Resonant Vibration Modes Research Articles

Piezoelectric Characterization with Mechanical Excitation in PZT Bar with Non-Electrode Boundary Condition–K31 Mode Case

We introduced an advanced piezoelectric characterization method with mechanical excitation on partial electrode samples, which can determine additional physical parameters the conventional full-electrode electrical excitation method cannot provide. A non-electrode sample with only 10% electrode at the center of a rectangular k31 piezoelectric plate has the benefits for measuring the extensive parameters directly and much precisely. In this paper, we derived first the exact analytical solutions on the partial electrode configuration, including the 10% mechanical excitation part in a partial non-electrode sample for calculating there sonance vibration mode and mechanical quality factors of the composite bar sample for obtaining the extensive elastic compliance and loss factor. The result suggests that the almost accurate values can be obtained even for a specimen with up to 40% center electrode area in the k31 mode samples. Second objective is to compare three different simulations (ATILA FEM, 6-terminal Equivalent Circuit and Analytical Solution). This mechanical excitation method has the benefit in measuring physical parameters which cannot be obtained directly from the IEEE Standard electrical excitation method. Keywords: Direct loss measurement; intensive and extensive parameters; resonance vibration mode; PZT; mechanical quality factor;

Micro-mechanical resonators for dynamically reconfigurable reduced voltage logic gates

Due to the limitations of transistor-based logic devices such as their poor performance at elevated temperature, alternative computing methods are being actively investigated. In this work, we present electromechanical logic gates using electrostatically coupled in-plane micro-cantilever resonators operated at modest vacuum conditions of 5 Torr. Operating in the first resonant mode, we demonstrate 2-bit XOR, 2- and 3-bit AND, 2- and 3-bit NOR, and 1-bit NOT gates; all condensed in the same device. Through the designed electrostatic coupling, the required voltage for the logic gates is reduced by 80%, along with the reduction in the number of electrical interconnects and devices per logic operation (contrary to transistors). The device is dynamically reconfigurable between any logic gates in real time without the need for any change in the electrical interconnects and the drive circuit. By operating in the first two resonant vibration modes, we demonstrate mechanical logic gates consisting of two 2-bit AND and two 2-bit XOR gates. The device is tested at elevated temperatures and is shown to be functional as a logic gate up to 150 °C. Also, the device has high reliability with demonstrated lifetime greater than 5 × 1012 oscillations.

Two modes resonant combined motion for insect wings kinematics reproduction and lift generation

This paper presents an original concept using a two resonant vibration modes combined motion to reproduce insect wings kinematics and generate lift. The key issue is to design the geometry and the elastic characteristics of artificial wings such that a combination of flapping and twisting motions in a quadrature phase shift could be obtained. This qualitatively implies to bring the frequencies of the two resonant modes closer. For this purpose, a polymeric prototype was micromachined with a wingspan of 3 cm, flexible wings and a single actuator. An optimal wings configuration was determined with a modeling and validated through experimental modal analyses to verify the proximity of the two modes frequencies. A dedicated lift force measurement bench was developed and used to demonstrate a lift force equivalent to the prototype weight. Finally, at the maximum lift frequency, high-speed camera measurements confirmed a kinematics of the flexible wings with flapping and twisting motions in phase quadrature as expected.

Evaluation of Direct Drive Capsule Fill-Tube Assembly Survivability in Support of the 100 GBar Campaign

