Axial Vibration Modes Research Articles

Modal analysis of functionally graded Timoshenko beam

Dynamic analysis of FGM Timoshenko beam is formulated in the frequency domain taking into account the actual position of neutral plane. The problem formulation enables to obtain explicit expressions for frequency equation, natural modes and frequency response of the beam subjected to external load. The representations are straightforward not only to modal analysis and modal testing of FGM Timoshenko beam with general end conditions but also to study coupling of axial and flexural vibration modes. Numerical study is carried out to investigate effect of true neutral axis position and material properties on the modal parameters.

Compliant Needle Vibration Cutting of Soft Tissue

This work investigates the performance of a novel compliant needle for cutting tissue. The novel cutting geometry transfers axial vibration to transverse motion at the tip. The cutting edge of the geometry is defined in terms of the time-dependent inclination and rake angle. Finite element analysis was performed to determine the compliant geometry effect on the axial vibration modes of the needles. An ultrasonic transducer is used to apply the axial vibration. An ultrasonic horn was developed to increase the amplitude of vibration. Experiments were performed to determine the effectiveness of the compliant needle geometry. The motion of the compliant needle is measured with a stereomicroscope. The two compliant geometries developed transverse motion of 4.5 μm and 16.0 μm. The control needle with fixed geometry developed no measured transverse motion. The insertion force was recorded for two different compliant geometries and a control geometry inserted into a polyurethane sheet. The puncture force of the control needle with applied vibration and the two compliant needles was up to 29.5% lower than the control insertion without applied vibration. The compliant needles reduced the friction force up to 71.0%. The significant reduction of the friction force is explained by the compliant needles' ability to create a larger crack in the material because of their transverse motion.

Experiments on active precision isolation with a smart conical adapter

Based on a conical shell adaptor, an active vibration isolator for vibration control of precision payload is designed and tested in this study. Flexible piezoelectric sensors and actuators are bonded on the adaptor surface for active vibration monitoring and control. The mathematical model of a piezoelectric laminated conical shell is derived and then optimal design of the actuators is performed for the first axial vibration mode of the isolation system. A scaled conical adaptor is manufactured with four MFC actuators laminating on its outer surface. Active vibration isolation efficiency is then evaluated on a vibration shaker. The control model is built in Matlab/Simulink and programmed into the dSPACE control board. Experimental results show that, the proposed active isolator is effective in vibration suppression of payloads with the negative velocity feedback control. In contrast, the amplitude responses increase with positive feedback control. Furthermore, the amplitude responses increases when time delay is added into the control signals, and gets the maximum when the delay is close to one quarter of one cycle time.

Axial vibration of single-walled carbon nanotubes using doublet mechanics

This paper investigates the axial vibration of single-walled carbon nanotubes based on doublet mechanics with a length scale parameter. A forth-order partial differential equation that governs the axial vibration mode of single-walled carbon nanotubes is derived. Using doublet mechanics, the relation between natural frequency and length scale parameter is derived in the axial mode of vibration. It is shown that length scale parameter plays significant roles in the axial vibration behavior of single-walled carbon nanotubes. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However, with increasing tube length, the scale effect on the natural frequency decreases.

Ratcheting analysis of joined conical cylindrical shells

The ratcheting and strain cyclic behaviour of joined conical-cylindrical shells under uniaxial strain controlled, uniaxial and multiaxial stress controlled cyclic loading are investigated in the paper. The elasto-plastic deformation of the structure is simulated using Chaboche non-linear kinematic hardening model in finite element package ANSYS 13.0. The stress-strain response near the joint of conical and cylindrical shell portions is discussed in detail. The effects of strain amplitude, mean stress, stress amplitude and temperature on ratcheting are investigated. Under strain symmetric cycling, the stress amplitude increases with the increase in imposed strain amplitude. Under imposed uniaxial/multiaxial stress cycling, ratcheting strain increases with the increasing mean/amplitude values of stress and temperature. The abrupt change in geometry at the joint results in local plastic deformation inducing large strain variations in the vicinity of the joint. The forcing frequency corresponding to peak axial ratcheting strain amplitude is significantly smaller than the frequency of first linear elastic axial vibration mode. The strains predicted from quasi static analysis are significantly smaller as compared to the peak strains from dynamic analysis.

