Fault Identification for Shear-Type Structures Using Low-Frequency Vibration Modes

Shear-type structures are common structural forms in industrial and civil buildings,such as concrete and steel frame structures.Fault diagnosis of shear-type structures is an important topic to ensure the normal use of structures.The main drawback of existing damage assessment methods is that they require accurate structural finite element models for damage assessment.However,for many shear-type structures,it is difficult to obtain accurate FEM.In order to avoid finite elementmodeling,amodel-freemethod for diagnosing shear structure defects is developed in this paper.This method only needs to measure a few low-order vibration modes of the structure.The proposed defect diagnosis method is divided into two stages.In the first stage,the location of defects in the structure is determined based on the difference between the virtual displacements derived from the dynamic flexibility matrices before and after damage.In the second stage,damage severity is evaluated based on an improved frequency sensitivity equation.Themain innovations of this method lie in two aspects.The first innovation is the development of a virtual displacement difference method for determining the location of damage in the shear structure.The second is to improve the existing frequency sensitivity equation to calculate the damage degree without constructing the finite elementmodel.Thismethod has been verified on a numerical example of a 22-story shear frame structure and an experimental example of a three-story steel shear structure.Based on numerical analysis and experimental data validation,it is shown that this method only needs to use the low-order modes of structural vibration to diagnose the defect location and damage degree,and does not require finite element modeling.The proposed method should be a very simple and practical defect diagnosis technique in engineering practice.

Deriving Vibration Modes of Semi-infinite Chain Model by “Invariant Eigen-operator”Method

For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.

Investigation of Microstructure, Natural Frequencies and Vibration Modes of Dragonfly Wing

In the present work, a thorough investigation on the microstructural and morphological aspects of dragonfly wings was carried out using scanning electron microscope. Then, based on this study and the previous reports, a precise three-dimensional numerical model was developed and natural frequencies and vibration modes of dragonfly forewing were determined by finite element method. The results shown that dragonfly wings are made of a series of adaptive materials, which form a very complex composite structure. This bio-composite fabrication has some unique features and potential benefits. Furthermore, the numerical results show that the first natural frequency of dragonfly wings is about 168 Hz and bending is the predominant deformation mode in this stage. The accuracy of the present analysis is verified by comparison of calculated results with experimental data. This paper may be helpful for micro aerial vehicle design concerning dynamic response.

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.

Coupling of quasi-localized and phonon modes in glasses at low frequency

Boson peak of glasses,a THz vibrational excess compared to Debye squared-frequency law,remains mysterious in condensed-matter physics and material science.It appears in many different kinds of glassy matters and is also argued to exist in damped crystals.A consensus is that boson peak originates from the coupling of the(quasi)-localized non-phonon modes and the plane-wave-like phonon modes,but the coupling behavior is still not fully understood.In this paper,by modulating the content of localized modes and the frequencies of phonon modes,the coupling is clearly reflected in the localization and anharmonicity of low-frequency vibrational modes.The coupling enhances with increasing cooling rate and sample size.For finite sample size,phonon modes do not fully intrude into the low frequency to form a dense spectrum and they are not sufficiently coupled to the localized modes,thus there is no Debye level and boson peak is ill-defined.This suggestion remains valid in the presence of thermal motions induced by temperature,even though the anharmonicity comes into play.Our results point to the coupling of quasi-localized and phonon modes and its relation to the boson peak.

Low-frequency hybridized excess vibrations of two-dimensional glasses

One hallmark of glasses is the existence of excess vibrational modes at low frequenciesωbeyond Debye’s prediction.Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses.However,there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations.In particular,excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D_(exc)(ω)~ω^(2)in 2D glasses with an inverse power law potential.Yet,the universality of the quadratic scaling remains unknown,since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum.Here,we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion.Moreover,we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion,which is accompanied by a suppression of the strength of the sound attenuation.Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

Energy Transfer among Modes in a Non-Slender Elastic Beam Subject to Vortex-Induced Vibration

The vibration of an elastic beam experiencing vortex-induced vibration is numerically analyzed employing a wake-oscillator model. The influence of the excited mode, the initial velocity, the shedding pulsation and the mass ratio on the energy transfer among modes and the vibration amplitude is determined. Multiple frequencies are detected, and the power spectral density of the beam tip time series is used to calculate the dominant frequency.