Capsule fill-tube target assemblies (CFTAs) for direct drive have been demonstrated in the past for Laboratory for Laser Energetics (LLE) cryogenic layering studies, evolving and building upon successful deliveries for the National Ignition Facility [Saito et al., Fusion Sci. Tech., Vol. 55, p. 337 (2009); Johal et al., Fusion Sci. Tech., Vol. 55, p. 331 (2009); Saito et al., Fusion Sci. Tech., Vol. 59, p. 271 (2011); Moreno et al., Fusion Sci. Tech., Vol. 59, p. 46 (2011); and Rice et al., High Power Laser Sci. Eng., Vol. 5, p. 7 (2017)]. The current 100 Gigabar (GBar) Campaign requires tighter specifications over prior CFTA work in terms of robustness and reduced fill-tube diameter and glue spot size, which impact the survivability of the CFTA. To tackle these challenges, General Atomics and LLE are developing a direct-drive CFTA that survives all fabrication activities, from assembly and qualification testing to transport, cryogenic layering, and target chamber insertion at the Omega Laser Facility.Fifty-five CFTAs of three main designs have been constructed and tested to date, building off the current LLE cryogenic layering study of CFTA design (typically 870-μm-diameter × 25-μm-thick wall capsule). Variations of glass fill tube sizes ranged from 30, 20, and 10 µm in diameter. Testing protocols were developed to enable comparison of different designs against one another and to evaluate their robustness at room temperature. The testing protocols include leak checks, resonant vibration mode identification, and vibration survival testing against a power spectral density input. This paper compares the different design trade-offs, measurements, and results including room temperature survivability, ringdown response, leak tests, and scanning electron microscope images taken of failed fill tubes and glue joints. A design recommendation is put forth meeting the design constraints, which consists of a polymicro-composite tube and 10-µm fill tube, ensuring survivability at cryogenic temperature, a higher first-resonance mode, and smaller fuel volume.

Vibration Characteristics of Rock Under Harmonic Impact

Modal analysis of rock is done in this study, and the results of numerical analysis are presented. Meanwhile, the amplitude-frequency characteristic curve of rock in steady state response is investigated based on the principle of vibration. In addition, indoor experiments are carried out to further analyze the vibration characteristics of rock under harmonic impact. Three main control parameters are considered, including drilling way, excitation frequency and impacting amplitude. Our investigations confirm that the rock has different resonant frequencies and vibration modes in different orders for free vibration system, and there is only one resonant frequency for a rock with one degree of freedom. Based on theoretical analysis and indoor experiments, it can be concluded that the vibration amplitude under resonant frequency of rock is significantly higher than that under non-resonant frequency and in conventional drilling. Also, the vibration response of rock is in the harmonic form by the harmonic impact, and increases with the increase of the impacting amplitude. The vibration characteristics of rock by harmonic impact are validated by numerical analysis and experimental results. Harmonic vibration impact drilling can greatly enhance the vibration amplitude of rock, and further improve the rate of penetration.

Electrostrictive microelectromechanical fibres and textiles

Microelectromechanical systems (MEMS) enable many modern-day technologies, including actuators, motion sensors, drug delivery systems, projection displays, etc. Currently, MEMS fabrication techniques are primarily based on silicon micromachining processes, resulting in rigid and low aspect ratio structures. In this study, we report on the discovery of MEMS functionality in fibres, thereby opening a path towards flexible, high-aspect ratio, and textile MEMS. The method used for generating these MEMS fibres leverages a preform-to-fibre thermal drawing process, in which the MEMS architecture and materials are embedded into a preform and drawn into kilometers of microstructured multimaterial fibre devices. The fibre MEMS functionality is enabled by an electrostrictive P(VDF-TrFE-CFE) ferrorelaxor terpolymer layer running the entire length of the fibre. Several modes of operation are investigated, including thickness-mode actuation with over 8% strain at 25 MV m−1, bending-mode actuation due to asymmetric positioning of the electrostrictive layer, and resonant fibre vibration modes tunable under AC-driving conditions.

