzed for different boundary conditions. Automation tools for applied theory computations were developed. Second model is a disk with transvers polarization in the central part and opposite longitudinal polarization in two layers of outer part. It also showed output voltage growth. Appling polarization to the device is an important part of manufacturing process. In some cases, parts can be polarized with imperfections as incomplete polarization of deviation of polarization direction. Polarization process for predefined model geometry and electrode scheme can be performed in ACELAN package. Vector field of the polarization were transferred to finite element meshes and used for solving problems with non-uniform polarization. Difference between simplified block model presented in applied theory and full model solved with FEM was estimated. Some problems can be reduced from full to simplified model without significant accuracy loss. Described programs, models and techniques are developed for advanced analysis of non-uniformly polarized energy storage devices.

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Ha, Dong Ho, Jinkyo F. Choo, Chang Hyung Lee, Won Seo Jang, and Nam Seo Goo. "Dynamic Characteristics of a Multi-Functional Bridge Bearing with Built-In Piezocomposite Element." Applied Mechanics and Materials 432 (September 2013): 275–80. http://dx.doi.org/10.4028/www.scientific.net/amm.432.275.

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A multi-functional bridge bearing with built-in piezocomposite electricity generating element (PCGE) is being developed by our research team to respond to the growing demand of self-powered sensing devices for the monitoring of bridges by harvesting the energy produced by the traffic-induced vibrations. For the intended application, a multilayered piezoelectric PCGE structure composed of layers of piezoceramic, glass/epoxy, and carbon/epoxy, has been developed to improve the durability, output voltage and power of the piezoceramic. The output voltage of this PCGE can be used for real-time traffic monitoring like in bridge-weigh-in-motion systems and can eventually be exploited to generate the electricity needed for the lighting and functioning of other embedded sensors. This paper presents the results of the dynamic loading tests conducted on a prototype of the proposed multi-functional bridge bearing to enhance its design details and verify the accuracy of the measurement. The results show that the bearing provides reliable measurement for traffic monitoring and enable to conceive details for the improvement of the output voltage of the PCGE. Since bridge bearings, as indispensable devices transferring the loads and movements from the deck to the substructure and foundations of the bridge, are continuously subjected to traffic loads, the proposed bridge bearing appears to be a natural and economic solution that can be applied to existing or newly built bridges without modification of the conventional design while providing additional and valuable functions for the maintenance of the structure.

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32

Peelamedu, S. M., C. B. Kosaraju, R. V. Dukkipati, and N. G. Naganathan. "Numerical approach for axisymmetric piezoceramic geometries towards fluid control applications." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 214, no. 2 (2000): 87–97. http://dx.doi.org/10.1243/0959651001540834.

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Piezoceramics have been increasingly popular and utilized for the purpose of micro-actuation. The choice of material internal poling directions for such geometries depends upon the type of actuation desired in each application. There are no generalized analysis procedures that have been developed to be able to predict the response of such actuator geometries. In this work, a finite element model has been developed to analyse axisymmetric piezoceramic actuators with arbitrary internal poling. The finite element methodology is verified by demonstrating favourable agreement between the numerical results obtained in this study with the results published for an inkjet printer application. In addition, the design of a piezoceramic nozzle is investigated with both single-layer and stacked axisymmetric piezoceramic geometries. Such piezoceramic nozzles and orifices can be effectively employed in various sensitive fluid control applications.

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Yoon, Kwang Joon, J. D. Lee, K. B. Kim, Hoon Cheol Park, and Nam Seo Goo. "Design and Manufacturing of IDEAL with Stacked Ceramic Layers and Inter-Digitated Electrodes." Key Engineering Materials 306-308 (March 2006): 1175–80. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.1175.

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This paper is concerned with the development of stacked ceramic thin actuation layer IDEAL (Inter-Digitated Electrode Actuation Layer) using d33 actuation mechanism of piezoelectric ceramic. Most of the thin piezoelectric actuators are operated with d31 actuation mechanism. Many kinds of piezoelectric ceramic actuators are strived now to improve the actuation performance. One of efforts to improve performance of piezoceramic actuators is the research trying to develop an actuator using the piezoelectric coefficient d33. The piezoelectric coefficient d33 is almost twice larger than piezoelectric coefficient d31. Therefore, the induced strain of PZT thin layer with d33 actuation mechanism is bigger than that with d31 actuation mechanism. The AFC and LaRC-MFC used d33 actuation mechanism with surface interdigitated electrode to enhance its actuation performance. But their actuation mechanism is not perfect d33 actuation mechanism since the interdigitated electrodes are placed at the surface of the actuation layer. In this research, the stacked ceramic thin actuation layer with imbedded inter-digitated electrodes is designed and manufactured. The actuation strain of stacked ceramic thin actuation layer is measured and compared with the actuation strain of the LaRC-MFC. The comparison shows that the developed stacked ceramic thin actuation layer can produce 10% more actuation strain than LaRC-MFC at relatively high electric field.

