Longitudinal Vibration Mode Research Articles

Resonance frequencies of the multilayered piezotransducers

Piezoelectric transducers used in high power ultrasonic applications are composed of piezoelectric ceramics, metallic blocks and a central bolt that pre-stresses the assembly. The impedance characterization of these transducers has been done by using numerical methods but, in many cases, one-dimensional simplified models are enough to a good physical interpretation of the problem. In this work was used the Mason's equivalent electric circuit for one-dimensional modeling of composed transducers. It was derived Thevénin's equivalent circuit to simplify the problem and evaluate the effects of the central bolt on the resonances. Some transducers were mounted and the transmission line circuit was used to measure the resonance frequencies. The results show a good fitting between the experimental and simulated by electric circuit. By using the presented model it was identify other longitudinal vibration modes further that considered in previous models and, so that, it was increased the possibility of investigate the behavior of the transducers using the frequency spectrum.

Piezoelectric properties of textured Bi3.25La0.75Ti2.97V0.03O12 ceramics fabricated by reactive templated grain growth method

We have fabricated Bi3.25La0.75Ti2.97V0.03O12 (BLTV) ceramics by reactive templated grain growth method using a Bi4Ti3O12 template and investigated the electromechanical coupling coefficient (k) and temperature coefficient of a resonant frequency as a function of temperature. The highly preferentially [00l] oriented BLTV ceramics were obtained and the grain-orientation factor (Lotgering factor) was 83%. The electromechanical coupling coefficient of the longitudinal vibration mode (k 33) and the temperature coefficient of resonant frequency of textured BLTV ceramics were enhanced compared to those of nontextured BLTV ceramics.

Forced vibration analysis for dynamic coupling of finite-element spring-reduced suspension system

The current paper studies the dynamic behaviour of a coil spring in a vehicle suspension system. A portion of the coil spring is contacted with the top and bottom spring pads. The contact interface is modelled as a set of linear spring elements on the contact nodes of the coil spring. The eigensensitivity analysis is conducted to investigate the frequency variation of the stiffness-coupled system with respect to the contact stiffness variation. In the forced vibration analysis, the transfer function through the coil spring is obtained. The contribution of the coil spring modes to the load transfer is calculated by the modal contribution factor. It is shown that some of the longitudinal and bending vibration modes participate on the load transfer.

Radial vibration mode of 0.71Pb(Mg1∕3Nb2∕3)O3–0.29PbTiO3 single crystal and its applications

Ferroelectric single crystal (1−x)Pb(Mg1∕3Nb2∕3)O3–xPbTiO3 (PMNT) has attracted considerable attention for its outstanding piezoelectric properties after poled along the ⟨001⟩ or ⟨101⟩ directions and it is being actively applied to various ultrasonic devices. However, almost all previous applications focus on the longitudinal extension, transverse extension, thickness extension and thickness shear vibration mode. Here, we investigated the radial vibration mode of the ⟨001⟩ poled 0.71Pb(Mg1∕3Nb2∕3)O3–0.29PbTiO3 single crystal. Both the finite element simulation and experimental results have shown that the performance of radial vibration mode is excellent. The coupling coefficient of radial vibration mode can reach 0.84 and the anisotropy of the circular plate is very weak after it was poled along the ⟨001⟩ direction. Based on this mode, we further designed and fabricated a disk-type piezoelectric transformer and the open circuit voltage step-up ratio reached about 50 with no spurious vibration mode around the resonance frequency. All these have shown that the radial vibration mode of PMNT single crystal is also promising and useful for other piezoelectric device applications.

Operating frequency tracking of single phase driving type piezoelectric motors

We developed a multi (or mixed) mode excitation type piezoelectric motor that uses a rectangular bar type piezoelectric multilayer stator as the vibrating element. The stator has a first longitudinal vibration mode in a direction of longest length and second flexural mode in a direction of thickness. During operation of the motor, these two modes are coupled so at the two end surfaces, elliptical motions are generated. The elliptical motion at one end of the stator is transferred to a moving element through frictional contact. This paper introduces structure and operating principal of the piezoelectric multilayer stator. An equivalent circuitry model for the free stator and a frequency tracking method to operate the motor at its optimum operating frequency are also proposed. The frequency tracking method not only finds the best operating frequency, it also tracks the frequency variations from sample to sample and operating frequency shift due to temperature change.