Vibration mode and vibration shape under excitation of a three phase model transformer core

Structural vibration characteristics and vibration shapes under three-phase excitation of a archetype transformer core were investigated to consider their influences on transformer noise. Acoustic noise and vibration behavior were measured in a three-limb model transformer core. Experimental modal analysis by impact test was performed. The vibration shapes were measured by a laser scanning vibrometer at different exciting frequencies. Vibration amplitude of the core in out-of-plane direction were relatively larger than those in other two in-plane directions. It was consistent with the result that the frequency response function of the core in out-of-plane direction was larger by about 20 dB or more than those in in-plane directions. There were many vibration modes having bending deformation of limbs in out-of-plane direction. The vibration shapes of the core when excited at 50 Hz and 60 Hz were almost the same because the fundamental frequencies of the vibration were not close to the resonance frequencies. When excitation frequency was 69 Hz which was half of one of the resonance frequencies, the vibration shape changed to the one similar to the resonance vibration mode. Existence of many vibration modes in out-of-plane direction of the core was presumed to be a reason why frequency characteristics of magnetostriction and transformer noise do not coincide.

Нормирование динамического коэффициента к временной нагрузке при расчете мостов на высокоскоростных железнодорожных магистралях

Objective: Improvement of dynamic analysis method of simple beam spans in the process of high-speed trains impact. Methods: Mathematical modeling with numerical and analytical methods of building mechanics was applied. Results: The parameters of high-speed trains influence on simple beam spans of bridges were analyzed. The method of dynamic factor to live load determination was introduced. The reliability of the method in question was corroborated by the results of numerical simulation of high-speed trains’ movement by beam spans with different speeds. The introduced algorithm of dynamic analysis was based on the connection between maximum acceleration of a beam span in resonance vibration mode and the basic factors of stress-strain state. The method in question makes it possible to determine both maximum and bottom values of main loading in a construction, which determines the possibility of endurance tests. It was noted that dynamic additions for the components of stress-strain state (bending moments, shear force, vertical deflections) were different. The fact in question determines the necessity of differential approach application to identify dynamic factors in the process of calculation testing on the first and the second groups of limit states. Practical importance: The method of dynamic factors’ determination presented in the study makes it possible to perform dynamic analysis and determine the main loading in simple beam spans without application of numerical modeling and direct analytical analysis, which considerably reduces labor costs on engineering.

Piezoelectric particle sizer for measuring bed load using a combination of resonance vibration modes

To predict environmental changes and prevent disasters in rivers it is important to track how the size distributions of sand and stones in the riverbed change over time. In this paper, we used a passive piezoelectric sensor to measure the particle distribution of a simulated bed load. The sensor had a simple, robust structure consisting of a circular aluminum plate and an annular piezoelectric transducer. The detection characteristics were evaluated by measuring the impact of alumina spheres with diameters of 3–8mm in air. When particles hit the sensor, the impact excited a flexural vibration in the circular plate, generating electric power through the piezoelectric effect. The electric output signal exhibited two main frequency peaks, at 16.3 and 66.7kHz, whose amplitude ratio depended on particle size. These two frequencies correspond to the fundamental and third resonance vibration modes. When particles hit the sensor surface sequentially, we could determine their particle sizes from short-term frequency analysis of the observed voltage waveform.

A novel squeeze-film air bearing with flexure pivot-tilting pads: Numerical analysis and measurement

This study proposes a novel squeeze-film air bearing based on near-field acoustic levitation technology. Unlike previous squeeze-film bearings, the new bearing employs flexure pivot-tilting pads as vibration surfaces and provides higher vibration amplitude and better stability for rotor systems. The flexure pad structure eases processing and adapts well to squeeze action. This paper presents a theoretical model of the new bearing that combines models for squeeze film and flexure pivot-tilting pads to study the float characteristics. Resonant frequency and vibration mode of the bearing were obtained by using finite element modelling and validated by experimental results. The authors investigated the mechanism of pressure generation of squeeze film and pad movement. The load carrying capacity of the bearing was experimentally investigated. Numerical and experimental results show that the proposed bearing is a feasible non-contact bearing for high-speed and high-precision rotating machineries.