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Nouraei, Mostafa, Vahid Zamani, and Ömer Civalek. "Vibration of smart sandwich plate with an auxetic core and dual-FG nanocomposite layers integrated with piezoceramic actuators." Composite Structures 315 (July 2023): 117014. http://dx.doi.org/10.1016/j.compstruct.2023.117014.

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Nasedkin, Andrey, and Mohamed Elsayed Nassar. "Effective properties of a porous inhomogeneously polarized by direction piezoceramic material with full metalized pore boundaries: Finite element analysis." Journal of Advanced Dielectrics 10, no. 05 (2020): 2050018. http://dx.doi.org/10.1142/s2010135x20500186.

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This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces. To determine the effective properties, we used the effective moduli method and the finite element approaches, realized in the ANSYS package. As a simple model of the representative volume, we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore. We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary. Then we simulated the nonuniform polarization field around the pore. For taking this effect into account, we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure. From this problem, we obtained the polarization field in the porous piezomaterial; after that, we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors. As a result, we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix. From the solutions of these homogenization problems, we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli, and effective dielectric constants compared to the conventional porous piezoceramics. The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics; however, it is more significant on the porous piezoceramics with metalized pore surfaces.

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Lee, Young Sup, Dong Jin Yoon, Sang Il Lee, and Jaehwa Kwon. "An Active Piezo Array Sensor for Elastic Wave Detection." Key Engineering Materials 297-300 (November 2005): 2004–9. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.2004.

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This paper describes an array sensor of piezoceramic PZT discs with flexible covering layers, which is designed to detect surface elastic waves in structures, such as Rayleigh waves. The sensor is distinguished from conventional “passive” sensors for elastic waves detection because it possesses an ability to actuate an “active” pulse. This indicates that the function of active pulse generation ensures the diagnosis of the structures, where the sensor attached or embedded into, can be accomplished in a smart way including an easy inspection of faults. Actually the sensor has been inspired from human sensory systems in order to apply for smart structure sensing. They utilized 6mm diameter and 0.25mm thick PZT discs for the active array sensor. The performance of the sensor was demonstrated at various experiments of some metal and composite structures that the sensor can be applied for the health monitoring of the advanced smart structure system.

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37

Renzi, E. "Hydroelectromechanical modelling of a piezoelectric wave energy converter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2195 (2016): 20160715. http://dx.doi.org/10.1098/rspa.2016.0715.

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We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

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Pereira, Tiago Leite, Aline Souza de Paula, Adriano Todorovic Fabro, and Marcelo Amorim Savi. "Random Effects in a Nonlinear Vibration-Based Piezoelectric Energy Harvesting System." International Journal of Bifurcation and Chaos 29, no. 04 (2019): 1950046. http://dx.doi.org/10.1142/s0218127419500469.

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Vibration-based energy harvesting is of increasing importance and there is a current challenge to improve energy harvesting capacity exploiting nonlinear and random effects. This article investigates random effects in a nonlinear energy harvesting system. The system is represented by a magnetoelastic structure with two piezoceramic layers attached to the root of a cantilever beam, obtaining a bimorph generator. The energy harvesting system is subjected to three excitation conditions: pure harmonic, pure random and a combination of harmonic and random excitations. Noise-to-Signal Ratio (NSR) is employed to quantify different combinations of the forcing terms, establishing a procedure to evaluate the system performance. This approach is based on Power Spectral Density (PSD) of input and output signals. Numerical simulations are carried out, identifying the better combinations of harmonic and random excitations for energy harvesting purposes. Discussions about the influence of the kind of response are carried out evaluating the differences between periodic and chaotic motions. Conclusions show that both random and nonlinear effects can be tuned in order to enhance energy harvesting capacity.

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39

Burdin, Dmitri, Dmitri Chashin, Leonid Fetisov, et al. "Towards Fabrication of Planar Magnetoelectric Devices: Coil-Free Excitation of Ferromagnet-Piezoelectric Heterostructures." Actuators 10, no. 11 (2021): 294. http://dx.doi.org/10.3390/act10110294.

