Coupling Vibrational Frequencies Research Articles

Coupled vibration analysis of partially liquid-filled cylindrical shell considering free surface sloshing

In this paper, a semi-analytical method is proposed to analyze the dynamic behavior of horizontal cylindrical shells partially filled with liquid, considering the sloshing effect of the free surface. Two coordinate systems are set at the midpoint of the free liquid surface and the geometric center of the cylindrical shell’s cross-section, respectively. The internal fluid is an inviscid, irrotational, and incompressible fluid. The liquid potential functions which satisfy the Laplace function are described in the anti-symmetrical/symmetrical forms based on the liquid surface coordinate system. Meanwhile, the coupled motion functions of the shell are established on the structural coordinate system using the Flugge shell theory. Through the continuous condition on the internal wet surface, the coupled system’s governing equations are achieved and solved by the coordinate transformation and the Galerkin method. The fluid sloshing frequencies and the coupled vibration frequencies of the shell are simultaneously obtained in this coupled model. The accuracy of this method is verified by the published data and the finite element method. Furthermore, the influences of the coupled system’s parameters on the shell’s natural frequencies and sloshing frequencies are discussed, and the coupling effect is revealed between the shell’s vibration and the sloshing of the free surface.

Coupled Dynamic Analysis and Decoupling Optimization Method of the Laser Gyro Inertial Measurement Unit.

The mechanical dithered ring laser gyro (RLG) effectively overcomes the lock-in effect and ensures the sensitive accuracy of the low angular rate for the gyro. However, in the inertial measurement unit (IMU) system, the dither excitation of three RLGs causes the coupled vibration of the IMU structure, which could seriously limit the measuring accuracy of RLGs. In this paper, the vibration frequency response characteristic of laser gyro IMU is taken as the focus point, and the method of multi-rigid body dynamics is used to establish the dynamic model of IMU suitable for vibration frequency response analysis. On the basis of the model, the multi-degree-of-freedom coupling vibration of IMU with the gyro dither excitation is clearly described. A new IMU dynamic decoupling optimization method is proposed to minimize the coupled vibration frequency response, and compared with the previous optimal design method. The prototype experimental test results show that the coupled vibration of IMU is restrained more effectively by the proposed new method than by the previous optimal design method. Finally, on the basis of this new method, the measuring accuracy of the RLGs in the IMU system is improved, which is quite useful for practical engineering application.

An Impact-Based Frequency Up-Converting Hybrid Vibration Energy Harvester for Low Frequency Application

In this paper, a novel impact-based frequency up-converting hybrid energy harvester (FUCHEH) was proposed. It consisted of a piezoelectric cantilever beam and a driving beam with a magnetic tip mass. A solenoid coil was attached at the end of the piezoelectric beam. This innovative configuration amplified the relative motion velocity between magnet and coil, resulting in an enhancement of the induced electromotive force in the coil. An electromechanical coupling model was developed and a numerical simulation was performed to study the principle of impact-based frequency up-converting. A prototype was fabricated and experimentally tested. The time-domain and frequency-domain analyses were performed. Fast Fourier transform (FFT) analysis verified that fundamental frequencies and coupled vibration frequency contributes most of the output voltage. The measured maximum output power was 769.13 µW at a frequency of 13 Hz and an acceleration amplitude of 1 m/s2, which was 3249.4%- and 100.6%-times larger than that of the frequency up-converting piezoelectric energy harvesters (FUCPEH) and frequency up-converting electromagnetic energy harvester (FUCEMEH), respectively. The root mean square (RMS) voltage of the piezoelectric energy harvester subsystem (0.919 V) was more than 16 times of that of the stand-alone PEH (0.055 V). This paper provided a new scheme to improve generating performance of the vibration energy harvester with high resonant frequency working in the low-frequency vibration environment.

Vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid

The vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid has received plenty of attention in recent years. To apply frequency analysis to defect detection for example, it is necessary to investigate the vibrational behavior under appropriate boundary conditions. In this paper, we present a detailed theoretical study of the three dimensional modal analysis of compressible fluid within an elastic cylinder. The dispersion equations of flexural, torsional and longitudinal modes are derived by elastodynamic theory and the unsteady Stokes equation. The symbolic software Mathematica is used in order to find the coupled vibration frequencies. The dispersion equation is deduced and analytically solved. The finite element results are compared with the present method for validation and an acceptable match between them are obtained.