Vibration analysis and development of an ultrasonic elliptical vibration tool based on a portal frame structure

An ultrasonic elliptical vibration tool utilizing the coupled resonant vibration modes is the key component in the elliptical vibration cutting/texturing process, which has been successfully applied to ultra-precision machining and surface texturing. In this paper, an analytical approach is proposed to analyze the resonant frequency and mode shapes of the ultrasonic elliptical vibration tool. A new design of ultrasonic elliptical vibration tool based on a portal frame structure is presented and analyzed using the proposed model. The model assumes Euler-Bernoulli beams and utilizes the transfer matrix technique to reduce the order of the system to only six variables. The model can be utilized to provide a systematic approach for an optimal design and be extended to dynamic analysis of the tool for study of machine-tool dynamics. Finite element simulation results as well as experimental data based on the prototype design are presented to verify the model. An application of the proposed tool is also demonstrated in machining micro/nano-structured surfaces for structural coloration.

Resonance of damping

Considered is a linear forced vibrating structure (primary structure) to which another linear passive structure (absorber) is attached at a number of points. It is shown analytically that the vibration power flow from the primary structure to the absorber reaches its absolute maximum if two conditions are met simultaneously. The first condition is well known: there must be a frequency resonance when the forcing frequency coincides with one of the eigen frequencies of the primary structure/absorber system. The second condition is also of the resonant type: at the frequency resonance vibration mode, the amount of damping in the absorber must be equal to the amount of damping in the primary structure. This can be called the resonance of damping. The vibration or sound absorber that satisfies both resonance conditions can be called the best or the perfect absorber. The theoretical result obtained has been verified in a laboratory experiment with a simple primary structure and a dynamic vibration absorber as well as in an impedance tube on a resonant sound absorber. Relation to results known from the literature and possible applications using metamaterials are discussed.

A New Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motions of an Axially Moving Beam With Internal Resonance Under Single-Tone External Excitation

Quasi-periodic motion is an oscillation of a dynamic system characterized by m frequencies that are incommensurable with one another. In this work, a new incremental harmonic balance (IHB) method with only two time scales, where one is one of the m frequencies, referred to as a fundamental frequency, and the other is an interval distance of two adjacent frequencies, is proposed for quasi-periodic motions of an axially moving beam with three-to-one internal resonance under single-tone external excitation. It is found that the interval frequency of every two adjacent frequencies, located around the fundamental frequency or one of its integer multiples, is fixed due to nonlinear coupling among resonant vibration modes. Consequently, only two time scales are used in the IHB method to obtain all incommensurable frequencies of quasi-periodic motions of the axially moving beam. The present IHB method can accurately trace from periodic responses of the beam to its quasi-periodic motions. For periodic responses of the axially moving beam, the single fundamental frequency is used in the IHB method to obtain solutions. For quasi-periodic motions of the beam, the present IHB method with two time scales is used, along with an amplitude increment approach that includes a large number of harmonics, to determine all the frequency components. All the frequency components and their corresponding amplitudes, obtained from the present IHB method, are in excellent agreement with those from numerical integration using the fourth-order Runge–Kutta method.

Calibration of piezoelectric RL shunts with explicit residual mode correction

Piezoelectric RL (resistive-inductive) shunts are passive resonant devices used for damping of dominant vibration modes of a flexible structure and their efficiency relies on the precise calibration of the shunt components. In the present paper improved calibration accuracy is attained by an extension of the local piezoelectric transducer displacement by two additional terms, representing the flexibility and inertia contributions from the residual vibration modes not directly addressed by the shunt damping. This results in an augmented dynamic model for the targeted resonant vibration mode, in which the residual contributions, represented by two correction factors, modify both the apparent transducer capacitance and the shunt circuit impedance. Explicit expressions for the correction of the shunt circuit inductance and resistance are presented in a form that is generally applicable to calibration formulae derived on the basis of an assumed single-mode structure, where modal interaction has been neglected. A design procedure is devised and subsequently verified by a numerical example, which demonstrates that effective mitigation can be obtained for an arbitrary vibration mode when the residual mode correction is included in the calibration of the RL shunt.