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Magnetoelectric (ME) effects in composite ferromagnet-piezoelectric (FM/PE) heterostructures realize the mutual transformation of alternating magnetic and electric fields, and are used to create magnetic field sensors, actuators, inductors, gyrators, and transformers. The ME effect in composite structures is excited by an alternating magnetic field, which is created using volumetric electromagnetic coils. The coil increases the size, limits the operating frequencies, and complicates the manufacture of devices. In this work, we propose to excite the ME effect in composite heterostructures using a new coil-free excitation system, similar to a “magnetic capacitor”. The system consists of parallel electrodes integrated into the heterostructure, through which an alternating current flows. Modeling and measurements have shown that the excitation magnetic field is localized mainly between the electrodes of the magnetic capacitor and has a fairly uniform spatial distribution. Monolithic FM/PE heterostructures of various designs with FM layers of amorphous Metglas alloy or nickel-zinc ferrite and PE layers of lead zirconate titanate piezoceramic were fabricated and investigated. The magnitude of the ME effect in such structures is comparable to the magnitude of the ME effect in structures excited by volumetric coils. However, the low impedance of the coil-free excitation system makes it possible to increase the operating frequency, reducing the size of ME devices and the power consumption. The use of coil-free excitation opens up the possibility of creating planar ME devices, and accelerates their integration into modern electronics and microsystem technology.

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40

Lee, Chang-Yull, Jin-Young Jung, and Se-Min Jeong. "Active Vibration Suppression of Stiffened Composite Panels with Piezoelectric Materials under Blast Loads." Applied Sciences 10, no. 1 (2020): 387. http://dx.doi.org/10.3390/app10010387.

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Transient responses of stiffened panels with piezoelectric sensors and actuators are studied under normal blast loads. The air vehicles could be exposed to blast pulses generated by an explosion or shock-wave disturbances. Thus, active vibration suppression of the vehicles is important under blast loadings. The structural model is designed as a laminated composite panel with lead zirconate titanate (PZT) piezoceramic layers embedded on both top and bottom surfaces. A uniformly distributed blast load is assumed over the whole of the panel surface. The first-order shear deformation theory of plate is adopted, and the extended Hamilton’s principle is applied to derive the equations of motions. The numerical model is verified by the comparison with previous data. Using linear quadratic regulator (LQR) control algorithm, vibration characteristics and dynamic responses are compared. As piezoelectric patches are attached on the whole of the surface, the effect of the stiffener’s location is studied. Furthermore, the influences of the patch’s positions are also investigated through subjection to the blast wave. From various results, in order to get the best control performances, the research aims to find the optimum position of sensor and actuator pairs that is most effective under blast load environments.

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41

Abramovich, Haim, Eugeny Tsikchotsky, and Gregory Klein. "An experimental investigation on PZT behavior under mechanical and cycling loading." Journal of the Mechanical Behavior of Materials 22, no. 3-4 (2013): 129–36. http://dx.doi.org/10.1515/jmbm-2013-0018.

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AbstractThe drive to produce electrical energy by directly compressing piezoceramic material using mechanical stress stands behind the present test series. To be able to correctly choose the right material, PZT disks manufactured by three different manufacturers have been tested under static mechanical compressive and cyclic loads. It was shown that although the disks can withstand high mechanical stresses (up to 100 MPa) without any visible damage, their transduction is confined to much lower stresses (50–75 MPa), a range in which the electrical output is a function of the square of the applied stress. This range is further reduced, when the PZT is subjected to cyclic mechanical loading, yielding an applicable mechanical stress in the range of 30–40 MPa, from which electrical power can be produced without further deterioration. To compensate for the low electric power, due to relatively low mechanical stresses applied on the PZT disks, one can increase the volume of the material used by placing layers of piezoelectric material one on top of the other, each subjected to the same mechanical stress. This will yield the required electric power from a safe given mechanical stress without reduction in its output.

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42

Loza, I. A. "About the propagation of axisymmetric elastoelectric waves in a hollow layered cylinder from metal and piezoceramic layers at electric modes of excitation." Reports of the National Academy of Sciences of Ukraine, no. 8 (August 20, 2015): 51–57. http://dx.doi.org/10.15407/dopovidi2015.08.051.