Vibration Analysis of Euler-Bernoulli Beams Partially Immersed in a Viscous Fluid

The vibrational characteristics of a microbeam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical study of the modal analysis of microbeams partially immersed in a viscous fluid. A fixed-free microbeam vibrating in a viscous fluid is modeled using the Euler-Bernoulli equation for the beams. The unsteady Stokes equations are solved using a Helmholtz decomposition technique in a two-dimensional plane containing the microbeams cross sections. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results is compared with present method for validation and an acceptable match between them was obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

Research on a Model of Nonlinear Coupled-Vibration of Directional Well Drill String

Drill string vibrations are inevitable movement patterns during drilling process, the drill string vibrations form including longitudinal, lateral and torsional are recognized by most scholars. In the actual drilling process, the coupled vibration exhibits nonlinear features due to the impact of the eccentric rotation of the drill string and the influence of drilling fliud. Taking the whole drill string of directional well as the research object, a three-direction of longitudinal, transverse and torsional nonlinear coupled vibration model of drill string is established based on the nonlinear coupled deformations analysis in the longitudinal, transverse and torsional directions by using finite element analysis method. The nonlinear coupled vibration of drill string is studied by considering the effects of viscous forces of drilling fluid during the drilling process. The results show that the drill string resonance interval is relatively concentrated and the nonlinear coupled vibration frequency increase with the decrease of the length of the drill string.

Molecular model for hydrated biological tissues.

A density-functional microscopic model for soft tissues (STmod) is presented. The model was based on a prototype molecular structure from experimentally resolved type I collagen peptide residues and water clusters treated in periodic boundary conditions. We obtained the optimized geometry, binding and coupling energies, dipole moments, and vibrational frequencies. The results concerning the stability of the confined water clusters, the water-water, and water-collagen interactions were successfully correlated to some important experimental trends of normal and inflammatory tissues.

Transverse vibration analysis of Euler-Bernoulli beam carrying point masse submerged in fluid media

In the present paper, an analytical method is developed to investigate the effects of added mass on natural frequencies and mode shapes of Euler-Bernoulli beams carrying concentrated masse at arbitrary position submerged in a fluid media. A fixed-fixed beams carrying concentrated masse vibrating in a fluid is modeled using the Bernoulli-Euler equation for the beams and the acoustic equation for the fluid. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of a beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results are compared with present method for validation and an acceptable match between them were obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

Dirac‐exact relativistic methods: the normalized elimination of the small component method

Dirac‐exact relativistic methods, i.e., 2‐ or 1‐component methods which exactly reproduce the one‐electron energies of the original 4‐component Dirac method, have established a standard for reliable relativistic quantum chemical calculations targeting medium‐ and large‐sized molecules. Their development was initiated and facilitated in the late 1990s by Dyall's development of the normalized elimination of the small component (NESC). Dyall's work has fostered the conversion of NESC and related (later developed) methods into routinely used, multipurpose Dirac‐exact methods by which energies, first‐order, and second‐order properties can be calculated at computational costs, which are only slightly higher than those of nonrelativistic methods. This review summarizes the development of a generally applicable 1‐component NESC algorithm leading to the calculation of reliable energies, geometries, electron density distributions, electric moments, electric field gradients, hyperfine structure constants, contact densities and Mössbauer isomer shifts, nuclear quadrupole coupling constants, vibrational frequencies, infrared intensities, and static electric dipole polarizabilities. In addition, the derivation and computational possibilities of 2‐component NESC methods are discussed and their use for the calculation of spin‐orbit coupling (SOC) effects in connection with spin‐orbit splittings and SOC‐corrected energies are demonstrated. The impact of scalar relativistic and spin‐orbit effects on molecular properties is presented. WIREs Comput Mol Sci 2014, 4:436–467.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Structural and Dynamic Properties of a Hydrogen Bond from the Study of the CH3Cl–HCl Complex and Isotopic Species

The microwave (4-20 GHz range) and infrared (HCl and DCl stretch ranges) spectra of six isotopic species of the CH3Cl-HCl hydrogen bond complex have been recorded for the first time and analyzed with the support of high level ab initio calculations (MP2 and CCSD(T) levels). Accurate molecular parameters, including rotational, quartic centrifugal distortion, and nuclear-quadrupole coupling constants, vibrational frequencies, and anharmonic coupling constants, are presented in this paper. These parameters have then been used to estimate the hydrogen bond geometry and confirm the strong coupling between intramolecular and low frequency intermolecular modes. Experimental and theoretical evidence, in agreement with each other, tend to point out a free rotation of the CH3Cl unit in the complex, emphasizing the very peculiar dynamical properties of a hydrogen bond and, consequently, the necessity of taking those effects into account to correctly model the intra- and intermolecular interactions.

