Analysis of the sandwich piezoelectric ultrasonic transducer in coupled vibration

The coupled vibration of the sandwich piezoelectric transducer with a large cross-section is analyzed using an approximate analytic method. The resonance frequency equations of the transducer are derived and the effect of the geometrical dimensions on the resonance frequency is studied. It is illustrated that when the radial vibration in the transducer is considered, the vibration of the sandwich transducer becomes more complex. Apart from the longitudinal resonance frequency, the radial resonance frequency can also be obtained. For comparison, numerical methods are also used to simulate the coupled vibration; the resonance frequency and the vibrational displacement distribution are computed. Compared with one-dimensional longitudinal theory, the radial dimensions of the transducer are no longer limited because the coupled vibration is considered. Compared with numerical methods, the physical meaning of the analytic method is concise. It is illustrated that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with those from numerical methods, and they are in better agreement with the measured results than those from one-dimensional theory. Since the radial and the coupled vibration are considered in the analysis, more resonance frequencies can be obtained. Therefore, using the coupled resonance frequency equations, the sandwich transducer with multifrequency or wide frequency bandwidth can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry and other applications.     

Forced vibration of a damped sandwich beam subjected to moving forces

The response of a sandwich beam subjected to moving forces (constant as well as pulsating) is analyzed by the use of Fourier and Laplace transforms and compared with the response of an equivalent elastic beam. The results indicate that the critical speed of force on a sandwich beam is always greater than that on an elastic beam of identical mass per unit length and flexural rigidity, and depends on its geometric and shear parameters. For subcritical speeds, the maximum deflection of a sandwich beam is shown to occur earlier than that of an equivalent elastic beam. An increase in the core shear stiffness is shown to be beneficial in reducing the dynamic magnification of the central deflection of the sandwich beam.     

Coupling analysis of a matched piezoelectric sensor and actuator pair for vibration control of a smart beam

This paper presents a theoretical and experimental study of the in-plane and out-of-plane coupling of a matched piezoelectric sensor/actuator pair bonded on a beam. Both the sensor and actuator are triangularly shaped polyvinylidene fluoride (PVDF) transducers and are intended to provide a compact sensor/actuator system for beam vibration control. The measured sensor-actuator frequency response function has shown an unpredicted increase in magnitude with frequency, which was found, to be due to in-plane vibration coupling. An analytical model has been developed to decompose the sensor-actuator response function into an in-plane contribution and an out-of-plane contribution. This in-plane coupling can limit the feedback control gains when a direct velocity feedback control is applied. A method called the j omega s compensation method is proposed to identify the effect of the in-plane vibration coupling at low frequencies. Even after this compensation, however, there was unexpected strong out-of-plane coupling at even modes, which may have been caused by a lack of accuracy in the shaping of the PVDF sensor and actuator. Numerical simulations have confirmed the sensitivity of the matched sensor/actuator pair with shaping errors.     

Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam

This study presents a novel resonant fuzzy logic controller (FLC) to minimize structural vibration using collocated piezoelectric actuator/sensor pairs. The proposed fuzzy controller increases the damping of the structures to minimize certain resonant responses. The vibration absorber is first experimentally examined by a cantilever beam test bed for impulse and near-resonant excitation cases. Moreover, the effectiveness of the new fuzzy control design to a state-of-the-art control scheme is compared through the experimental studies. The experimental results indicate the proposed controller is highly promising for this application field. Our results further demonstrate that the fuzzy approach is much better than traditional control methods. In summary, a novel vibration absorption scheme using fuzzy logic has been demonstrated to significantly enhance the performance of a flexible structure with resonant response.     

Bending analysis of a functionally graded piezoelectric cantilever beam

A new analysis based on Airy stress function method is presented for a functionally graded piezoelectric material cantilever beam. Assuming that the mechanical and electric properties of the material have the same variations along the thickness direction, a two-dimensional plane elasticity solution is obtained for the coupling electroelastic fields of the beam under different loadings. This solution will be useful in analyzing FGPM beam with arbitrary variations of material properties. The influences of the functionally graded material properties on the structural response of the beam subjected to different loads are also studied through numerical examples.     