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Rongong, J. A., J. R. Wright, R. J. Wynne, and G. R. Tomlinson. "Modelling of a Hybrid Constrained Layer/Piezoceramic Approach to Active Damping." Journal of Vibration and Acoustics 119, no. 1 (1997): 120–30. http://dx.doi.org/10.1115/1.2889679.

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It has been shown that significant reductions in structural vibration levels can be achieved using a hybrid system involving constrained layer damping and active control with piezoceramics. In this paper, mathematical models based on the Rayleigh Ritz approach, are developed to describe the longitudinal and flexural vibration behaviour of a cantilevered beam when excited using piezoceramic patches bonded to a constrained layer damping treatment. Predictions of static and steady state dynamic behaviour, obtained using the models are validated by comparison with results from finite element analysis and laboratory experiments. The models are then used in open loop and closed loop velocity feedback control simulations to demonstrate the improvements in stability and performance achieved using this method over that achieved using conventional active control.

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Teplykh, Andrey, Boris Zaitsev, Alexander Semyonov, and Irina Borodina. "The Study of the Acoustic Characteristics of Chitosan Acetate Film Using a Radial Electric Field Excited Resonator." Sensors 23, no. 4 (2023): 1808. http://dx.doi.org/10.3390/s23041808.

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Currently, the lateral electric field excited resonators are used for the creation of various sensors. We have recently proposed a new type of acoustic resonator called radial electric field excited disk acoustic resonator. The advantage of this type of resonator is its high sensitivity to mechanical and electrical boundary conditions on its free surface. This makes it possible to determine both the acoustic and electrical properties of a thin layer of material deposited on the free end of the resonator. In this work, we used a radial electric field excited disk acoustic resonator of Russian-made barium plumbum zirconate titanate (BPZT) piezoceramics. With the help of this resonator, the material constants for the piezoceramic sample were refined, and their temperature dependencies were determined. Then, this resonator was used to determine the elastic modulus, viscosity, and conductivity of the chitosan acetate film in air and ammonia vapors of various concentrations. It was shown that the chitosan acetate film under the influence of ammonia vapor significantly changes its mechanical properties and increases its electrical conductivity thousands of times, and then completely restores its properties.

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45

MASLOV, A. A., S. G. MIRONOV, A. N. KUDRYAVTSEV, T. V. POPLAVSKAYA, and I. S. TSYRYULNIKOV. "Wave processes in a viscous shock layer and control of fluctuations." Journal of Fluid Mechanics 650 (March 18, 2010): 81–118. http://dx.doi.org/10.1017/s0022112009993533.

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Generation and development of disturbances in a hypersonic viscous shock layer on a flat plate is studied both experimentally and numerically. The study is performed at the Mach number M∞ = 21 and the Reynolds number ReL = 1.44 × 105 and is aimed at elucidating the physical mechanisms that govern the receptivity and instability of the shock layer at extremely high hypersonic velocities. The experiments are conducted in a hypersonic nitrogen-driven wind tunnel. An electron-beam fluorescence technique, a Pitot probe and a piezoceramic transducer are used to measure the mean density and Mach number contours, as well as density and pressure fluctuations, their spectra and spatial distributions in the shock layer. Direct numerical simulations are performed by solving the Navier–Stokes equations with a high-order shock-capturing scheme in a computational domain including the leading and trailing edges of the plate, so that the bow shock wave and the wake behind the plate are also simulated. It is demonstrated that computational and experimental data characterizing the mean flow field, intensity of density fluctuations and their spatial distributions in the shock layer are in close agreement. It is found that excitation of the shock layer by external acoustic waves leads to generation of entropy–vortex disturbances with two maxima of density fluctuations: directly behind the shock wave and on the external edge of the boundary layer. At the same time, the pressure fluctuations decay inward into the shock layer, away from the shock, which agrees with the linear theory of interaction of shock waves with small perturbations. Thus, the entropy–vortex disturbances are shown to dominate in the hypersonic shock layer at very high Mach numbers, in contrast with the boundary layers at moderate hypersonic velocities where acoustic modes are most important. A parametric numerical study of wave processes in the shock layer induced by external acoustic waves is performed with variations of frequency, amplitude and angle of propagation of external disturbances. The amplitude of generated disturbances is observed to grow and decay periodically along the streamwise coordinate, and the characteristics of these variations depend on the frequency and direction of incident acoustic waves. The hypersonic shock layer excited by periodic blowing and suction near the leading edge is also investigated; in the experiments, this type of excitation is obtained by using an oblique-cut whistle. It is shown that blowing/suction generates disturbances resembling those generated by external acoustic waves, with similar spatial distributions and phase velocities. This result paves the way for active control of instability development in the shock layer by means of destructive interference of two types of disturbances. Numerical simulations are performed to show that instability waves can be significantly amplified or almost entirely suppressed, depending on the relative phase of blowing/suction and acoustic disturbances. Wind-tunnel experiments completely confirm this numerical prediction. Thus, the feasibility of delaying instability development in the hypersonic shock layer has been demonstrated for the first time.

