Vibration Resonant Frequencies Research Articles

Research into excitation of dual frequency vibrational-rotational vibrations of screen duct by ball-type auto-balancer

The 3D model of the screen stand with the vibrational-rotational duct motion was developed. The ball-type auto-balancer, which makes it possible to create the two-frequency vibrations, is used as the vibration exciter. The main parameters, which influence the stability of the dual frequency vibrations, were defined after adjusting and testing the model. It was established that the ranges of the dual frequency vibrations are relatively large, which makes it possible to change the characteristics of vibrations with a change in the parameters from these ranges. An increase in the summary mass of the spheres increases the amplitude of slow vibrations of the duct masses in direct proportion. This increases in direct proportion the vibration energy directed toward the execution of the main technical process. An increase in the unbalanced mass on the auto-balancer case increases the amplitude of rapid vibrations of the duct masses center in direct proportion. It was established that an increase in the rotation frequency of the rotor increases the amplitude of the rapid vibration speeds of the duct in direct proportion. This increases the vibration energy directed toward the duct self-cleaning and the change through the vibrations of the mechanical properties of the workable material in proportion to the square of rotation frequency of the rotor. The simulation showed that the auto-balancer works as two separate vibration exciters. In the first one, the spheres rotate practically evenly with the resonance frequency of the duct vibrations, at this, independent of its loads, the spheres automatically adjust to this frequency, by which they excite the slow resonance duct vibrations (12 Hz) with a large amplitude. In the second one, the mass on the AB case excites the rapid duct vibrations with (any) existing non-resonant rotation frequency of the rotor.

Size-dependent resonance frequencies of longitudinal vibration of a nonlocal Love nanobar with a tip nanoparticle

Axial free vibration of a nanobar carrying a nanoparticle is studied based on the nonlocal elasticity theory and Love’s assumption. By considering inertia of radial motion during longitudinal vibration, a governing equation for a nanobar–mass oscillation system is derived via Hamilton’s principle. An exact frequency equation is obtained and an approximate simple expression for the fundamental-mode resonance frequency is given. The size effect of the resonance frequencies is elucidated. The classical Love bar theory and the nonlocal bar theory can be recovered from two special cases by setting the nonlocal parameter and Poisson’s ratio to zero, respectively. Numerical examples are given to show the influence of the nonlocal scaling parameter and attached mass on the resonance frequencies and frequency shifts. Identification formulas for estimating the mass of an attached nanoparticle and predicting the nonlocal parameter are established through the frequency change.

Energy trapping of thickness-shear modes in inverted-mesa AT-cut quartz piezoelectric resonators

abstractWe studied thickness-shear vibration frequencies and modes in an inverted-mesa AT-cut quartz plate piezoelectric resonator thinner in the center and thicker near the edges. It is electroded in the central part and unelectroded near the edges. A theoretical analysis was performed using the scalar differential equations by Stevens and Tiersten for thickness-shear vibrations of electroded and unelectroded quartz plates. Based on the variational formulation of the scalar differential equations established in a previous paper and the variation-based Ritz method with trigonometric functions as basis functions, free vibration resonant frequencies and the corresponding thickness-shear modes were obtained. It was found that the electrodes tend to trap the vibration in the central part of the resonator (energy trapping) but the curvature of the resonator surface has an opposite effect. The trapping is sensitive to the electrode thickness, the electrode length, and the curvature of the resonator surface. Hence accurate design is needed to achieve proper energy trapping in inverted-mesa resonators.

Investigations of the transverse vibration characteristics of piezoceramic circular plates with V-notches

This article pertains to experimental validation of the study presented in a previous paper by the same authors , in which the transverse vibration characteristics of piezoceramic circular plates with V-notches were investigated theoretically using Ritz’s method incorporating defined equivalent constants. For experimental measurement, two optical methods – amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometry (LDV) – were employed to conceptualize the analytical results. The AF-ESPI method demonstrates the advantages of combining high fringe sensitivity and noise reduction, which are achieved using the time-averaged and subtraction electronic speckle pattern interferometry methods, respectively. Both vibration mode shapes and resonant frequencies of V-notched piezoceramic plates were obtained using the AF-ESPI method; in addition, the resonant frequencies were also determined quickly using the LDV method. By varying the corner angles and notch–depth ratios, various types of piezoceramic plate (V-notched, sectorial, semicircular, segmented, and sharp-notched) were used for experimental measurements. Numerical calculations were performed using the finite element method, and the results were compared with the experimental measurements and theoretical predictions. It was shown that the resonant frequencies and mode shapes obtained using the two experimental methods agreed fairly closely with the theoretical and numerical results.

