Rotational Vibration Mode Research Articles

Stiffness identification of reinforced concrete beams using rotation rate sensors

Monitoring flexural stiffness variations of cracked reinforced concrete (r/c) structures is one of the most challenging problems of the dynamics of these structures. In this article, the application of rotation rate sensors for structural health monitoring of reinforced concrete beams is proposed as an alternative SHM method to, e.g. those utilising more expensive and laborious fiber optics. This subject was investigated with progressively damaged 6 m long reinforced concrete beams. During each damage state, the cracks were located and described in detail. Experimental modal analyses were carried out. Translational and rotational vibration modes were acquired using translational accelerometers and rotation rate sensors. The stiffness distributions of the damaged reinforced concrete beams were identified from the modal properties using model-updating techniques. It is demonstrated that stiffness distributions calculated using rotational modes are more accurate than those obtained from the familiar translational natural modes of vibrations. Further improvement of stiffness identification of r/c beams from their vibrations was obtained by combining the directly measured rotational modes and their approximations from translational modes by the central difference method.

SIMULATION OF OSCILLATIONS OF WATER MOLECULES USING THE MODEL OF A TWO-FREQUENCY PENDULUM IN THE JAHN-TELLER POTENTIAL

The interaction potential for water molecules is considered, which corresponds to the presence of bends in hydrogen bonds in it. To explain the nature of this phenomenon, the theory of the Jahn-Teller effect (JTE) is applied. A model of the Jahn–Teller potential (JTP) was constructed, which has a minimum at a certain angle Θ. To simulate oscillations of water molecules in JTP using a pendulum, a correction of the angular potential U1 in the potential of directed forces (PDF) of intermolecular interaction is proposed using a wavelet type additive ΔU1 = c cos(mΘ)/exp(sΘ2). The parameters for the wavelet are selected based on the magnitude of the bending of hydrogen bonds in water (m=s=8, c=0…0.1). Modeling of rotational oscillations of molecules in JTP was carried out using the model of a two-frequency pendulum, which takes into account the ratio of the moments of inertia of the molecule (pendulum) along the axes k=3 and the PDF index n=8 in JTP Un =U1n. New types of pendulum oscillations in the JTP are determined in comparison with the original PDF (c=0) and their features. It is established that several types of oscillations are observed for this potential. These are new: sector, rotation of the pendulum in the potential trough – disordered or ordered, as well as types for PDF: two-frequency independent oscillations (IO) along the axes and ellipse-like oscillations (ELO) at one frequency. Oscillations in the JTP chute are observed for the main range of initial velocities inside an elliptical ring compressed along the Y axis, and only for the ELO, in an elliptical region elongated along the Y axis, as in the PDF. The methodology for calculating and analyzing the oscillation parameters of a two-frequency pendulum has been improved. The boundaries of oscillation types are determined for given parameters of the potential and a number of initial data. The difference between the patterns of oscillations is established for cases when the initial displacement of the pendulum is greater or less than the position of the minimum of the JTP. It is shown that the velocities at the boundary of the transition from the rotation of the pendulum in the potential trough to the IO correlate with the magnitude of the JTP maximum on the axis of the pendulum. The presence of stable transverse vibrations in the JTP for the case of protons of water molecules can apparently be considered as a new degree of freedom for vibrations of water molecules, which can lead to an explanation of the large contribution of rotational vibration modes to its heat capacity.

Revealing the Origin of Fast Delayed Fluorescence in a Donor Functionalized Bisterpyridine.

A new carbazole-substituted bisterpyridine with pronounced delayed fluorescence is presented. While the molecular donor-acceptor-donor design suggests the origin of this to be thermally activated delayed fluorescence (TADF), results from various photophysical characterizations, OLED characteristics, temperature-dependent NMR spectroscopy, and DFT calculations all point against the involvement of triplet states. The molecule exhibits blue emission at about 440 nm with two or more fast decay channels in the lower nanosecond range in both solution and thin films. The delayed emission is proposed to be caused by rotational vibrational modes. We suggest that these results are generally applicable, especially for more complex molecules, and should be considered as alternative or competitive emissive relaxation pathways in the field of organic light emitting materials.

Influence of the internal degrees of freedom of coronene molecules on the nonlinear dynamics of a columnar chain.

The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.

Design and simulation of broadband multiphase pentamode metamaterials

Pentamode metamaterial (PM) has great potential in controlling underwater waves due to its broadband and solid-state merits. The reported underwater PM devices were all designed with single metallic materials, which largely limited the realizable properties range of PM. Pentamode metamaterials for simulating water with dual phase and triple phase were proposed and investigated in this article. It was revealed that the acoustic scattering of the proposed PM in water is very weak within the simulation frequency range except at some resonance frequencies. The mean total scattering cross section of the proposed pentamode metamaterials is about two orders smaller than that of the titanium alloy block, while the far-field sound pressure of pentamode microstructures was only about 1/3 of that of titanium alloy block. It also illustrates that the second and third phase of the unit cell could not only broaden the realizable properties range of PM but also suppress the bending and rotational vibration modes, demonstrating the efficacy and broadband characteristic of the multiphase pentamode metamaterial.

Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition

We comprehensively study mechanical and vibrational properties of dimer packings in three-dimensional space with particular attention on critical scaling behaviors near the jamming transition. First, we confirm the dependence of the packing fraction at the transition on the aspect ratio, the isostatic contact number at the transition, and the scaling dependence of the excess contact number on the excess density. Second, we study the elastic moduli, bulk and shear moduli, and establish power-law scaling of them. Finally, we study the vibrational density of states and its characteristic frequency. The vibrational density of states shows two plateaus in the lower- and higher-frequency regions, which are characterized by rotational and translational vibrational modes, respectively. The onset frequency of the lower-frequency plateau scales linearly to the square root of excess density. The scaling laws in the mechanical and vibrational properties are consistent between two- and three-dimensional dimers, and they are identical to those in spheres.

Structural-distortion modes and transport properties of La0.5Ca0.5MnO3 by co-doping Dy3+ and Sr2+ ions

La0.5-xDyxCa0.5-ySryMnO3 (x=0, 0.05, 0.08, 0.1, 0.14, 0.16, 0.2) polycrystalline samples were prepared by high-temperature solid-state reaction. The A-site disordering is increased with the doping concentration x, and meanwhile the average ionic radius of A-site is kept constant. X-ray diffraction and Raman spectroscopy were combined to investigate the microstructural distortion of MnO6 octahedron. Results show that the rotational vibration (RV) is the dominant distortion mode. With the A-site disordering increasing, RV mode is obviously hardened, and the Jahn-Teller distortion is enhanced. Properties investigation shows that the insulation is strengthened because of FM double exchange effect suppressed with A-site disordering increasing, and the magnetoresistance effect is weakened. A relatively significant magnetoresistance effect was observed in the low temperature region for the high-doped concentration sample, which may be related to the strong magnetic moment of Dy3+.

Design of a Spatial Vibration System for Prescribed Ratio of Energy Peaks

The work ratio is a primary factor in the applications relevant to wide bandwidth requirements because a bandwidth depends on resonant peaks. Especially, since a single-body system can have up to six resonant peaks, a six degree-of-freedom spatial system is more desirable for a broad bandwidth design. This paper presents a novel design method of a spatial vibration system for any prescribed ratio of energy peaks. Firstly, we introduce an important and concise geometric nature of a spatial vibration system with a single rigid body when it has only rotational vibration modes. The vibration modes represent vibration axes and six lines of action can be obtained by transforming the vibration modes by the mass matrix. It is shown that the six axes of vibration and six lines of action form two orthocentric tetrahedra that share the orthocenter coincident with the mass center. It is also shown that the stiffness matrix determined from two tetrahedra can always be realized by means of parallel connection of line springs. Using the orthocentric tetrahedra, we acquire analytical expressions for the energy produced by external forces at resonant frequencies, which is used to determine vibration modes that satisfy the requirements for given mass properties and six target resonant frequencies. Finally, the stiffness matrix that satisfies requirements is found and realized. To illustrate the process of the presented method, we use four numerical examples with different work ratios and demonstrate that the method is useful for a wide bandwidth.

Gas identification with graphene plasmons

Identification of gas molecules plays a key role a wide range of applications extending from healthcare to security. However, the most widely used gas nano-sensors are based on electrical approaches or refractive index sensing, which typically are unable to identify molecular species. Here, we report label-free identification of gas molecules SO2, NO2, N2O, and NO by detecting their rotational-vibrational modes using graphene plasmon. The detected signal corresponds to a gas molecule layer adsorbed on the graphene surface with a concentration of 800 zeptomole per μm2, which is made possible by the strong field confinement of graphene plasmons and high physisorption of gas molecules on the graphene nanoribbons. We further demonstrate a fast response time (<1 min) of our devices, which enables real-time monitoring of gaseous chemical reactions. The demonstration and understanding of gas molecule identification using graphene plasmonic nanostructures open the door to various emerging applications, including in-breath diagnostics and monitoring of volatile organic compounds.

Wave propagation in elastic metamaterial beams and plates with interconnected resonators

In this work, new beam and plate metamaterials with interconnected local resonators are proposed. This design promotes the splitting and coupling between transverse and rotational vibration modes of the resonator chain. It produces a particular band structure with two band gaps: a wide band gap opens at the in-phase transverse natural frequency of the resonator chain and a second band gap, with narrower width, appears at higher frequencies. The Timoshenko beam and Mindlin–Reissner plate models are used to compute the band structure as well as the dynamic forced response. A parametric analysis of the band gaps is performed by varying the interconnection properties. The metamaterial plate presents a directional wave propagation pattern due to partial band gaps. In addition, a metamaterial beam manufactured by additive manufacturing is investigated. The experimental results are in agreement with the numerical predictions. Therefore, the proposed concept showed to be promising for metamaterial design aiming at creating singular band gaps with broadband absorption and directional/focalization features.

Modeling and Dynamic Analysis of Cutterhead Driving System in Tunnel Boring Machine

Failure of cutterhead driving system (CDS) of tunnel boring machine (TBM) often occurs under shock and vibration conditions. To investigate the dynamic characteristics and reduce system vibration further, an electromechanical coupling model of CDS is established which includes the model of direct torque control (DTC) system for three-phase asynchronous motor and purely torsional dynamic model of multistage gear transmission system. The proposed DTC model can provide driving torque just as the practical inverter motor operates so that the influence of motor operating behavior will not be erroneously estimated. Moreover, nonlinear gear meshing factors, such as time-variant mesh stiffness and transmission error, are involved in the dynamic model. Based on the established nonlinear model of CDS, vibration modes can be classified into three types, that is, rigid motion mode, rotational vibration mode, and planet vibration mode. Moreover, dynamic responses under actual driving torque and idealized equivalent torque are compared, which reveals that the ripple of actual driving torque would aggravate vibration of gear transmission system. Influence index of torque ripple is proposed to show that vibration of system increases with torque ripple. This study provides useful guideline for antivibration design and motor control of CDS in TBM.

Statistically steady states of forced isotropic turbulence in thermal equilibrium and non-equilibrium

We investigate statistically steady states of turbulent flows when molecular degrees of freedom, in particular vibration, are taken into account. Unlike laminar flows initially in thermal non-equilibrium which asymptotically relax towards thermal equilibrium, turbulent flows present persistent departures from thermal equilibrium. This is due to fluctuations in temperature and other thermodynamic variables, which are known to increase with turbulent Mach number. Analytical results are compared to direct numerical simulations at a range of Reynolds and Mach numbers as well as molecular parameters such as relaxation times. Turbulent fluctuations are also shown to disrupt the distribution of energy between translational–rotational–vibrational modes even if thermal equilibrium is attained instantaneously relative to turbulence time scales, an effect that increases with characteristic relaxation times. Because of the nonlinear relation between temperature and vibrational energy in equilibrium, the fluctuation of the latter could be strongly positively skewed with long tails in its probability density function. This effect is stronger in flows with strong temperature fluctuations and when vibrational modes are partially excited. Because of the finite-time relaxation of vibration, departures from equilibrium result in very strong transfers of energy from the translational–rotational mode to the vibrational mode. A simple spectral model can explain the stronger departures from thermal equilibrium observed at the small scales. The spectral behaviour of the instantaneous vibrational energy can be described by classical phenomenology for passive scalars.

Nonlinear dynamic co-rotational formulation for membrane elements with in-plane drilling rotational degree of freedom

Purpose nonlinear dynamic analysis of triangular and quadrilateral membrane elements with in-plane drilling rotational degree of freedom. Design/methodology/approach The nonlinear analysis is carried out using the updated co-rotational Lagrangian description. In this purpose, in-plane co-rotational formulation that considers the in-plane drilling rotation is developed and presented for triangular and quadrilateral elements, and a tangent stiffness matrix is derived. Furthermore, a simple and effective in-plane mass matrix that takes into account the in-plane rotational inertia, which permit true representation of in-plane vibrational modes is adopted for dynamic analysis, which is carried out using the Newmark direct time integration method. Findings The proposed numerical tests show that the presented elements exhibit very good performances and could return true in-plane rotational vibrational modes. Also, when using a well-chosen co-rotational formulation these elements shows good results for nonlinear static and dynamic analysis. Originality/value Publications that describe geometrical nonlinearity of the in-plane behaviour of membrane element with rotational d.o.f are few, and often they are based on the total Lagrangian formulation or on the rate form. Also these elements, at the author knowledge, have not been extended to the nonlinear dynamic analysis. Thus, an appropriate extension of triangular and quadrilateral membrane elements with drilling rotation to nonlinear dynamic analysis is required.

Modulations of Transition-State Control of State-to-State Dynamics in the F + H2O → HF + OH Reaction.

The full-dimensional quantum dynamics of the F + H2O → HF + OH reaction is investigated at the state-to-state level for the first time using a transition-state wave packet method on an accurate global potential energy surface. It is found that the H2O rotation enhances the reactivity and the product-state distribution is dominated by HF vibrational excitation while the OH moiety serves effectively as a spectator. These observations underscore the transition-state control of the reaction dynamics, as both the H2O rotational and HF vibrational modes are strongly coupled to the reaction coordinate at the transition state. It is also shown that the transition-state dominance of the reaction dynamics is modulated by other features on the potential energy surface, such as the prereaction well.