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Seemann, Wolfgang E. "Stresses in a Thin Piezoelectric Element Bonded to a Half-Space." Applied Mechanics Reviews 50, no. 11S (1997): S204—S209. http://dx.doi.org/10.1115/1.3101836.

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In this paper, a thin piezoceramic element is considered which is bonded to an elastic or a rigid half-space. Such a model may be an approximation of the interaction between piezoceramic elements and elastic structures like beams and plates. For an elastic half-space, the determination of the shear stress in the bonding layer leads to a singular integral equation. A half-space which is very stiff may be modeled as a rigid substrate. For this case, displacement functions are introduced. Hamilton’s principle for electromechanical systems allows the use of Lagrange multipliers to incorporate the condition of a stress free upper surface of the piezoceramic element. The stresses in the bonding layer and in the piezoceramic element are estimated by this method and compared with Finite Element results. Though the singularity near the ends of the piezoceramic element cannot be modeled by both methods, stress concentrations can clearly be seen for the shear stress as well as for the normal stress. As infinite stresses due to the singularity do not occur in reality, the results allow an estimation of the bonding stresses except in the near vicinity of the edges. The knowledge of these stresses is important to prevent failure due to delamination.

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Chetwynd, Daley, T. L. Lew, Keith Worden, and Jem A. Rongong. "Damage Detection in an Aluminium Plate with an Active Constrained Layer Damping Treatment." Key Engineering Materials 347 (September 2007): 205–12. http://dx.doi.org/10.4028/www.scientific.net/kem.347.205.

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This work was conducted as part of the European Union project ARTIMA and it investigates the potential for a dual use active constrained layer damping treatment for both vibration control and structural health monitoring. It examines a curved aluminium plate with an ACLD treatment formed by mounting a large piezoceramic patch with Araldite 2027. The plate was investigated by ultrasonic Lamb waves generated by the patch, and several smaller piezoceramic transducers were used as sensors. Damage was simulated by adding incrementally increasing saw cuts to the plate, and the technique of outlier analysis was used to classify when this damage had occurred.

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Karpuk, M. M., D. A. Kostyuk, Yu A. Kuzavko, and V. G. Shavrov. "Ultrasonic piezoceramic transducers with a magnetoacoustic layer." Technical Physics Letters 30, no. 12 (2004): 1005–8. http://dx.doi.org/10.1134/1.1846841.

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Shul’ga, N. A., and L. O. Grigor’eva. "Electroelastic nonstationary vibration of a piezoceramic layer." International Applied Mechanics 45, no. 3 (2009): 282–89. http://dx.doi.org/10.1007/s10778-009-0186-7.

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Rusev, Rostislav, Boriana Tzaneva, and George Angelov. "Electrophoretic Deposition of Rochelle Salt Nanocrystals on Aluminum Plate." Coatings 13, no. 6 (2023): 1074. http://dx.doi.org/10.3390/coatings13061074.

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A straightforward and inexpensive electrophoretic method for obtaining environment-friendly nanocrystalline piezo layers from Rochelle salt (RS) is presented here. The electrophoretic deposition process includes the formation of nanocrystals by precipitation of Rochelle salt/water solutions in ethanol (anti-solvent method) under the influence of a high electric field. A nanoporous anodic aluminum oxide membrane is used to separate the electrochemical cell into two chambers. The composition of the RS:H2O:EtOH mixture and the spatial separation of the process of precipitation from electrophoretic deposition allow control of the nanocrystal size and the uniformity of the layer. The reaction kinetics, the morphology, and the piezo response to the resulting layers are all investigated. The best samples were obtained at RS:H2O:EtOH ratio 1:22.5:37.5. Under these conditions, the nanocrystals are preferentially oriented on the aluminum substrate and form a dense and homogeneous layer. Although the obtained structure is polycrystalline, the resulting piezo effect is 1120 pC/N, which is comparable to inorganic monocrystals and piezoceramics. This allows the use of electrophoretically deposited polycrystalline piezo layers in applications such as energy harvesting.

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