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

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

The coupling frequency of bioliquid-filled microtubules considering small scale effects

This paper presents an investigation on the effects of bioliquid density and the constrained stiffness of surrounding bio-medium on the coupling frequency characteristics of bioliquid-filled microtubules. Here, the nonlocal elastic theory is utilized to describe the nano-scale effect of the microtubule. Results show that the influence of small scale on the coupled vibration frequency of bioliquid-filled microtubules embedded in bio-medium gradually increases when the bioliquid density in microtubules is larger than the density of the microtubules. The new investigation results may be used as a useful reference for the ultrasonic examine of microtubule organization and some biomedical clinical applications.

Magnetic coupling constants and vibrational frequencies by extended broken symmetry approach with hybrid functionals

The description of the electronic structure and magnetic properties of multi-centers transition metal complexes, especially of mixed-valence compounds, still represents a challenge for density functional theory (DFT) methods. The energies and the geometries of the correctly symmetrized low-spin ground state are estimated using the Heisenberg-Dirac-van Vleck spin Hamiltonian within the extended broken symmetry method introduced by Marx and co-workers [Nair et al., J. Chem. Theory Comput. 4, 1174-1188 (2008)]. In the present work we extend the application of this technique, originally implemented using the DFT+U scheme, to the use of hybrid functionals, investigating the ground-state properties of di-iron and di-manganese compounds. The calculated magnetic coupling and vibrational properties of ferredoxin molecular models are in good agreements with experimental results and DFT+U calculations. Six different mixed-valence Mn(III)-Mn(IV) compounds have been extensively studied optimizing the geometry in low-spin, high-spin, and broken-symmetry states and with different functionals. The magnetic coupling constants calculated by the extended broken symmetry approach using B3LYP functional presents a remarkable agreement with the experimental results, revealing that the proposed methodology provides a consistent and accurate DFT approach to the electronic structure of multi-centers transition metal complexes.

Impact-driven, frequency up-converting coupled vibration energy harvesting device for lowfrequency operation

This paper presents experiments and models of an energy harvesting device in which a lowfrequency resonator impacts a high frequency energy harvesting resonator, resulting inenergy harvesting predominantly at the system’s coupled vibration frequency. Analysisshows that a reduced mechanical damping ratio during coupled vibration enables increasedelectrical power generation as compared with conventional technology. Experimentsdemonstrate that the efficiency of electrical power transfer is significantly improved withthe coupled vibration approach. An average power output of 0.43 mW is achieved under0.4g acceleration at 8.2 Hz, corresponding to a power density of25.5 µW cm − 3. The measured power and power density at the resonant frequency are respectively 4.8times and 13 times the measured peak values for a conventional harvester created from alow frequency beam alone.

Dynamic response of structure coupled with liquid sloshing in a laminated composite cylindrical tank with baffle

Baffles are used effectively to reduce the sloshing response of liquid in the liquid storage containers. In this paper, the dynamic interaction that exists between the liquid and elastic tank–baffle system has been considered to evaluate the coupled response of liquid and tank–baffle system using the finite element method. The baffle and tank wall are made up of lightweight laminated composite materials. The liquid is assumed to be incompressible and inviscid, and the flow is irrotational. The finite element equations of motion of liquid and structure domains are numerically integrated by Newmark’s integration scheme. The interaction effect between the two fields is studied by transferring the structural normal acceleration to the liquid domain and liquid pressure to the structure domain. Effects of different parameters, such as being composite baffles, lamination scheme on the slosh frequencies and coupled vibration frequencies in the liquid filled composite tanks have been studied. The effects of composite baffle parameters, such as being its dimensions and position in the tank wall, on the sloshing response of liquid and structural response of liquid filled composite tank are studied under translational base excitation.

Dynamic response analysis of a liquid-filled cylindrical tank with annular baffle

Baffles are generally used as damping devices in liquid storage tanks. The focus of the present paper is to study the influence of a baffle on the dynamic response of a partially liquid-filled cylindrical tank. A baffle is assumed here to have the shape of a thin annular circular plate. The natural frequencies of an inviscid and incompressible liquid are determined for varying positions and dimensions of a baffle attached normal to the tank wall. The flexibility of both the baffle and the tank are considered in studying the effects of liquid–baffle and liquid–tank interactions on the sloshing mode frequencies. Finite element codes are developed and are then used to analyze both the liquid domain and the structural domain (i.e., the tank and the baffle). The coupled vibration frequencies of the tank–baffle system are computed considering the effect of sloshing of liquid. The results obtained for a liquid-filled elastic tank without a baffle and a rigid tank with a rigid baffle are in good agreement with the available results. The slosh amplitude of liquid in a rigid tank with and without a rigid baffle is studied under translational base excitation. The effects of the tank wall and baffle flexibility on the slosh response are also investigated.

FREE-VIBRATION ANALYSIS OF LIQUID-FILLED TANK WITH BAFFLES

The natural frequencies of liquid in a liquid-filled cylindrical rigid tank without and with baffles are evaluated. An annular plate is used as a baffle, which is fitted to the inner periphery of a cylindrical tank. Both rigid and flexible baffles are considered. Finite elements are used to discretize both the liquid and the structural domain. The slosh frequencies of liquid are computed for different dimensions, thicknesses and positions of baffles, both rigid and flexible considering the circumferential wave number as one. The axisymmetric and other asymmetric modes are not studied. The results obtained for rigid baffle case are comparable with the existing results. The coupled vibration frequencies of the tank-flexible-baffle system are computed considering the effect of sloshing of liquid.

Vibration predictions and verifications of disk drive spindle system with ball bearings

With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year, it is becoming increasingly more difficult to maintain the precise positioning required of the ever-smaller GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track, even the vibration amplitude is very small. Consequently, the dynamic behaviors of HDD spindle systems and their potential influence on track misregistration rate must be clearly understood. This paper is to apply an approach based on efficient component mode synthesis (CMS), incorporating multi-body system dynamics technology to predict dynamic characteristics of HDD ball-bearing spindle systems. First, the discrete governing equations of motion for HDD spindle systems, which consist of several flexible and rigid components, are derived through the use of Lagrangian equations. The elastic component modal frequencies and modal shape vectors are then obtained using a finite-element analysis. For ball bearing inherently defects, a mathematical model is used as a time-varying force, resulting in spindle vibrations. The time-varying force and component modal shape vectors are incorporated into the governing equations of the whole spindle systems. An implicit numerical integration method is used to obtain the forced vibration of the HDD spindle system. Finally, the dynamic responses of two typical HDD spindle systems are investigated numerically to predict the significant coupled vibration frequencies, mode shapes and resonance interactions. The results well agree with the solutions predicted by other analytical methods and the experimental results, respectively.

Correlations between structural, NMR and IR spectroscopic properties ofN-methylacetamide

Bond lengths, quadrupole coupling constants, chemical shifts and vibrational frequencies are important probes of hydrogen bonding. This was previously demonstrated for liquid N-methylacetamide (NMA) showing that cooperativity and non-additive contributions of hydrogen bonds play a significant role. The spectroscopic properties were calculated by standard ab initio methods in combination with a quantum cluster equilibrium (QCE) model and compared with measured data from NMR and IR spectroscopy. We have now extended the QCE model to larger molecular clusters and obtained better agreement between calculated and measured liquid-phase properties over large temperature ranges. The obtained linear correlations between spectroscopic properties and bond lengths and between different spectroscopic properties allow predictions for the gas- and the solid-phase values. The results can be used as a prediction tool for larger biomolecular structures where some experimental methods cannot be used or are not accurate enough. Copyright © 2001 John Wiley & Sons, Ltd.

Microwave spectrum, conformational equilibrium, 14N quadrupole coupling constants, dipole moment, vibrational frequencies and quantum chemical calculations for acrylamide

The microwave spectrum of acrylamide (CH2CHCONH2) has been investigated in the 20.0–60.5GHz spectral region at room temperature. Two conformers were assigned. The most stable rotamer is planar with the carbonyl and vinyl groups in the syn conformation. Five vibrationally excited states of the C–C torsional motion and six other vibrationally excited states have been assigned for this conformer, as have three deuterated species (amide group). The frequencies of most of these excited states have been determined by relative intensity measurements. The dipole moment of this rotamer is (in units of Debye) μa=0.269(3), μb=3.42(2), μc=0.12(24) and μtot=3.44(5). The 14N quadrupole coupling constants were found to be χaa=1.87(26) and χbb=2.73(16)MHz, respectively.The second, less stable skew form is non-planar with the CC–CO chain of atoms approximately 155° from syn. The ground vibrational state and two excited states were assigned. The syn form was found to be 6.5(6)kJmol−1 more stable than the skew conformer by relative intensity measurements.Quantum chemical calculations at HF, MP2 and DFT levels of theory using the rather large basis sets 6-311+G∗∗, 6-311++G∗∗ and cc-pVTZ have been made to assist the experimental work.