Computational analysis of vibration modes of disk-shaped piezoelectric traveling wave motors

According to Kirchhoff-Love's assumptions, this paper establishes linear system of equations for solving eigen frequency constant and corresponding mode shape. Using engineer-ing and numerical analysis software Matlab5.2 and method of coefficient determinant searching arithmetic, eigen frequency constant and mode shape of the stator with i.d./ o.d. ratio of 0.1, 0.3, 0.35, 0.6 and different vibration modes are accurately solved and analyzed. By means of Newton interpolation method, contributions of transverse deflection amplitude and vibration energy corresponding to various modes are determined. This paper offers a valid theoretical foundation for the optimum design of the stator of disk-shaped ultrasonic motors. Furthermore, according to results of numerical analysis, several choosing principles of vibration modes are summarized.

Changes in Coupled Vibration Frequencies and Modes of Wall-Cavity Systems Induced by Stiffness Variation in the Structure

Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity systems when the structural rigidity is modified. Numerical results are constructed using ANSYS software with triangular finite elements for both the fluid （2D acoustic elements） and the solid （plane stress） domains. These former results are compared to proposed analytical expressions, showing an alternative benchmark tool for the analyst. Very rigid wall structures imply in frequencies and mode shapes almost identical to those achieved for an acoustic cavity with Neumann boundary condition at the interface. In this case, the wall behaves as rigid and fluid-structure system mode shapes are similar to those achieved for the uncoupled reservoir case.

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.

Analysis of Low-Frequency Vibrational Modes and Particle Rearrangements in Marginally Jammed Amorphous Solid under Quasi-Static Shear

We present the numerical simulation results of a model granular assembly formed by spherical particles with tIertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low- frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.

Effect of Vibrational Modes on Sand Pressure and Pattern Deformation in the EPC Process

During the EPC (expendable pattern casting) process, one of the essential requirements is to prevent pattern distortion duringsand filling and compaction. A new method which vibrates the system in a two-dimensional circular mode has been appliedto the EPC process. The molding properties of unbonded sand obtained by this new vibration mode are investigated andcompared with those in the one-dimensional vertical mode. For adequate compaction of sand. the circular vibration mode ismore effective than the vertical mode. Sand became more fluidized by the circular vibration and the particle pressure coefficientwas close to unity The particle pressure coefficient, which is defined as the ratio of horizontal to vertical sand pressure, isresponsible for the effectiveness of sand filling.

Low-frequency vibrational modes of glutamine

High-resolution terahertz absorption and Raman spectra of glutamine in the frequency region 0.2 THz-2.8 THz are obtained by using THz time domain spectroscopy and low-frequency Raman spectroscopy. Based on the experimental and the computational results, the vibration modes corresponding to the terahertz absorption and Raman scatting peaks are assigned and further verified by the theoretical calculations. Spectral investigation of the periodic structure of glutamine based on the sophisticated hybrid density functional B3LYP indicates that the vibrational modes come mainly from the inter-molecular hydrogen bond in this frequency region.

Quantum computation and simulation with vibrational modes of trapped ions

Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource,beyond the role as a mediator for entangling quantum operations on internal degrees of freedom,because of the large available Hilbert space.The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions.Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes,including bosonic encoding schemes in quantum information,reliable and efficient measurement techniques,and quantum operations that allow various quantum simulations and quantum computation algorithms.We describe experiments using the vibrational modes,including the preparation of non-classical states,molecular vibronic sampling,and applications in quantum thermodynamics.We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

Softening of C-H Symmetric Stretching Vibrational Modes for CH2 and CH3 Radicals Adsorbed on Cun （n=1-6） Clusters

The properties of C-H vibration softening for CH2 and CHa radicals absorbed on Cun（n=1-6） clusters have been investigated, using the density functional theory with hybrid functional. The results indicate that the absorption of CH2 on Cu clusters is stronger than the case of CH3. The vibrational frequencies of C-H bonding agree with the experimental results obtained for CH2 and CH3 absorbed on Cu（111）. With the increase of cluster size, the softening （Einstein shift） of C-H vibrational modes become stronger.

Vibrational Normal Modes of an Equilateral Triangular Mechanical Molecule

Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica. For a comprehensive understanding, the frequency of the normal mode is used for a visual animation;an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.

Investigation on Mesh and Sideband Vibrations of Helical Planetary Ring Gear Using Structure, Excitation and Deformation Symmetries

Time?variant excitations in planetary gear trains can cause excessive noise and vibration and even damage the system on a permanent basis. This paper focuses on the elastic vibrations of a helical planetary ring gear subjected to mesh and planet?pass excitations. Motivated by the structure, excitation and deformation symmetries, this paper proposes dual?frequency superposition and modulation methods to capture the mesh and sideband vibrations. The transi?tion between ring gear tooth and planet is introduced to address the excitations and vibrations. The phasing e ect of ring gear tooth and planet on various deformations is formulated. The inherent connections between the two types of vibrations are identified. The vibrations share identical exciting rules and the wavenumber and modulating signal order both equal the linear combination of tooth and planet counts. The results cover in?plane bending and extensional, out?of?plane bending and torsional deformations. Main findings are verified by numerical calculation and comparisons with the open literature. The analytical expressions can be used to determine whether the sideband is caused by component fault or only by elastic vibration. The methods can be extended to other power?transmission systems because little restriction is imposed during the analysis.

Vibration properties of low-fraction hydrogen in deuterium ices

Inelastic incoherent neutron scattering spectra of D2O high-density amorphous （hda） ice, ice-Ⅷ and ice-Ⅱ mixed with small amount of H2O （（5%） have been measured recently on high-energy transfer spectrometer at Rutherford Appleton Laboratory （UK）. The hydrogen atom on D2O ice lattices has three distinguished vibrational modes, two bending at low frequencies and one stretching at high frequencies, and their frequencies are slightly different for different phases of ice. It was found that the lower one of the bending modes is located at -95 meⅤ for hda-ice, at -95 meⅤ for ice-Ⅷ and at -96 meⅤ for ice-Ⅱ and they are all lower than the value of 104 meⅤ for ice-Ih. It was also measured that the O-D and O-H covalent bond stretching modes of ice-Ⅷ are at -315 and -425 meⅤ, ice-Ⅱ at 307 and -415 meⅤ, hda-ice at 312 and -418 meⅤ, respectively. They are significantly higher than the values of ice-Ih at -299 and -406 meⅤ, respectively.

VIBRATION ANALYSIS OF TURBINE BASED ON FLUID-STRUCTURE COUPLING

The vibration of a Francis turbine is analyzed with the additional quality matrix method based on fluid-structure coupling （FSC）. Firstly, the vibration frequency and mode of blade and runner in air and water are calculated. Secondly, the influences to runner frequency domain by large flow, small flow and design flow working conditions are compared. Finally the influences to runner modes by centrifugal forces under three rotating speeds of 400 r/rain, 500 r/min and 600 r/rain are compared. The centrifugal force and small flow working condition have greatly influence on the vibration of small runner. With the increase of centrifugal force, the vibration frequency of the runner is sharply increased. Some order frequencies are even close to the runner natural frequency in the air. Because the low frequency vibration will severely damage the stability of the turbine, low frequency vibration of units should be avoided as soon as possible.

Influence of vibration mode on the screening process

The screening of particles with different vibration modes was simulated by means of a 3D discrete element method (3D-DEM). The motion and penetration of the particles on the screen deck were analyzed for linear, circular and elliptical vibration of the screen. The results show that the travel velocity of the particles is the fastest, but the screening efficiency is the lowest, for the linear vibration mode. The circular motion resulted in the highest screening efficiency, but the lowest particle travel velocity. In the steady state the screening efficiency for each mode is seen to increase gradually along the longitudinal direction of the deck. The screening efficiency increment of the circular mode is the largest while the linear mode shows the smallest increment. The volume fraction of near-mesh size particles at the underside is larger than that of small size particles all along the screen deck. Linear screening mode has more near-mesh and small size particles on the first three deck sections, and fewer on the last two sections, compared to the circular or elliptical modes.