The sudden vector projection model for reactivity: mode specificity and bond selectivity made simple.

CONSPECTUS: Mode specificity is defined by the differences in reactivity due to excitations in various reactant modes, while bond selectivity refers to selective bond breaking in a reaction. These phenomena not only shed light on reaction dynamics but also open the door for laser control of reactions. The existence of mode specificity and bond selectivity in a reaction indicates that not all forms of energy are equivalent in promoting the reactivity, thus defying a statistical treatment. They also allow the enhancement of reactivity and control product branching ratio. As a result, they are of central importance in chemistry. This Account discusses recent advances in our understanding of these nonstatistical phenomena. In particular, the newly proposed sudden vector projection (SVP) model and its applications are reviewed. The SVP model is based on the premise that the collision in many direct reactions is much faster than intramolecular vibrational energy redistribution in the reactants. In such a sudden limit, the coupling of a reactant mode with the reaction coordinate at the transition state, which dictates its ability to promote the reaction, is approximately quantified by the projection of the former onto the latter. The SVP model can be considered as a generalization of the venerable Polanyi's rules, which are based on the location of the barrier. The SVP model is instead based on properties of the saddle point and as a result capable of treating the translational, rotational, and multiple vibrational modes in reactions involving polyatomic reactants. In case of surface reactions, the involvement of surface atoms can also be examined. Taking advantage of microscopic reversibility, the SVP model has also been used to predict product energy disposal in reactions. This simple yet powerful rule of thumb has been successfully demonstrated in many reactions including uni- and bimolecular reactions in the gas phase and gas-surface reactions. The success of the SVP model underscores the importance of the transition state in controlling mode-specific and bond-selective chemistry.

A model for quasi-parity-doublet spectra in odd-mass nuclei

A model of a quadrupole–octupole vibrating and rotating core plus a particle is proposed to describe and classify the quasi-parity-doublet spectra in odd-mass nuclei. The yrast levels are described as low-energy rotation–vibration modes built on the ground state. The non-yrast split parity-doublet sequences are considered as higher-energy rotation–vibration modes coupled to one-quasi-particle states. The even–even core is considered within the model of a coherent quadrupole–octupole motion, while the odd nucleon is described within the reflection-asymmetric deformed shell model with pairing interaction. The Coriolis decoupling and K-mixing interactions are calculated microscopically through a parity projection of the single-particle wave function. The unified model scheme was tested on the yrast and non-yrast quasi-parity-doublet spectra in the nuclei 223Ra and 221Fr.

Features of rotational modes of vibrations of water molecules in free and bound states

The paper considers rotational (including librational - dimensional rotational) vibrations and the number of corresponding vibrational modes for molecules of water in its various physical phase states - liquid, ice and bound. The main purpose of the research is comparative analysis of vibrational modes of molecules of water in different phase states, taking into account the results of previous paper [6] on vibrational modes of molecules in liquid water. The analysis of changes in the number of rotational modes of molecules of water for its various phase states and physical consequences of these changes for physical and thermal properties of water was conducted. Increased force of hydrogen bonds of water molecules in ice or ice-like state leads to reducing the number of rotational vibration modes, and accordingly, the number of degrees of freedom of molecules and heat capacity of the phase. State, mobility and structure of macromolecules in aqueous solutions are determined by the strength of ice-like skeleton/corset of their hydration shell formed by bound water molecules.

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.

Nonlinear excitation of a rotational mode in a piezoelectrically excited square-extensional mode resonator

We present an experimental study of the nonlinear behavior of a square-extensional (SE) mode microelectromechanical resonator, actuated with a piezoelectric AlN thin film. The acoustic vibration fields of the device are characterized using laser probing. A nonlinear vibration behavior of the SE mode is observed above a drive power level of −10 dBm such that the vibration amplitude of the SE mode saturates and a rotational in-plane vibration mode is excited at a significantly lower frequency (0.725 MHz) than the SE mode (16.670 MHz). Interestingly, the measured ∼10 nm saturation amplitude of the SE mode is more than a decade below the amplitude value at which mechanical or electromechanical nonlinearities are estimated to become significant.

C32 超精密加工機の動特性評価(OS11 超精密加工(1))

This paper discuss the dynamic stiffness of guideways of a ultra-precision machine tool. v-v roller guideways are employed in this ultra-precision machine tool,as they can provide very smooth motion and good straightness. Stiffness is identified from the measured data and compared with that of linear guideways. As a result, rotational vibration mode was identified from simple designed model, and its natural frequency was calculated with the designed static stiffness.