Piezoelectric particle counter using the resonance vibration modes of a circular plate

In the field of environmental measurements, robust and simple sensors with no electric power supply are required. In the river, the size distributions of sand and small stones in river-bed are important factor for river disaster prevention. In this report, a passive piezoelectric sensor for measurement of the particle distribution in flow was investigated. The sensor consists of an aluminum circular plate (diameter: 50 mm; thickness: 2 mm) and an annular piezoelectric transducer (inner radius: 5 mm; outer radius: 10 mm). Alumina spheres with several diameters (φ = 3, 5, and 8 mm) were employed as small particles. When the particles hit the surface of the sensor, the flexural vibration is excited on the circular plate and the electric power is generated through the piezoelectric effect. Two main peaks at 16.3 and 66.7 kHz appeared in the output signal, and the ratio of these peaks depended on the particle size. From the finite element analysis, it was found that these frequencies of 16.3 and 66.7 kHz correspond with the fundamental and second resonance vibration modes. These results indicate that the particle size can be determined from the frequency spectrum of the output signal.

Higher resonant mode effect on the performance of piezo actuated 2-DOF rectangular cantilever shaped resonators (2-DOF RCR) for liquid viscosity and density sensing

According to the demand for a highly sensitive resonant sensor, a 2-DOF RCR (2-degrees of freedom rectangular cantilever shaped resonators) with higher resonant mode of vibration is developed for sensing of liquid viscosity and density. The measurement principle is based on tracking the resonant characteristics of 2-DOF RCR system which depends on the density and viscosity of liquids it operates in. The 2-DOF RCR consists of a driver and absorber mass of identical natural frequency with a disparity in mass and connected by a strong mechanical coupling unit, thus the resonant amplitude and resonant frequency is enhanced at 1st mode compared with 1-DOF (1-degree of freedom) system. For further improving the sensitivity performance, the 3rd resonant mode vibration of 2-DOF RCR system is investigated. The system is evaluated for its performance in liquids of viscosity ranging from 0.23 to 1400 mPas and density ranging from 713 to 1261 kg/m3 at 3rd mode and compared with 1st mode of vibration. Good agreement with the simulated results from theoretical model and experimental results is reported and the enhanced performance of 2-DOF RCR system by using higher mode is also confirmed. Compared to the 1st mode, the sensitivity in terms of resonant frequency against density is improved with 22.75 % and 19 % in aqueous based and oil based liquids respectively and the sensitivity in terms of quality factor against viscosity is improved by 22.4 % and 30 % in aqueous and oil based liquids, at 3rd mode of vibration.

Phase stability and lattice thermal conductivity reduction in CoSb3 skutterudites, doped with chalcogen atoms

We report a significant reduction in the lattice thermal conductivity of the CoSb3 skuttertudites, doped with chalcogen atoms. Te/Se chalcogen atoms doped CoSb3 skutterudite samples (Te0.1Co4Sb12, Se0.1Co4Sb12, Te0.05Se0.05Co4Sb12) are processed by ball milling and spark plasma sintering. X-ray diffraction data combined with energy dispersive X-ray spectra indicate the doping of Te/Se chalcogen atoms in the skutterudite. The temperature dependent X-ray diffraction confirms the stability of the Te/Se doped CoSb3 skutterudite phase and absence of any secondary phase in the temperature range starting from 300 K to 773 K. The Raman spectroscopy reveals that different chalcogen dopant atoms cause different resonant optical vibrational modes between the dopant atom and the host CoSb3 skutterudite lattice. These optical vibrational modes do scatter heat carrying acoustic phonons in a different spectral range. It was found that among the Te/Se chalcogen atoms, Te atoms alter the host CoSb3 skutterudite lattice vibrations to a larger extent than Se atoms, and can potentially scatter more Sb related acoustic phonons. The Debye model of lattice thermal conductivity confirms that the resonant phonon scattering has important contributions to the reduction of lattice thermal conductivity in CoSb3 skutterudites doped with Te/Se chalcogen atoms. Lattice thermal conductivity ∼ 0.9 W/mK at 773 K is achieved in Te0.1Co4Sb12 skutterudites, which is the lowest value reported so far in CoSb3 skutterudites, doped with single Te chalcogen atom.

