Electromechanical nonstationary thickness vibrations of a piezoceramic layer

The methods of characteristics and difference schemes are used to study the nonstationary thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to electrical and mechanical loads. The propagation of waves under loading of various types is studied. The dynamic electroelastic state of the layer is analyzed. It is established that the characteristics of the electroelastic state are in a linear relationship     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

Forced vibrations and vibroheating of shallow viscoelastic laminated shells with the piezoelectric effect

The vibrations and dissipative heating of a hinged shallow shell made of viscoelastic piezoelectric material and subject to harmonic electric loading are considered. The basic relations are obtained by using the Kirchhoff-Love mechanical hypotheses supplemented with the respective hypotheses for electric quantities. Analytical solutions of both electromechanical and thermal problems are derived for the case where the temperature is constant along the shell thickness. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 78–87, June, 2000.     

On electromagnetic radiation under destruction of ultrathin glass fibers

We study how the characteristics of electric signals emitted in the course of vibrations and fracture of ultrathin fibers under tension depend on the geometric parameters and physical properties of the fibers. A unique highly sensitive experimental plant was developed, and glass fibers of diameter 6.5, 10, 18, 150µm, as well as polyethylene fibers of thickness 0.2–0.06mm, were tested. It turned out that the signals emitted by fracture of fibers made of different dielectric materials (d < 20µm) are qualitatively the same in shape and have a negative phase of length 100–400µs and a much longer positive phase. An electric signal induced by a fiber thinner than a human hair by an order of magnitude was recorded for the first time. Unexpectedly, the average values of amplitudes of signals for fibers significantly different in diameter turned out to be close to each other. This can be explained by the well-known fact that the number of fragments in fracture increases with the glass strength (a scale effect). The potentialities of the method for measuring electric signals in studying the spectra of fiber vibrations were discovered.     

Free vibration of layered truncated conical shell frusta of differently varying thickness by the method of collocation with cubic and quintic splines

Free vibrations of layered conical shell frusta of differently varying thickness are studied using the spline function approximation technique. The equations of motion for layered conical shells, in the longitudinal, circumferential and transverse displacement components, are derived using extension of Love’s first approximation theory. Assuming the displacement components in a separable form, a system of coupled equations on three displacement functions are obtained. Since no closed form solutions are generally possible, a numerical solution procedure is adopted in which the displacement functions are approximated by cubic and quintic splines. A generalized eigenvalue problem is obtained which is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibrations of two-layered conical shells, made up of several types of layer materials and supported differently at the ends are considered. Linear, sinusoidal and exponential variations in thickness of layers are assumed. Parametric studies are made on the variation of frequency parameter with respect to the relative layer thickness, cone angle, length ratio, type of thickness variation and thickness variation parameter. The effect of neglecting the coupling between bending and stretching is also analysed.     

Studying the harmonic vibrations of a cylindrical shell made of a nonlinear elastic piezoelectric material

The paper examines the harmonic vibrations of an infinitely long thin cylindrical shell made of a nonlinear elastic piezoceramic material and subjected to periodic electric loading. Amplitude-frequency characteristics are plotted for different amplitudes of the load. Points of these characteristics are analyzed for stability. The transients occurring while harmonic vibrations attain the steady state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 101–106, April 2008.     

Influence of the Geometry of a Piezotransformer Transducer on Its Electric Potential During Electroelastic Vibrations of a Piezoceramic Disk

The resonant radial vibrations of a thin piezoceramic disk with solid electrodes and thickness polarization are considered as an example to study the influence of the geometry of piezotransformer transducers on their electric potentials and the mutual influence of neighboring transducers__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 75–80, February 2005.     

On the fundamental equations of electromagnetoelastic media in variational form with an application to shell/laminae equations

The fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials, and the uniqueness of solutions is examined. Alternatively, the fundamental equations are stated as the Euler–Lagrange equations of a unified variational principle, which operates on all the field variables. The variational principle is deduced from a general principle of physics by modifying it through an involutory transformation. Then, a system of two-dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell. Also, a theorem is given, which states the conditions sufficient for the uniqueness in solutions of the shell equations. On the basis of a discrete layer modeling, the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers, whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness. The resulting equations in differential and fully variational, invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well. The invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell (plate) or laminae. The results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material, geometry and/or effects.     

Electromechanical behaviour of a finite piezoelectric layer under a flat punch

This paper solves the problem of a smooth and frictionless punch on a piezoelectric ceramic layer. Different electrical boundary conditions that employ conducting or insulating punches are presented. The stress and electric displacement intensity factors are used to characterize the electromechanical fields at the punch tip. The field intensity factors are obtained numerically for finite layer thickness. Effects of the thickness of the piezoelectric layer on the stress and electric displacement, and the stress and electric displacement intensity factors at the punch tip are discussed. Solution technique for two identical and collinear surface punches on the piezoelectric layer is also provided and the effect of relative distance between the punches is investigated. Numerical results for some interesting special cases, such as conducting punch and insulating punch, and infinite piezoelectric layer thickness, are presented.     