Dynamical responses and stabilities of axially moving nanoscale beams with time-dependent velocity using a nonlocal stress gradient theory

A higher-order mechanical model of axially moving nanoscale beams with time-dependent velocity was developed in the framework of nonlocal stress gradient theory. Based on the correlation between effective and common nonlocal bending moments, a sixth-order partial differential equation of motion with respect to the transverse displacement was derived. Unlike some previous work which assumed the velocity of axially moving nanoscale beam to be a constant, a time-dependent axial velocity was considered for the nanoscale beams. The resonance vibration frequencies were obtained according to the governing equation of motion and corresponding boundary conditions. It was concluded a nonlocal nanoscale strengthening effect that the vibration frequencies of such axially moving nanostructure increase with stronger nonlocal effects, or a larger dimensionless nonlocal nanoscale parameter causes a higher vibration frequency. A jumping phenomenon in frequency field was observed, and the vibration frequency may decrease or increase with an increase in the axial average velocity. Critical speeds of the axially non-uniformly moving nanoscale beams were defined and determined, and the critical speed versus nonlocal nanoscale revealed step and strengthening effects. The theoretical results obtained were compared with some experimental data and good agreement was achieved. Subsequently, the steady-state and stability of such moving nanostructures including the principal parametric and combination resonances were analyzed using a multiple-scale method. Some beneficial analytical procedures and theoretical formulations at nanoscale were provided. Based on specific boundary conditions, the stability boundaries of the axially accelerating nanoscale beams were determined and the unstable regions were influenced by nonlocal nanoscale significantly.

Development of tunable miniature piezoelectric-based scanners validated by the combination of two scanners in a direct image relay technique.

Miniature piezoelectric actuators are commonly used as a compact means to relay images for numerous endoscopic applications. These scanners normally consist of an electrically driven lead zirconate titanate (PZT) tube that oscillates an optical fiber at its resonant frequency. The diameter and length of the PZT and fiber, the attachment of the fiber to the PZT, as well as the driving signal determine the main characteristics of the scan-frequency and amplitude of vibration. We present a new, robust, and repeatable method for producing miniature PZT actuators. The described technology allows for continuous tuning of the scanner mechanical properties during the assembly stage, enabling adjustment of resonant frequency and subsequent amplitude of vibration without a priori knowledge of the fiber's mechanical properties. The method consists of manufacturing high-precision fiber-holding plastic inserts with diamond turning lathes that allow for the fiber length to be quickly varied and locked during operation in order to meet the preferred performance. This concept of tuned PZTs was demonstrated with an imaging technique that combined two scanners oscillating in unison at the ends of a single optical fiber to relay images without the need to correlate the driving signal with a detector.

Influence of Sandwich-Type Constrained Layer Damper Design Parameters on Damping Strength

This paper presents a theoretical study of the parameters that influence sandwich-type constrained layer damper design. Although there are different ways to reduce the noise generated by a railway wheel, most devices are based on the mechanism of increasing wheel damping. Sandwich-type constrained layer dampers can be designed so their resonance frequencies coincide with the wheel’s resonant vibration frequencies, and thus the damping effect can be concentrated within the frequency ranges of interest. However, the influence of design parameters has not yet been studied. Based on a number of numerical simulations, this paper provides recommendations for the design stages of sandwich-type constrained layer dampers.

