Torsional Vibration Modes Research Articles

Quantum Chemical Characterization of 4-({4-[Bis(2-Cyanoethyl)Amino]Phenyl}Diazinyl)Benzene Sulfonamide by Ab-Initio Calculation

4-({4-[Bis(2-cyanoethyl)amino]phenyl}diazinyl)benzene sulfonamide is the azo dye material which has general application in the textile industry. Experimentally, it has been synthesized and geometrically characterized by G. