Low Vibrational Modes Research Articles

Far-IR/THz spectral characterization of the coherent synchrotron radiation emission at diamond IR beamline B22

Diamond is the new UK 3rd generation light source that opened to users since 2007 and now allocates more than 22 operational beamlines. Beamline B22 is dedicated to Infrared microspectroscopy and started operations in December 2009. By exploiting the Diamond SR source brightness it is optimized for mid-IR (2–25 μm wavelength) absorption spectroscopy, for fingerprint microprobe analysis and imaging mostly in Life Sciences but also Materials Sciences and Cultural Heritage. Vibrational spectroscopy analysis on condensed matter and material sciences can be performed at B22 by means of Fourier transform IR interferometry in a broader range from the visible up to the so-called THz region. Due to the uniquely wide B22 front end design (30 × 50 mrad2 angle and about 32 mm vacuum vessel internal height), the IR beamline B22 operational range spans across the far-IR/THz region, with effective performances tested up to 2 mm wavelength or, equivalently, well below 0.15 THz (FE cut off ~4 mm wavelength). Especially in low-alpha mode of operation of Diamond, by compressing the e− bunch length to a few millimeters coherent SR emission can be stimulated at comparable wavelengths. In the far-IR, a dramatic intensity increase can be observed at Diamond even at only a few μA of circulating current. A summary of the first performances so far achieved in the Far-IR/THz on the IR beamline B22 is here reported for what concerns the CSR emission at Diamond; this is for the storage ring running in dedicated low-alpha mode both in a stable configuration, as well as in the so-called “bursting” or unstable CSR emission. The former is particularly interesting to reach the longest wavelengths (<20 cm−1) so to address the lower energy vibrational modes in condensed matter, the latter is promising for the wider spectral far-IR/THz coverage allowed (around 100 cm−1), and consequently appealing for extending the spectroscopy capability into a broader range of applications.

Research on Dynamic Characteristic of the Engine Cylinder Based on ANSYS and Pro/E

The connecting rod is an important part in the engine cylinder. This paper studied the engine cylinder by using Pro/E and ANSYS and achieved some interest results. It used the Pro/E to establish three-dimensional model of the engine and to simulate on it. It also analyzes the connecting rod of cylinder by using the finite element analysis software ANSYS, its modal analysis method was put forward and the low natural frequency and vibration mode were calculated. The analysis method and the results can provide reference for the dynamic design of the connecting rod, and also provide a method for the fault diagnosis engine system.

Active Control of the Accordion Modes of a Submerged Hull

This work investigates active vibration control of tonal hull axial resonances to attenuate the structural and acoustic responses of a submarine. A submerged hull can be idealised as a ring-stiffened finite cylinder with external fluid loading. At low frequencies, rotation of the propeller results in discrete tones at the blade passing frequency and its harmonics. The fluctuating forces at the propeller are transmitted through the propulsion system, resulting in excitation of the low frequency hull vibrational modes, which in turn results in a high level of structure-borne radiated noise. Global hull modes are difficult to attenuate since passive control techniques such as damping materials and isolators are not practical due to size and weight constraints. This work numerically investigates the application of active vibration control based on a feedforward algorithm to suppress the axial and radial hull displacements. The effect of various cost functions and control arrangements on the structure-borne radiated noise is presented.

Seismic analysis of the hung curtain wall structure in Shanghai Center Tower

SUMMARYShanghai Center Tower, which is 632 m in height with 126 stories, will be the tallest building in China at the end of 2014. The extreme height of the building combined with the exterior shrink‐constructed and torsion‐constructed curtain wall imposes a great challenge on the seismic design of the curtain wall. This paper establishes a finite element (FE) model of the real‐scale building by considering the combination of the curtain wall and the main structure. The lower order modes of the building's vibration have been predicted, and good agreement has been observed between the numerical and experimental data, which validates the FE model of the building. Seismic response of the curtain wall was then investigated under three earthquake levels, including frequent, moderate and severe earthquakes. The acceleration magnification factors, the inter‐story drift ratios and the interior forces of the curtain wall met the requirements of the Chinese Design Code, which indicates that the structure is a good solution to withstand earthquakes. The present study provides an important database for the seismic design of curtain wall structure in Shanghai Center Tower, and it can be used as a seismic design reference for similar projects. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Chaotic vibrations of a post-buckled L-shaped beam with an axial constraint

Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an axial constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.

Finite Element Modeling and Modal Analysis of the Human Spine Vibration Configuration

This study was designed to investigate the modal characteristics of the human spine. A 3-D finite element model of the spine T12-Pelvis segment was used to extract resonant frequencies and modal modes of the human spine. By finite element modal analysis and harmonic response analysis, several lower vibration modes in the flexion-extension, lateral bending, and vertical directions were obtained and its vibration configurations were shown in this paper. The results indicate that the lowest resonant frequency of the model is in the flexion-extension direction. The second-order resonant frequency is in the lateral bending direction and the third-order resonant frequency of the T12-Pelvis model is in the vertical direction. The results also show that lumbar spinal vertebrae conduct the rotation action during whole body vibration (WBV). The vibration configurations of the lumbar spine can explore the motion mechanism of different lumbar components under WBV and make us to understand the vibration-induced spine diseases. The findings in this study will be helpful to understand WBV-related injury of the spine in clinics and the ergonomics design and development of mechanical production to protect human spine safety.

Born–Oppenheimer DFT molecular dynamics studies of S2O2: Non-harmonic effects on the lowest energy isomers

Born–Oppenheimer DFT molecular dynamics (BO-DFT-MD) simulations were performed on the three lowest energy isomers of S2O2. After a careful calibration of the electronic structure method, the calculations were done using the B3PW91/aug-cc-pVTZ method. The dynamic vibrational spectra are reported and the lowest vibrational modes are identified, which correlate well with ab initio static predictions. The non-harmonic effects are non-negligible for the studied isomers. The largest non-harmonic contributions (up to 22%) were found for the third and fourth modes of the cis-OSSO C2v isomer. The relative vibrational peak intensities provide valuable information for the identification of this as yet undetected stable species.

Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the acetic acid dimer in the gas phase

In the paper are described studies of the double proton transfer (DPT) processes in the cyclic dimer of acetic acid in the gas phase using Car-Parrinello (CPMD) and path integral molecular dynamics (PIMD). Structures, energies and proton trajectories have been determined. The results show the double proton transfer in 450 K. In the classical dynamics (CPMD) a clear process mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. The DPT mechanism is also asynchronic when quantum tunneling has been allowed in the simulation. It has been found that the calculated values of barrier height for the proton transfer depends very strongly on the used approaches. Barrier received from the free-energy profile at the CPMD level is around 4.5 kcal mol(-1) whereas at the PIMD level is reduced to 1 kcal mol(-1). The nature of bonding in acetic acid dimer and rearrangement of electron density due to the proton movement has been also studied by the topological analysis of Electron Localization Function and Electron Localizability Indicator function.

Dynamic testing of a damaged bridge

In this paper the results of a campaign of dynamic tests carried out on an existing reinforced concrete single-span bridge subjected to increasing levels of damage are presented. The deck structure consists of a slab and three simply supported beams. The damage is represented by a series of notches made on a lateral beam to simulate the effect of incremental concentrated damage. The modal parameters of the lower vibration modes were estimated from frequency response measurements obtained under harmonic excitation. The variation of natural frequencies shows an anomalous increase in the transition from one intermediate configuration to the next damage configurations. Changes in vibration modes are appreciable from the earliest level of damage. In particular, changes in modal curvature of lower modes do provide indication on the damage location.

Driving Modes and Material Stability of a Vibrating Polyethylene Membrane Viscosity Sensor

In this contribution a macroscopic double membrane rheometer presented earlier is modified to a single membrane configuration in order to study further characteristics of driving modes and material properties. Excitation and read- out of the membrane vibration are based on Lorentz forces induced in a static magnetic field. First, the possibility to influence on the excited vibration mode by pre-stressing the membrane is studied. It results that pre-stressing slightly increases the frequency of the resonance peaks and furthermore enables the excitation of lower order vibration modes at lower frequencies. By changing the pre-stress, the induced vibration modes and consequently the sensitivity range of the sensor can be altered. A second focus of the present work was to study the robustness of the Poly-Ethylene material and the resulting change of the vibration behavior with respect to temperature and aging. It was found that heating of the material increases the internal friction and decreases frequency and quality factor of the eigenmode. Furthermore, aging results in a considerable increase of the polymer stiffness leading to an increase of the eigenfrequency.

First Principle Kinetic Studies of Zeolite-Catalyzed Methylation Reactions

Methylations of ethene, propene, and butene by methanol over the acidic microporous H-ZSM-5 catalyst are studied by means of state of the art computational techniques, to derive Arrhenius plots and rate constants from first principles that can directly be compared with the experimental data. For these key elementary reactions in the methanol to hydrocarbons (MTH) process, direct kinetic data became available only recently [J. Catal.2005, 224, 115-123; J. Catal.2005, 234, 385-400]. At 350 °C, apparent activation energies of 103, 69, and 45 kJ/mol and rate constants of 2.6 × 10(-4), 4.5 × 10(-3), and 1.3 × 10(-2) mol/(g h mbar) for ethene, propene, and butene were derived, giving following relative ratios for methylation k(ethene)/k(propene)/k(butene) = 1:17:50. In this work, rate constants including pre-exponential factors are calculated which give very good agreement with the experimental data: apparent activation energies of 94, 62, and 37 kJ/mol for ethene, propene, and butene are found, and relative ratios of methylation k(ethene)/k(propene)/k(butene) = 1:23:763. The entropies of gas phase alkenes are underestimated in the harmonic oscillator approximation due to the occurrence of internal rotations. These low vibrational modes were substituted by manually constructed partition functions. Overall, the absolute reaction rates can be calculated with near chemical accuracy, and qualitative trends are very well reproduced. In addition, the proposed scheme is computationally very efficient and constitutes significant progress in kinetic modeling of reactions in heterogeneous catalysis.

Variable kinematic models applied to free-vibration analysis of functionally graded material shells

Closed-form solutions of free-vibration problems of simply supported multilayered shells made of Functionally Graded Material have been examined in the present paper. A variable kinematic shell model, which is based on Carrera’ sU ni fied Formulation is extended, in this work, to dynamic shell cases. Classical shell theories are compared to refined ones as well as to layer-wise kinematics and mixed assumptions based on the Reissner mixed variational theorem. A comparison with the few results available in the open literature is presented and conclusions are drawn regarding the accuracy of classical and advanced shell modeling to evaluate lower and higher vibration modes as well as the behavior of these modes in the shell thickness direction.

Multitemperature synchrotron powder diffraction and thermoelectric properties of the skutterudite La0.1Co4Sb12

Compounds with the skutterudite structure have potential use in thermoelectric power generation and the role of the filler atoms in filled skutterudites is still an open question regarding their effects on thermal conductivity. Partially filled skutterudite La0.1Co4Sb12 has been investigated by synchrotron powder x-ray diffraction between 90 and 700 K, as well as heat capacity, electrical and thermal transport property measurements, and Hall effect measurements. Anomalously large atomic displacement parameters (ADPs) are found for the La filler atoms, indicating that the La atoms are weakly bound in the structure. Analysis of the multitemperature ADPs of La using the Einstein model and the ADPs of the framework atoms using the Debye model gives an Einstein temperature of 79 K and a Debye temperature of 268 K. The heat capacity estimated from the Debye and Einstein temperatures is in good agreement with the measured experimental data. The ADP analysis also indicates that the La atoms are slightly displaced (0.06 Å) from the cage center possible due to covalent bonding with the host structure. Compared with unfilled CoSb3, the low energy La vibration modes significantly increase the heat capacity of La0.1Co4Sb12 at lower temperature despite the low La occupancy (refined occupancy of 4.9%). The small content of filling atoms results in a large reduction in the thermal conductivity.

One-dimensional anharmonic oscillator: Quantum versus classical vibrational partition functions

We analyze vibrational partition functions of low vibrational modes within the independent mode approximation to gain insight pertinent to the development of anharmonic corrections for transition state rate constants. As an example, we use a transition state for hydrogen abstraction on a lignin model compound. We found that for low frequencies, anharmonic effects are far more important than quantum effects. Our results suggest a hybrid model, where low-frequency modes are treated fully coupled using the classical or the Wigner–Kirkwood approximation, while high frequencies are described by the harmonic approximation. Mid-range frequencies could be expressed as independent anharmonic quantum modes.

Boson peak in low‐frequency Raman spectra of AsxS100‐x glasses: nanocluster contribution

AbstractThe origin of the Boson peak was investigated using Raman spectroscopy and ab initio calculations. Low frequency Raman active vibrational modes of different branchy‐, ring‐ and cage‐like AsmSn nanoclusters were calculated and compared to experimentally determined Raman spectra of AsxS100‐x glasses with different compositon. A good correlation was found between the spectral features and the calculated Raman modes. The possible structural nature of the Boson peak in arsenic chalcogenides is proposed and discussed. (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

20605 円形と矩形の混合境界を有する平板のカオス振動実験(OS6 非線形振動・カオス振動(1),オーガナイズドセッション)

Experimental results are presented on a plate with mixed boundary of circular and rectangular shape. The plate is excited by lateral periodic acceleration. In a typical frequency range, a non-periodic response is observed. The non-periodic response is examined by the Fourier spectrum and the maximum Lyapunov exponent. The response is found to be the chaotic response which is generated from the internal resonance with the lowest mode and three higher modes. The time response also shows the irregular movement with amplitude modulation. Applying the principal component analysis on the long time interval responses, it is found that five modes of vibration are generated in the chaos. The lowest mode of vibration and the sixth mode of vibration contribute to the chaos dominantly. Furthermore, the principal component is calculated on the chaotic response with short time intervals. In the larger amplitude response, the response is dominated by the lowest mode of vibration. On the contrary, in the smaller amplitude of the response, the responses of higher modes of vibration are increased.