Electron-phonon coupling and longitudinal mechanical-mode cooling in a metallic nanowire

We investigate electron-phonon coupling in a narrow suspended metallic wire, in which the phonon modes are restricted to one dimension but the electrons behave three-dimensionally. Explicit theoretical results related to the known bulk properties are derived. We find out that longitudinal vibration modes can be cooled by electronic tunnel refrigeration far below the bath temperature provided the mechanical quality factors of the modes are sufficiently high. The obtained results apply to feasible experimental configurations.

Vibrational Behavior of Laminated Annular Plates

In order to study the vibrational behavior of laminated annular plates,and effects of laminations on the vibrations of the plates,the vibrations of a series of solid annular plates are calculated by using the finite element method to obtain reference for comparison with experimental data.An extensive range of experiments is performed on both a series of solid plates and a series of laminated plates under a range of normal clamping pressures.Based on the calculated and experimental results,it is found that vibrational behavior of the laminated plates is dominated by that of the individual plate,of which the laminated plates are composed. However,laminations have great effects on the vibrational behavior of the laminated plates,and the effects depend upon the mode type,the clamping pressure and the number of plate assembly.With increasing of the numbers of laminations and increasing of the claming pressure,the longitudinal vibration modes vanish quickly,and only the in-plane modes persist and dominate the vibrations of laminated annular plates.

Hyper-Raman Spectrum of Vitreous Silica from First Principles

We introduce a scheme for the calculation of nonresonant hyper-Raman spectra of vitreous materials within a density-functional formulation. Hyper-Raman tensors are obtained through the application of finite electric fields and explicitly account for the nonlinear modulation of the dielectric susceptibility by longitudinal vibrational modes. We apply our scheme to a model of vitreous silica in various scattering geometries and polarization conditions, finding good agreement with experiment. The calculated spectra are analyzed both in terms of transverse and longitudinal modes and in terms of underlying atomic vibrations.

Piezoelectric Materials for Biomedical Applications

A piezoelectric microactuator for minimally invasive surgery procedures was developed using the piezoelectric tube actuator. The tube was fabricated by electrophoretic deposition of a doped PZT powders on the graphite rod substrate and co-sintering. The obtained tube shows maximum strain 0.045% in 31 mode and coercive field 1.5 kV/mm under static condition. Under dynamic condition, bending and longitudinal vibration modes can be identified from impedance spectrum and simulation. Theoretical analysis indicates that the displacement of the two modes depends on the geometry, material property, driving condition and damping conditions. The developed device uses bending mode to create rotation mechanical motion, and longitudinal mode to produce ultrasonic energy to soften and break up the target into fragments.

Several key issues in developing of cylinder type 3-DOF ultrasonic motor

A cylinder type 3-DOF ultrasonic motor consists of a cylinder-shaped stator and a spherical rotor. Two bending vibration modes with orthogonality and a longitudinal vibration mode are excited in the stator by three groups of piezoelectric ceramic elements, respectively. The combinations of any two modes mentioned above push the rotor to rotate in one plane. Totally, the rotor can rotate around x, y or z-axes. This paper summarizes some key issues in developing the motor whose output properties and efficiency can be improved. These key issues include selection of the vibration modes, consistency of the modal frequencies, placement of the piezoelectric ceramic elements and the supporting plane, setting of pre-pressure and rotor–stator contact angle, influence of interfering modes.

P-07 Evaluation of Dynamic Elastic Modulus Distribution of Prismatic Concrete Specimens Based on Flexural and Longitudinal Vibration Modes by Resonance Method

P-07 Evaluation of Dynamic Elastic Modulus Distribution of Prismatic Concrete Specimens Based on Flexural and Longitudinal Vibration Modes by Resonance Method

Laminated piezoelectric transformer

A laminated piezoelectric transformer is provided using the longitudinal vibration modes for step-up voltage conversion applications. The input portions are polarized to deform in a longitudinal plane and are bonded to an output portion. The deformation of the input portions is mechanically coupled to the output portion, which deforms in the same longitudinal direction relative to the input portion. The output portion is polarized in the thickness direction relative its electrodes, and piezoelectrically generates a stepped-up output voltage.