Patterned growth of carbon nanotubes obtained by high density plasma chemical vapor deposition

Patterned growth of carbon nanotubes by chemical vapor deposition represents an assembly approach to place and orient nanotubes at a stage as early as when they are synthesized. In this work, the carbon nanotubes were obtained at room temperature by High Density Plasmas Chemical Vapor Deposition (HDPCVD) system. This CVD system uses a new concept of plasma generation, where a planar coil coupled to an RF system for plasma generation was used with an electrostatic shield for plasma densification. In this mode, high density plasmas are obtained. We also report the patterned growth of carbon nanotubes on full 4-in Si wafers, using pure methane plasmas and iron as precursor material (seed). Photolithography processes were used to pattern the regions on the silicon wafers. The carbon nanotubes were characterized by micro-Raman spectroscopy, the spectra showed very single-walled carbon nanotubes axial vibration modes around 1590 cm-1 and radial breathing modes (RBM) around 120-400 cm-1, confirming that high quality of the carbon nanotubes obtained in this work. The carbon nanotubes were analyzed by atomic force microscopy and scanning electron microscopy too. The results showed that is possible obtain high-aligned carbon nanotubes with patterned growth on a silicon wafer with high reproducibility and control.

Energy aspects and workpiece surface characteristics in ultrasonic-assisted cylindrical grinding of alumina–zirconia ceramics

Ultrasonic assisted grinding is a novel method for improving the grinding process of difficult-to-cut materials. In the present research a novel setup has been designed and manufactured for utilizing ultrasonic vibrations in external cylindrical grinding. The designed ultrasonic head vibrates a rotating workpiece in axial direction. An alumina–zirconia ceramic (AZ90) has been selected as the workpiece material. Energy aspects and workpiece surface characteristics of ultrasonic assisted cylindrical grinding (UACG) and conventional cylindrical grinding (CG) processes have been analytically modeled and corresponding grinding experiments have been performed. The combined kinematics of the cylindrical plunge grinding process and axial ultrasonic vibrations provide a unique surface treatment conditions, which leads to reduced peak heights and increased valley depths of the surface topography. The main axial vibration mode provides the overlap of the adjacent cutting traces and consequently smoothens the surface topography in cylindrical plunge grinding. It has been analytically and experimentally shown that, applying ultrasonic vibrations, grinding energy can be reduced up to more than 35% depending on the process parameters. The surface characteristics of the ground workpieces have been investigated in terms of four surface roughness parameters and the roundness error.

Length dependence of the resonant magnetoelectric effect in Ni/Pb(Zr,Ti)O3/Ni long cylindrical composites

Magnetoelectric (ME) effect was studied in the long cylindrical Ni/Pb(Zr,Ti)O3/Ni layered composites prepared by electroless deposition. Three significant resonant peaks have been observed in the dependence of the ME voltage coefficient on the magnetic field frequency. The height of the composite cylinder has an important impact on the ME effect. With the height of the cylinder increase, the value of ME coefficient at static or low-frequency case increases, while the resonant frequencies decrease. Furthermore, the ME effect at the individual resonant frequencies can be weakened or enhanced due to the coupling of radial and axial vibration modes. The experimental values of resonant frequencies are in good agreement with the calculated ones. The results are useful for magnetoelectric devices with controllable multifrequency operation.

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor.