Ab initio molecular dynamics studies on the ground singlet potential energy surface of the tetraoxygen molecule, O 4

We study the finite temperature dynamical process followed by the D 2d singlet ground state of tetraoxygen, O 4. Born–Oppenheimer ab initio molecular dynamics (AIMD) simulations are done at near-room temperature and at 700 K using a calibrated DFT-based electronic structure description. The vibrational spectra are reported and the lowest vibrational modes are identified, which correlate well with ab initio static predictions. The largest non-harmonic contributions on the spectra are found for the modes involving ν 5(B 1) and ν 6(A 1) quanta. The relative vibrational peak intensities provide valuable information for the identification of this as yet undetected stable polyoxygen species.

Modeling of surface stress effects on bending behavior of nanowires: Incremental deformation theory

The surface stress effects on bending behavior of nanowires have recently attracted a lot of attention. In this letter, the incremental deformation theory is first applied to study the surface stress effects upon the bending behavior of the nanowires. Different from other linear continuum approaches, the local geometrical nonlinearity of the Lagrangian strain is considered, therefore, the contribution of the surface stresses is naturally derived by applying the Hamilton's principle, and influence of the surface stresses along all surfaces of the nanowires is captured. It is first shown that the surface stresses along all surfaces have contribution not only on the effective Young's modulus of the nanowires but also on the loading term in the governing equation. The predictions of the effective Young's modulus and the resonance shift of the nanowires from the current method are compared with those from the experimental measurement and other existing approaches. The difference with other models is discussed. Finally, based on the current theory, the resonant shift predictions by using both the modified Euler–Bernoulli beam and the modified Timoshenko beam theories of the nanowires are investigated and compared. It is noticed that the higher vibration modes are less sensitive to the surface stresses than the lower vibration modes.

全周単純支持された初期変形を有する円板のカオス振動実験(&lt;特集&gt;D&amp;D 2008)

Experimental resuls are presented on chaotic vibrations of a simply supported circular plate with initial deformation. The plate is excited by lateral periodic excitation. In typical frequency range, non-periodic response is observed. The amplitude of response shows the irregular movement with amplitude modulation. The response is examined by the Fourier spectra, the maximum Lyapunov exponent and the Poincare projection. The response is found to be the chaotic response and that is generated from internal resonance condition of one to four. Time responses at the five points of the plate are measured simultaneously within long time interval. Applying the principal component analysis on the response of long time interval, it is found that three lower modes of vibration are generated in the chaos. The lowest mode of vibration contributes to the chaos dominantly. The second mode with one nodal diameter and the third mode with two nodal diameters contribute with small amount. The principal component is calculated with every short time intervals, the large amplitude of the chaotic response the contribution of the lowest mode of vibration predominantly. When the amplitude of the chaotic response decreases, the contribution of the lowest mode is decreased by 10 percent while the higher modes increase.

Experiments on Chaotic Vibrations of a Rectangular Plate under an In-Plane Elastic Constraint at Clamped Edges

Experimental results are presented on chaotic vibrations of a rectangular plate with in-plane elastic constraint. The plate has initial imperfection. Opposite edges of the plate are clamped and the other edges are simply supported. One side of clamped edges is connected to elastic springs and is movable to in-plane direction. The simply-supported edges are connected to the boundaries with adhesive flexible films. Loading in-plane compressive force to the plate, the plate shows pre-buckled configuration with the type of a softening-and-hardening spring. Under periodic lateral excitation, chaotic responses are obtained in specific frequency regions. Predominant chaotic responses are examined with the Fourier spectra, the Poincare projections and the maximum Lyapunov exponents. Furthermore, applying the Karhunen-Loeve method, contributions of vibration modes on the chaotic responses are confirmed. It is found that the chaotic responses are generated from the internal resonant vibrations with the first mode of vibration and higher modes of vibration. The chaotic responses are dominated by the lowest mode of vibration. The higher modes of vibration contribute from 11 to 20 percent to the chaos. As the exciting amplitude increases, the amplitude of the chaotic responses increases and frequency regions of the chaotic responses shift. In the larger amplitude of the response, the frequency region shifts to the higher range owing to the resonant response with the type of a hardening spring. In contrast, the frequency region shifts to the lower range when the amplitude of the chaotic response is smaller comparatively. The resonant response with the smaller amplitude corresponds to the type of a softening spring.