Energy trapping of thickness-extensional modes in thin film bulk acoustic wave filters

This paper presents the thickness-extensional vibration of a rectangular piezoelectric thin film bulk acoustic wave filter with two pairs of electrodes symmetrically deposited on the center of the zinc oxide film. The two-dimensional scalar differential equations which were first derived to describe in-plane vibration distribution by Tiersten and Stevens are employed. The Ritz method with trigonometric functions as basis functions is used based on a variational formulation developed in our previous paper. Free vibration resonant frequencies and corresponding modes are obtained. The modes may separate into symmetric and antisymmetric ones for such a structurally symmetric filter. Trapped modes with vibrations mainly under the driving electrodes are exhibited. The six corner-type regions of the filter neglected by Tiersten and Stevens for an approximation are taken into account in our analysis. Results show that their approximation can lead to an inaccuracy on the order of dozens of ppm for the fundamental mode, which is quite significant in filter operation and application.

Prognostic and Remaining Life Prediction of Electronic Device under Vibration Condition Based on CPSD of MPI

Prognostic of electronic device under vibration condition can help to get information to assist in condition-based maintenance and reduce life-cycle cost. A prognostic and remaining life prediction method for electronic devices under random vibration condition is proposed. Vibration response is measured and monitored with acceleration sensor and OMA parameters, including vibration resonance frequency, especially first-order resonance frequency, and damping ratio is calculated with cross-power spectrum density (CPSD) method and modal parameter identification (MPI) algorithm. Steinberg vibration fatigue model which considers transmissibility factor is used to predict the remaining life of electronic component. Case study with a test board is carried out and remaining life is predicted. Results show that with this method the vibration response characteristic can be monitored and predicted.

An electromechanical coupling model of a bending vibration type piezoelectric ultrasonic transducer

An electromechanical coupling model of a bending vibration type piezoelectric ultrasonic transducer is proposed. The transducer is a Langevin type transducer which is composed of an exponential horn, four groups of PZT ceramics and a back beam. The exponential horn can focus the vibration energy, and can enlarge vibration amplitude and velocity efficiently. A bending vibration model of the transducer is first constructed, and subsequently an electromechanical coupling model is constructed based on the vibration model. In order to obtain the most suitable excitation position of the PZT ceramics, the effective electromechanical coupling coefficient is optimized by means of the quadratic interpolation method. When the effective electromechanical coupling coefficient reaches the peak value of 42.59%, the optimal excitation position (L1=22.52mm) is found. The FEM method and the experimental method are used to validate the developed analytical model. Two groups of the FEM model (the Group A center bolt is not considered, and but the Group B center bolt is considered) are constructed and separately compared with the analytical model and the experimental model. Four prototype transducers around the peak value are fabricated and tested to validate the analytical model. A scanning laser Doppler vibrometer is employed to test the bending vibration shape and resonance frequency. Finally, the electromechanical coupling coefficient is tested indirectly through an impedance analyzer. Comparisons of the analytical results, FEM results and experiment results are presented, and the results show good agreement.

Analysis of thickness-shear and thickness-twist modes of AT-cut quartz acoustic wave resonator and filter

The thickness-shear (TS) and thickness-twist (TT) vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone families of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acoustic wave resonators and filters.

A digital measurement system based on laser displacement sensor for piezoelectric ceramic discs vibration characterization

This study describes the innovative design of a digital measurement system based on a laser displacement sensor (LDS) as a vibrometer which is capable to measure a dynamic displacement response dependence on a stimulated vibration. The frequency response of a piezoelectric ceramic disc is obtained by processing the input/output signals obtained from the function generator and digital oscilloscope (digitizer) cards driven by a personal computer. Resonant frequencies of vibration are achieved utilizing the swept-sine signal excitation following the peak values in the signal response measured by LDS. The analogue signal from LDS controller represents directly a mechanical vibration of a piezoceramic disc. The test measurement results indicate that the system can distinguish resonance frequencies of piezoelectric ceramic discs up to 40kHz with the resolution 1Hz. Piezoelectric coefficient d33 and its linearity along the excited voltage amplitudes have been calculated by the applied methods as a demonstration of a successful system concept. The results achieved are in compliance with the reference value declared by the manufacturer of the piezoceramic disc.