Coupled vibrations in hollow cylindrical shells of arbitrary aspect ratio

Vibrations of hollow cylinders have been the subject of considerable interest for many years. Piezoelectric cylinders offer a convenient system to study the vibration mode shapes, resonance frequencies and their mode coupling do to the ability to strongly and symmetrically excite extensional circumferential and axial vibration modes as well as flexural bending axial modes. While the mode repulsion of coupled circumferential and axial modes is generally widely known, their interaction gives rise to tubular flexural resonances in cylinders of finite thickness. Junger et al. [JASA 26, 709–713 (1954)] appears to have been first to discredit the notion of a forbidden zone, a frequency band free of resonant modes, as being an artifact of treating thin cylinders in the membrane limit. Aronov [JASA 125(2), 803–818 (2009)] showed experimental and theoretical proof of the presence of resonant modes throughout the spectrum as a result of the extensional mode coupling induced symmetric tubular bending modes in cylinders and their relationships as a function of different piezoelectric polarizations. That analysis used the energy method and the Euler-Lagrange equations based on the coupling of assumed modes of vibration and the synthesis of results using equivalent electromechanical circuits. This paper aims to both summarize and generalize those results for the applicability of passive cylindrical shells.

Free vibration analysis of functionally graded beams using an exact plane elasticity approach

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.

Three-dimensional modeling for predicting the vibration modes of twin ball screw driving table

As a redundant drive mechanism, twin ball screw feed system has the advantage of high stiffness and little yaw vibration in the feeding process, while leads to increased difficulty with vibration characteristics analysis and structure optimization. Only low-dimensional structure and dynamics parameters are considered in the existing research, the complete and effective model for predicting the table’s vibrations is lacked. A three-dimensional(3D) mechanical model of twin ball screw driving table is proposed. In order to predict the vibration modes of the table quantitatively, an analytical formulation following a comprehensive approach is developed, where the drive system is modeled as a lumped mass-spring system, and the Lagrangian method is used to obtain the table’s independent and coupled axial, yaw, and pitch vibration modes. The frequency variation of each mode is studied for different heights of the center of gravity, nut positions and table masses by numerical simulations. Modal experiment is carried out on the Z-axis feed table of the horizontal machining center MCH63. The results show that for each mode, the error between the estimated and the measured frequencies is less than 13%. The independent and coupled vibration modes are in accordance with the experimental results, respectively. The proposed work can serve a better understanding of the table’s dynamics and be beneficial for optimizing the structure parameters of twin ball screw drive system in the design stage.

Tapered Beam Axial Vibration Frequency: Linear Cross-area Variation Case

The expression describing a cross-area linear variation for a tapered beam vibrating axially is considered. It is utilized to formulate the first axial vibration mode shape. The later, results from the normalization of the displacement function obtained by solving the exact solution of the second order differential equation with none constant coefficients. This function is governing the non uniform bar element equilibrium. After this first step, the well known Rayleigh quotient is used for calculating the fundamental natural frequency. The obtained results are comparable to those issued from numerical and theoretical methods. These findings suggest a simply useable handle tool expressed by a curve which allows a quick fundamental frequency evaluation for various taper degrees.

Stability of transverse vibration of rod under longitudinal step-wise loading

The problem of dynamic stability of a simply supported rod subjected to axial jump loading is considered. A systematic application of the method of expansion in terms of the normal axial and bending vibration modes is utilised. Longitudinal vibrations give rise to periodic longitudinal forces which in turn causes unstable bending vibrations. Application of the Galerkin approach results in a system of ordinary differential equations with periodic coefficients which are reduced to Mathieu equation. The instability regions whose form depends on the spectral properties of the longitudinal and flexural vibrations, damping values and longitudinal force are obtained. An example of unusual shapes of the instability regions is shown: the twelfth transverse mode caused by the first longitudinal mode turns out to be unstable for some parameters of the rod. The critical value of the jump load leading to instability of the considered transverse vibration modes is derived.

Study of Vibration Milling for Improving Surface Finish of Difficult-to-Cut Materials

This work studies the influence of high-frequency excitation of a cutting tool during end milling of workpieces made of difficult-to-cut metallic alloys. It is demonstrated that high-frequency vibrations superimposed onto the continuous movement of the tool lead to milling process stabilization with superior surface finish in comparison to conventional machining. A finite element model of the vibration milling tool was built and verified experimentally. The model treats the tool as an elastic pre-twisted structure (mill cutter) characterised by its natural vibration modes. The resonance frequencies of the axial vibration mode of cutters of two different lengths were predicted numerically and subsequently used for excitation of the vibration milling tool during cutting experiments. Qualitative and quantitative characterization of the surface quality of the machined stainless steel and titanium alloys was performed. Measurement results have confirmed that excitation of a specific tool mode is a prerequisite for achieving maximal efficiency of the vibration milling process. Statistical analysis of the collected roughness measurement data identified factors that most significantly contribute to the improved surface finish of the workpieces.