Impact of surface bond-order loss on phonon dispersion relations and thermal conductivity of cylindrical Si nanowires

The effect of bond-order loss of atoms in the surface skin on the thermal conductivity in cylindrical silicon nanowires has been investigated based on the isotropic elastic continuum model. The frequency change of torsional, longitudinal, and flexural modes of phonon vibration have been examined with a core-shell cylindrical rod structure. Results suggest that the thermal conductivity of the wire increases significantly due to the effect of surface bond-order loss that modifies the Young's modulus in the surface atomic shells, yet atoms in the core region remain as they are in the bulk.

A Finite Element Model for Ultrasonic Cutting of Toffee

The performance of an ultrasonic cutting device critically relies on the interaction of the cutting tool and the material to be cut. A finite element (FE) model of ultrasonic cutting is developed to enable the design of the cutting blade to be influenced by the requirements of the toolmaterial interaction and to allow cutting parameters to be estimated as an integral part of designing the cutting blade. In this paper, an application in food processing is considered and FE models of cutting are demonstrated for toffee; a food product which is typically sticky, highly temperature dependent, and difficult to cut. Two different 2D coupled thermal stress FE models are considered, to simulate ultrasonic cutting. The first model utilises the debond option in ABAQUS standard and the second uses the element erosion model in ABAQUS explicit. Both models represent a single blade ultrasonic cutting device tuned to a longitudinal mode of vibration cutting a specimen of toffee. The model allows blade tip geometry, ultrasonic amplitude, cutting speed, frequency and cutting force to be adjusted, in particular to assess the effects of different cutting blade profiles. The validity of the model is highly dependent on the accuracy of the material data input and on the accuracy of the friction and temperature boundary condition at the blade-material interface. Uniaxial tensile tests are conducted on specimens of toffee for a range of temperatures. This provides temperature dependent stress-strain data, which characterises the material behaviour, to be included in the FE models. Due to the difficulty in gripping the tensile specimens in the test machine, special grips were manufactured to allow the material to be pulled without initiating cracks or causing the specimen to break at the grips. A Coulomb friction condition at the bladematerial interface is estimated from experiments, which study the change in the friction coefficient due to ultrasonic excitation of a surface, made from the same material as the blade, in contact with a specimen of toffee. A model of heat generation at the blade-toffee interface is also included to characterise contact during ultrasonic cutting. The failure criterion for the debond model assumes crack propagation will occur when the stress normal to the crack surface reaches the tensile failure stress of toffee and the element erosion model uses a shear failure criterion to initiate element removal. The validity of the models is discussed, providing some insights into the estimation of contact conditions and it is shown how these models can improve design of ultrasonic cutting devices.

Study of a new type linear ultrasonic motor with double-driving feet

A new type linear USM with double-driving feet has been developed. The stator consists of eight piezoelectric ceramic plates and one brass plate. Piezoelectric ceramics plates are polarized along the thickness and are symmetrically bonded to the two surfaces of one rectangle brass plate. Double-driving feet are assembled on the same side of the brass plate. The working vibration mode is a composite in-plane bimode, which consists of the first longitudinal in-plane vibration mode and the second bending one. The basic size of the linear USM is determined carefully by FEA. The characteristics of the prototype motor were measured experimentally.

Modeling rot in wood by replacement of wood with sand: an experimental study

Rot is known to affect the strength properties of wood. At the same time, the damping properties of the attacked material have also been shown to change. This article presents the results of an experimental study in which rot in wood was modeled by the replacement of wood with sand. The procedure entailed the drilling of holes in the body of a wooden beam, filling the holes with sand, and monitoring the changes induced by the sand-filled holes on the values of the modulus of elasticity (MOE) and of the loss factor. The MOE was calculated from the resonance frequency of the first longitudinal mode of vibration, and the loss factor was obtained indirectly from the impulse response by means of a room acoustical technique. The results show that the MOE value, and hence the strength characteristic of the wood specimen, decreases at the same time as the loss factor increases.