Structure Optimization of the Aluminum Alloy Frames of Flight Simulator

Frames are the main components of the flight motion simulator, which are the support for each shaft system, at the same time the rotating load for the external shaft, so the stiffness and dynamic characteristics of the frames in a large extent determines the final accuracy and dynamic performance of the flight motion simulator. For the cast aluminum alloy ZL114A frames of a 3-DOF flight motion simulator, using finite element analysis method, the dynamic characteristics are calculated and analyzed, and then the each order resonance frequency and mode of vibration are obtained. By using of the modal synthesis method and optimization algorithms, the structural dynamics of frames are designed optimally, so as to further reducing the moment of inertia, and improving the stiffness and dynamic characteristics of frames. This method has provided important reference for the reasonable design of the frame structure, and definitively established the foundation to further study the triaxial coupling dynamic characteristics and system mechanical optimization for the flight motion simulator.

Predicting electrostatic charge on single microparticles

Electrostatic charge significantly affects the adhesion of microparticles. Presently the nature of surface charge distribution on a single microparticle and the effect of electrostatic charge as a contributor to its adhesion are not well understood. As a result of the strong discrepancies between the experimental adhesion measurements data and theoretical predictions over the years, some questions regarding adhesion force contributors in charged microparticles still remain unresolved. One reason for the current state of knowledge is difficulties associated with accurate measurement of particle charge. In current work, a non-contact and non-destructive opto-ultrasonic method is presented and employed to predict the equivalent bulk charge on a single charged micro-scale toner particle and to provide insight into the nature of charge distribution on its surface. From the vibrational spectral response of the particle to the ultrasonic excitation of the substrate, irregular shifting patterns of the vibrational (in-plane rocking) resonance frequencies of the particle are observed for the applied levels of substrate surface voltage (0–1500V), implying non-uniform (patch-charges) surface charge distribution on the microparticle. For predicting the equivalent bulk charge on a single patch-charged toner particle from this resonance frequency shift, a mathematical model is developed and employed. In conclusion, it is demonstrated that, in a non-invasive/non-contact manner, the total charge on a single microparticle can be predicted using the presented experimental approach, and evidence for the non-uniform charge distribution on a single particle is observed and reported.

Method of excitation of dual frequency vibrations by passive autobalancers

Using ball, roller and pendulum autobalancers as dual-frequency vibration exciters was proposed, corresponding designs were developed. Kinematic diagrams of machines with different platform movements (plane or rectilinear translational, vibrational-rotational, plane-parallel, etc.), on which dual-frequency vibration exciters can be installed were proposed. One of the technical solutions was tested by 3D modeling in SolidWorks CAD system using the CosmosMotion module. Considered dual-frequency vibration exciters have complex structures, it is difficult to tune the resonance vibration frequency of the platform, etc. Therefore, a new method of excitation of dual-frequency vibrations in the resonance vibromachines, eliminating these disadvantages was developed in the paper. For excitation of dual-frequency vibrations, using a special movement regime of the rotor with AB - quasiperiodic was proposed. In it, the rotor rotates at the resonance speed, and CW in AB can not catch up with the rotor since they are stuck at one of its resonance rotation frequencies. One of the proposed technical solutions was tested in Solidworks CAD system using the Motion module. A 3D model of the vibration machine with vibroexciter in the form of ball autobalancer was developed and simulation has shown the following: the possibility of using autobalancer for the two-frequency vibration excitation in the resonance vibration machines was confirmed; features of dual-frequency vibrations can be varied within wide limits by changing the mass of corrector weights, unbalance mass in the auto-balancer housing, rotor speed. Application of new vibroexciters will allow to create new vibromacnines with the dual-frequency vibration of the platform. The energy efficiency of these machines will be provided by the fact that the lower vibration frequency of the platform will coincide with its resonance frequency, which will provide intense vibrations of the platform necessary to perform the basic technological operation. Further intensification of technological processes will be ensured by self-cleaning of the screen and changes in the mechanical properties of the material processed by fast vibrations.

Vibration analysis and acoustic identification for a power-split planetary gear set

Vibration and acoustic characteristics of a new power-split hybrid transmission with a four-shaft planetary for passenger car are investigated in this research. A dynamic model with three degrees of freedom for the new compound planetary is established in pure electric driving mode. The numerical analysis for distinctive natural frequencies and corresponding vibration modes of this system are produced. Furthermore, in order to identify the noise source, acoustic and vibration experiments are carried out. Moreover, the finite element model for the shell cover is studied for verification of structure vibration resonant frequencies. It is demonstrated by comparison between numerical results and test data that the noise at frequency of 692 Hz is evidently related to the transverse vibration of motor E1 shaft, and the structure vibration of shell cover at frequency of 2930 Hz is exactly contributed to noise source at frequency near 3029 Hz.

Variational analysis of thickness-shear vibrations of a quartz piezoelectric plate with two pairs of electrodes as an acoustic wave filter

We study thickness-shear vibrations of a piezoelectric plate of AT-cut quartz with two pairs of electrodes. The plate represents a monolithic, two-pole acoustic wave filter. The scalar differential equations by Tiersten and Smythe for thickness- shear vibrations of electroded and unelectroded quartz plates are employed. Based on the variational formulation of the scalar differential equations established in a previous paper and the Ritz method with trigonometric functions as basis functions, free vibration resonant frequencies and thickness-shear modes of the plate are obtained. For a structurally symmetric filter, the modes can be separated into symmetric and antisymmetric ones. Trapped modes with vibrations mainly under the electrodes are presented. The effects of the electrode inertia and the distance between the two pairs of electrodes are examined. It is also found that the classical frequency prediction given by Tiersten from an approximate analysis has an inaccuracy of tens of parts per million, significant in filter design and application.

Photothermal Behaviors of Flowing Media Caused by Localized Surface Plasmon Resonance of Au Nanorings

Based on the scanning of photothermal optical coherence tomography (PT-OCT), the photothermal behavior of a flowing medium generated by the enhanced absorption of localized surface plasmon resonance of incorporated Au nanorings (NRIs) is observed. In particular, the effects of air bubble generation and thermally induced bubble size oscillation in a flowing medium through the incorporation of Au NRIs and modulated laser illumination are demonstrated. The size oscillation of the air bubble produces the vibration of the flowing medium, which is synchronized with the laser modulation, for generating PT-OCT signal. At the resonance frequency of flowing-medium vibration, the PT-OCT signal reaches the maximum level. The resonance frequency is related to the mass density and viscosity of the flowing medium and is independent of the flow speed of the medium in a vessel. Such a relation can be used for in situ monitoring the mass density and viscosity of a flowing medium.

Bayesian normal modes identification and estimation of elastic coefficients in resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy is an experimental technique for measuring the stiffness of anisotropic solid materials. The free vibration resonant frequencies of a specimen are measured and the stiffness coefficients of the material adjusted to minimize the difference between experimental and predicted frequencies. An issue of this inverse approach is that the measured frequencies are not easily paired with their predicted counterpart, leading to ambiguities in the definition of the objective function. In the past, this issue has been overcome through trial-and-error methods requiring the experimentalist to find the correct pairing, or through involved experimental methods measuring the shapes of the normal vibration modes in addition to their frequencies. The purpose of this work is to show, through a Bayesian formulation, that the inverse problem can be solved automatically and without requiring additions to the usual experimental setup. The pairing of measured and predicted frequencies is considered unknown, and the joint posterior probability distribution of pairing and stiffness is sampled using Markov chain Monte Carlo. The method is illustrated on two published data sets. The first set includes the exact pairing, allowing validation of the method. The second application deals with attenuative materials, for which many predicted modes cannot be observed, further complicating the inverse problem. In that case, introduction of prior information through Bayesian formulation reduces ambiguities.

Thickness-shear Modes and Energy Trapping in a Rectangular Piezoelectric Quartz Resonator with Partial Electrodes

We analyze thickness-shear vibrations of a rectangular plate of quartz piezoelectric crystal for acoustic wave resonator application. The plate is partially electroded in the central region. The scalar differential equation derived by Tiersten and Smythe is employed. Exact solution for the free vibration resonant frequencies and modes are obtained. Trapped modes with vibrations mainly under the electrodes are found. The results are useful to the understanding and design optimization of crystal resonators.