Using a block diagram approach for the evaluation of electrical loading effects on piezoelectric reception

A model is presented for the analysis of thickness-mode piezoelectric receivers over a wide range of practical operating conditions. The systems feedback approach is employed to clearly explain electromechanical interaction within the system. Main features are emphasized via a number of simulation diagrams and specific design strategies relating to practical pulse-echo transducer systems are proposed.     

Effect of mechanical loading on the electrical durability of polymers

A decrease in the electrical durability, which is defined as an amount of time required for dielectric breakdown at a constant electric field strength, of polyethylene and Lavsan (polyethylene terephthalate) films under tensile loading is registered in a temperature range from 100 to 300 K. It is established that the pulling apart of the axes of neighbor chain molecules in consequence of tensile loading gives rise to a decrease in the energy level of the intermolecular electron traps. In the amorphous region of a polymer, this accelerates the release of electrons from the traps through over-barrier transitions at higher temperatures ranging from about 230 to 350 K and quantum tunneling transitions at lower temperatures in the range from about 80 to 200 K. As a result, the time required for the formation of a critical space charge, i.e., the waiting period of dielectric breakdown, decreases, which means a reduction in the electrical durability of polymers.

     

Flexural effects of sandwich beam with a plate insert under in-plane bending

The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study. An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stress.The shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces. The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure. The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads. The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert.     

Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions

The dynamic analysis of a three-layered symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to a periodic axial load have been carried out under various boundary conditions. As the skins of the sandwich beam are conductive, magnetic loads are applied to the skins during vibration. Due to the field-dependent shear modulus of MRE material, the stiffness of the MRE embedded sandwich beam can be changed by the application of magnetic fields. Using extended Hamilton’s principle along with generalized Galarkin’s method the governing equation of motion has been derived. The free vibration analysis of the system has been carried out and the results are compared with the published experimental and analytical results which are found to be in good agreement. The parametric instability regions of the sandwich beam have been determined for various boundary conditions. Here, recently developed magnetorheological elastomer based on natural rubber containing iron particles and carbon blacks have been used. The effects of magnetic field, length of MRE patch, core thickness, percentage of iron particles and carbon blacks on the regions of parametric instability for first three modes of vibration have been studied. These results have been compared with the parametric instability regions of the sandwich beam with fully viscoelastic core to show the passive and active vibration reduction of these structures using MRE and magnetic field. Also, the results are compared with those obtained using higher order theory.     

Effect of mechanical loading on the kinetics of electrical breakdown in polymers

The decrease in the electrical lifetime (time of expectation of a breakdown in an electric field of constant polarity) under tensile loading of disoriented polyethylene, Teflon, and lavsan films in the range of 100–300 K is studied. It is found that tensile loading decreases the depth of intermolecular electron traps due to an increase in the spacing of chain molecules in amorphous regions of polymers. This accelerates the hopping (from one trap to another) transport of electrons, leading to the formation of critical (breakdown) volume charges.     

On mechanical response of a non-uniform piezoelectric transducer under the influence of a body-force

The mechanical response of a non-uniform piezoelectric transducer when there is a body force acting on it has been evaluated using the methods of transform calculus.The author is grateful to Dr. D. K. Sinha of Jadavpur University for his kind help in the preparation of this note.     

Four-probe measurements of the electrical conductivity of semiconductor layers containing inhomogeneous regions

The possibility of performing four-probe measurements of conductivity of semi-conductor layers containing inhomogeneous regions is evaluated. Exact formulas are obtained for determination of semiconductor conductivity for arbitrary position of the probe near a circular inhomogeneity, and for two probe positions near two circular inhomogeneities. An approximate formula is presented for use with semiconductors containing several inhomogeneous regions. Theory is compared with experimental results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 30–33, July, 1977.     

Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model

The flexural vibration of the fluid-conveying single-walled carbon nanotube (SWCNT) is derived by the Timoshenko beam model, including rotary inertia and transverse shear deformation. The effects of the flow velocity and the aspect ratio of length to diameter on the vibration frequency and mode shape of the SWCNT are analyzed. Results show that the effects of rotary inertia and transverse shear deformation result in a reduction of the vibration frequencies, especially for higher modes of vibration and short nanotubes. The frequency is also compared with the previous study based on Euler beam model. In addition, if the ratio of length to diameter increased to 60, the influence of the shear deformation and rotary inertia on the mode shape and the resonant frequencies can be neglected. However, the influence is very obvious when the ratio decreased to 20. As the flow velocity of the fluid increases in the vicinity of 2π, the SWCNT reveals the divergence instability. It regains stability when the flow velocity reaches about 9. As the velocity increases further, the SWCNT undergoes a coupled-mode flutter and results in a larger amplitude.     

Effective properties of coated fibrous piezoelectric composites with spring-type interfaces under anti-plane mechanical and in-plane electrical loads

In this paper, we investigate the effective properties of three-phase(matrix/coating/fiber) cylindrical piezoelectric composites with imperfect interfaces under anti-plane mechanical and in-plane electrical loads. By using the electromechanically coupling spring-type interface model and the generalized self-consistent method(GSM), we analytically derived the effective electroelastic moduli. The present solutions include as special cases the three-phase cylindrical piezoelectric composites with perfect interfaces as well as the two-phase(matrix/fiber) case with imperfect or perfect interfaces. Selected calculations are graphically shown to demonstrate dependence of the effective moduli on the interfacial properties. The particular size-dependent characteristic due to the interfacial imperfection is also discussed.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

Energy analysis of a piezoelectric body under nonuniform deformation

One of the most powerful and clear methods for solving electromechanical transducer problems is the energy method based on the use of the Euler-Lagrange equations. The general expression is developed in a form convenient for applying the energy method to the calculation of the internal energy of a piezoelectric body under nonuniform deformation. The electrical and mechanical variables in this expression are separable under certain conditions and the underlying physics is illustrated with particular examples of bars made of piezoelectric ceramic for the case of transverse and axial polarization. In the case that the electrical and mechanical variables are not separable, the contribution of the mutual energy term to the total internal energy is expressed analytically.     

Anomalous dispersion of SH acoustic waves in a piezoelectric sandwich structure

A transformation of the dispersion spectrum of shear horizontal (SH) acoustic eigenwaves in a sandwich structure due to a piezoelectric effect is described. The structure consists of two plates separated by a gap whose thickness is considerably less than the wavelength. Under these conditions, acoustic fields induced in the plates interact through the piezoelectric effect. The piezoelectric effect brings about a distortion and divergence of the initially (in the zeroth approximation) independent dispersion curves; i.e., all points of intersection of the dispersion curves disappear. Each of the new dispersion branches is formed by a set of adjacent portions of initial branches. A change in the wave number (or in the frequency) results in a periodic gradual displacement of the localization zone of the acoustic field from one plate to the other.     

Boundary conditions for the bending of a piezoelectric beam

For beam bending in transversely isotropic piezoelectric media, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the beam of general edge geometry and loadings. By generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed edge-data of the beam must satisfy these conditions in order that they could generate a decaying state within the beam. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions for the case of bending deformation of piezoelectric beam are derived explicitly. They are then used for the correct formulation of boundary conditions for the beam theory solution (or the interior solution). Besides, an analytical solution of elastic beam is formulated to verify validity of our boundary conditions. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two sets of mixed edge-data are obtained for the first time.     

Free vibration analysis of a cracked beam by finite element method

In this paper, the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method. An ‘overall additional flexibility matrix’, instead of the ‘local additional flexibility matrix’, is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and therefore the stiffness matrix. Compared with analytical results, the new stiffness matrix obtained using the overall additional flexibility matrix can give more accurate natural frequencies than those resulted from using the local additional flexibility matrix. All the elements in the overall additional flexibility matrix are computed by 128-point (1D) or (128×128)-point (2D) Gauss quadrature, and then further best fitted using the least-squares method. The explicit form best-fitted formulas agree very well with the numerical integration results, and are very convenient for use and valuable for further reference. In addition, the authors constructed a shape function that can perfectly satisfy the local flexibility conditions at the crack locations, which can give more accurate vibration modes.