Modelling the Stationary Vibrations and Dissipative Heating of Thin-Walled Inelastic Elements with Piezoactive Layers

A coupled dynamic problem of thermoelectromechanics for thin-walled multilayer elements is formulated based on a geometrically nonlinear theory and the Kirchhoff–Love hypotheses. In the case of harmonic loading, an approximate formulation is given using the concept of complex moduli to characterize the cyclic properties of the material. The model problem on forced vibrations of sandwich beam, whose core layer is made of a passive physically nonlinear material, and face layers, of a viscoelastic piezoactive material, is considered as an example to demonstrate the possibility of damping the vibrations by applying harmonic voltage to the oppositely polarized layers of the beam. Substantiation is given for a linear control law with a complex coefficient for the electric potential, which provides damping of vibrations in the first symmetric mode at the linear and nonlinear stages of deformation. The stress–strain state and dissipative-heating temperature are studied     

Resonant flexural vibrations and dissipative heating of a piezoceramic ring plate with nonuniformly electroded surfaces

The forced flexural vibrations and dissipative heating of a bimorph ring plate are studied. The plate is made of viscoelastic piezoceramics and is polarized across the thickness. The outer surfaces of the plate are nonuniformly electroded, and harmonic electric excitation is applied to the electrodes. The viscoelastic behavior of the material is described using the concept of temperature-dependent complex moduli. The coupled nonlinear problem of thermoviscoelasticity is solved by time iteration using, at each iteration, the discrete-orthogonalization method to integrate the mechanics equations and the explicit finite-difference method to solve the heat-conduction equation with a nonlinear heat source. Numerical calculations demonstrate that by changing the size of the ring electrode we can influence the natural frequency, stress and displacement distributions, dissipative-heating temperature, and amplitude-and temperature-frequency characteristics. With certain boundary conditions, there is an optimal electrode configuration that produces deflections of maximum amplitudes when an electric excitation is applied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 102–109, March 2006.     

Vibrations of a piezoceramic cylinder subject to nonstationary electric excitation

The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder is examined. The region of end disturbances in a long cylinder is identified __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 73–79, March 2007.     

Electric effects of vibrations of capillaries filled with droplets of mercury and an electrolyte solution

The appearance of a time-dependent difference of the electric potentials due to mechanical vibrations of capillaries filled with droplets of mercury and an electrolyte solution was studied in [1–5]. The phenomenon is used in electrokinetic transducers [6, 7]. Equivalent electric and mechanical circuits of the transducers were proposed in [1–4]. The experimental dependences of the amplitude of the potential difference that arises between the mercury droplets on the vibration frequency (the amplitude-frequency characteristics of the transducers) were investigated in [2, 4]. In the present paper, expressions are obtained for the difference of the electric potentials between mercury droplets that arises in the case of harmonic vibrations of a capillary with small amplitudes. The theoretical and experimental amplitudefrequency characteristics of an electrocapillary transducer are constructed. Good agreement between the results of the calculations and the experimental data is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika-Zhidkosti i Gaza, No. 2, pp. 131–136, March–April, 1988.     

Resonant Vibrations and Dissipative Heating of an Infinite Piezoceramic Cylinder

The monoharmonic radial vibrations and dissipative heating of an infinite hollow piezoceramic cylinder are studied in dynamic formulation, taking into account the temperature dependence of the complex electromechanical characteristics over a wide range of temperatures, including depolarization temperatures. The influence of the heat exchange conditions, the level of electric load, and geometry on the thermoelectromechanical characteristics is studied in the case of forced vibrations at the first resonance__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 101–107, March 2005.     

Basic equations of the theory of thermoviscoelastic plates with distributed sensors and actuators

The basic equations of the theory of thermoviscoelastic thin-walled plates with piezoelectric sensors and actuators under monoharmonic mechanical and electric loading are derived using the Kirchhoff–Love hypotheses. The thermomechanical behavior of passive and piezoactive materials is described using the concept of complex characteristics. Methods of solving nonlinear problems of active damping of thermomechanical vibrations of plates with sensors and actuators are considered. The effect of dissipative heating on the damping of axisymmetric vibrations of a thermoviscoelastic solid circular plate is analyzed as an example     

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer (PMUT) actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezoelectric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deformation, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.     

Determination of the natural frequencies of vibration of nonuniform slabs

The natural frequencies of vibrations of laminated plates are determined in a three-dimensional formulation by analytical separation of the sought functions for plate thickness. The system of differential equations which describes the natural vibrations of the plates is solved analytically. The solution makes it possible to study plates with a large number of layers, including orthotropic plates with elastic characteristics that vary through the thickness. Numerical experiments show that a step approximation can be used to approximate the variable elastic modulus. Ukrainian Transportation University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 47–53, February, 1999.     

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity.Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.     

薄膜润滑中双电层效应的理论分析与实验研究

建立了考虑双电层效应的有限宽组合滑块薄膜润滑数学模型,并利用组合滑块与圆盘的滑动摩擦试验对双电层效应进行研究,利用实验结果修正了润滑过程中双电层效应的计算,给出电粘度的计算公式并进行数值分析.结果表明:在薄膜厚度较薄的情况下,双电层效应使得流体的等效粘度随膜厚减小而迅速增加;随着膜厚增加,双电层的电粘度效应逐渐减弱;随着电场强度增加,双电层的电粘度效应增加,当电场强度达到一定程度时,双电层的电粘度效应开始减弱.     

Symmetry groups and similarity analysis for boundary layer control over a wedge using electric forces

In this paper, we consider the control of laminar, incompressible boundary layer for the ionized air flow over a flat plate and wedges through the application of an electric field. Group theory is used to find equivalence transformations of the resulting boundary layer equations. These transformations in turn reveal forms of the electric field function which lead to reductions of the equations via similarity variables. Differences in boundary layer thickness growth and velocity profiles as well as wall shear stresses are shown for the specific choices of the electric field function. The effects of suction and blowing type of boundary conditions are also demonstrated. The applied electric fields lead to a thinning of boundary layer thickness and an increase in wall shear stress. They are also shown to stabilize the velocity component profiles and suppress flow separation in reentrant corners.