Electromechanical models of nanoresonators

The goal of this study is to construct simple electromechanical models of nanoresonators as mass detectors. A major obstacle in the achievement of sufficient measurement accuracy for the resonant frequency associated with the adsorption of additional mass onto the graphene layer is a low quality factor of the oscillatory system containing the graphene layer. A graphene resonator can be considered as an elastic system with distributed parameters. The application of the Galerkin method to study nearly resonant vibrational modes reduces the problem to considering an oscillatory system with a few degrees of freedom with pronounced nonlinear properties. These properties are, first of all, due to the nonlinear dependence of the forces produced by the electric field on the graphene deflection and, second, due to the nonlinear dependence of the graphene layer tension on its deflection. Taking into account the nonlinear properties leads to the appearance of characteristic drops in the resonance curve which allow for a more accurate resonant frequency measurement. Resonance curves with such characteristic drops can be obtained using a demonstration experimental macromodel of the resonator. Two absolutely new layouts are proposed, such as a differential resonator and resonator with parametric excitation. The oscillations excited in the differential resonator that contains two graphene layers resemble beats. In this case, small changes in the mass of the main layer correspond to significant changes in the frequency of the envelope. This effect is illustrated by oscillograms obtained for an experimental macromodel of the differential resonator. The parametric resonator has one graphene layer between two conducting surfaces. Parametric excitation of steady-state high amplitude oscillations is possible in this resonator only in a narrow frequency band close to the eigenfrequency. The band width reduces with a decrease in the quality factor of the oscillatory system. The latter fact can be useful for the improvement of eigenfrequency measurement accuracy at a low quality factor of the oscillatory system.

Dynamic stress analysis of the specimen gauge portion with a circular profile for the ultrasonic fatigue test

An hourglass-shaped specimen has been utilized for the ultrasonic fatigue test (UFT) at a resonance frequency around 20kHz. Although the gauge portion of the actual test specimens was made with a circular arc shape, the stress along the gauge portion has been measured by the conventional stress equation assuming a gauge portion with the form of a hyperbolic cosine. In this study, stress distribution results by finite element analysis (FEA) in forced resonant vibration mode showed that the shape of a circular arc caused considerably higher stresses at the center of the gauge portion than did the hyperbolic cosine. The error of the stress equation occurring due to the difference in the gauge portion profile was compensated for by using the forced vibration factor (C1) and the gauge shape factor (C2). Thus, stress concentration effects in specimens with various gauge lengths were quantified to determine the actual fatigue strength.

Study of Rubber Blends by Electronic Speckle Pattern Interferometry

Nowadays, the optical methods for deformation measurement are gaining more and more applications from the aspect of solution of problems relating to elasticity and strength. The advantage of such methods is based on the measurement of non-destructive way without assembly of measuring elements regarding to the critical areas of structures. One of these contactless measuring methods is Electronic Speckle Pattern Interferometry ESPI that is based on the discovery of so-called speckle patterns. Electronic Speckle Pattern Interferometry is an optical full-field measurement method for determination of deformations of object surfaces with sensitivity below fractions of the wavelength of light. A back scattered object beam of an object surface and a reference beam, originating from the same laser light source, are superimposed on a video camera and interfere to a speckle pattern. Speckle pattern is based on the record before and after deformation of the object yield to a non-unique fringe pattern. Using a phase shifting method, this non-uniqueness can be solved and the fringe pattern can be evaluated using a computer algorithm. In this study, experimental investigation of vibration behaviour of square rubber blends plates by electronic speckle pattern interferometry (ESPI) is employed. Resonant frequencies and corresponding mode shape are obtained experimentally using the introduced method. Frequencies of resonant vibrational modes depend on elastic properties of material, especially on Young modulus E, Poisson ratio μ and density of material ρ. This fact gives us, in principle, the possibility to estimate the elastic constant of materials from the vibrational measurement. The numerical calculations by the finite element method (Cosmos) are performed and the results are compared to the experimental measurements.