Improvement of EDM Properties of PCD with Electrode Vibrated by Ultrasonic Transducer

EDM machinability of PCD was investigated using a copper electrode giving ultrasonic vibrations. In this series of EDM experiments, three types of ultrasonic vibration modes were selected (axial vibration, flexural vibration and complex vibration). From the experimental results, it was found that EDM efficiency became 3 times higher than the ordinary EDM (no vibration given to the electrode) under the two specific vibration modes, namely, 1) the axial vibration (large) mode and 2) the complex vibration (axial vibration: large+flexural vibration: small) mode. Furthermore, it was shown that the effects resulted from not only the cavitation effect of the working fluid but also the vibrational action of the electrode itself.

Research on Dynamics of Double-Mesh Helical Gear Set

A dynamic model of double-mesh helical gear set was established including the torsional vibration, axial vibration and time varying mesh stiffness. The natural modes were systematically analyzed and classified into three types: rotational vibration mode, axial vibration mode and overall vibration mode. The influence of time varying mesh stiffness and the dynamic responses of the gear set were also investigated. The results showed that several natural frequencies are excited in the dynamic response and there is a frequency sensitive area which may cause large dynamic load.

Effects of Ultrasonic Vibrations Given to an Electrode on the EDM Performance in Processing PCD

EDM machinability of PCD was investigated using a copper electrode giving ultrasonic vibrations. In this series of EDM experiments, three types of ultrasonic vibration modes were selected (axial vibration, flexural vibration and complex vibration). From the experimental results, it was found that EDM efficiency became 3 times higher than the ordinary EDM (no vibration given to the electrode) under the two specific vibration modes, namely, 1) the axial vibration (large) mode and 2) the complex vibration (axial vibration: large + flexural vibration: small) mode. Furthermore, it was shown that the effects resulted from not only the cavitation effect of the working fluid but also the vibrational action of the electrode itself.

A Resonance Raman Enhancement Mechanism for Axial Vibrational Modes in the Pyridine Adduct of Myoglobin Proximal Cavity Mutant (H93G)

The proximal cavity mutant of myoglobin consists of a mutation of the proximal histidine to glycine (H93G), which permits exogenous ligands to bind to the heme iron. A non-native pyridine ligand can ligate to the heme to yield a five-coordinate adduct, H93G(Pyr), that cannot be formed freely in solution since the six-coordinate bis-pyridine adduct is more stable than the five-coordinate adduct. We have used resonance Raman spectroscopy in the Soret band region of the heme to study the enhancement of axial vibrations of bound pyridine in the H93G(Pyr) adduct. The observation that the pyridine ring breathing mode (ν(1)) and the symmetric ring stretching (ν(3)) modes are enhanced under these conditions is explained by a computational approach that shows that coupling of the π-system of the heme with the p-orbitals of the pyridine is analogous to π-backbonding in diatomic ligand adducts of heme proteins. The result has the broader significance that it suggests that the resonance enhancement of pyridine modes could be an important aspect of Raman scattering of pyridine on conducting surfaces such as those studied in surface enhanced Raman scattering experiments.

Active control of low-frequency sound radiation by cylindrical shell with piezoelectric stack force actuators

A novel active control method of sound radiation from a cylindrical shell under axial excitations is proposed and theoretically analyzed. This control method is based on a pair of piezoelectric stack force actuators which are installed on the shell and parallel to the axial direction. The actuators are driven in phase and generate the same forces to control the vibration and the sound radiation of the cylindrical shell. The model considered is a fluid-loaded finite stiffened cylindrical shell with rigid end-caps and only low-frequency axial vibration modes are involved. Numerical simulations are performed to explore the required control forces and the optimal mounting positions of actuators under different cost functions. The results show that the proposed force actuators can reduce the radiated sound pressure of low-frequency axial modes in all directions.