Broadband barrel-stave flextensional transducers

The last time I discussed underwater transduction technologies with Joe Blue was at the 125th Meeting of the Acoustical Society of America in May 1993. As we enjoyed lunch on the patio of a downtown Ottawa bistro under a sunny spring sky, the discussion touched on broadband transducers for naval applications. His ideas were insightful, motivating me to redesign and improve my original 1989 broadband barrel-stave flextensional transducer the following year. Over the last decade 30 experimental units were built at DRDC Atlantic, most of them used in marine mammal and coastal surveillance applications [D.F. Jones, J. Acoust. Soc. Am. 117, 2447 (2005); 118, 2038–2039 (2005)]. This paper will present electroacoustic measurements made at both the DRDC Atlantic Acoustic Calibration Barge on Bedford Basin near Halifax, Nova Scotia and the NAVSEA Seneca Lake Sonar Test Facility near Dresden in upstate New York. The performance parameters of interest include resonance frequencies, mechanical quality factors, transmitting voltage response versus water depth, and directivity patterns. [Work supported in part by the Office of Naval Research.]

Effect of viscous loss on mechanical resonators designed for mass detection

Simple models are presented for estimating viscous damping of fluid (gas or liquid) loaded mechanical resonators. The models apply to beams in flexural modes of vibration, and to thin beams and plates in longitudinal modes of vibration. Predictions of the associated quality factor are compared with measured values for several macroscale and microscale resonators. The scaling of viscous loss with oscillator size is discussed. The minimum detectable mass is estimated for several oscillator designs and it is shown that, for comparably sized devices, longitudinal resonators have the lowest threshold of detection. This minimum detectable mass is proportional to scale to the power 1.75 for all resonator architectures limited by viscous damping, and it is shown that the viscous loss is 220 times larger in water than in air.

Influence of the deposition parameters on the texture of boron nitride thin films synthesized in a microwave plasma-enhanced reactor

Thin films of boron nitride (BN) have been deposited at low temperature (below 300 °C) by microwave plasma-enhanced chemical vapor deposition (PECVD), using borane dimethyl amine, as boron precursor. The plasma was composed of a mixture of argon and nitrogen and was excited with a microwave power. In addition, a radiofrequency signal was applied to the substrate holder in order to negatively bias the sample during the deposition process. The characterization has been performed by infrared transmittance spectroscopy, and the influence of the bias on the deposition of the films has been studied. We have observed that the behaviour of the layers is that of an anisotropic uniaxial medium, and that they are composed of a collection of nanocrystallites of the hexagonal phase. These crystallites are textured with the very same orientation of their c-axis relative to the normal of the sample. By performing the IR transmittance measurements at oblique incidence, additional bands of absorption related to longitudinal optical vibration modes allow us to determine very easily this texturation. The applied bias is shown to have a direct influence on it, the larger the voltage, the more the crystallites are oriented parallel to the sample surface, until a sputtering regime is reached at an even higher voltage.

Skeletal silica characterization in porous-silica low-dielectric-constant films by infrared spectroscopic ellipsometry

Porous-silica low-dielectric-constant (low-k) films were prepared using a sol-gel method based on the self-assembly of surfactant templates. No change in the refractive index at 633 nm nor in the infrared-absorption intensities of C–H and O–H stretching vibrations at around 2900 and 3400cm−1 of porous-silica low-k films were observed after annealing at each temperature from 523 to 723 K. On the other hand, the Young’s elastic modulus and hardness increased with the increase of annealing temperature. The structure in the complex dielectric function of porous-silica low-k films observed in between 1000 and 1400cm−1 is assigned as the asymmetric stretching vibration mode of the Si–O–Si bond. By applying the effective-medium theory by Bruggeman to the experimental results from infrared spectroscopic ellipsometry, we analyzed the skeletal silica structures. The peak positions of transverse (ωTO) and longitudinal (ωLO) vibration modes for Si–O–Si network in the silica skeleton of porous-silica films changed from 1061 to 1068cm−1 and from 1219 to 1232cm−1, respectively, with the annealing temperature. It is shown that the ωLO2∕ωTO2 of skeletal silica correlates with Young’s elastic modulus of porous-silica low-k films.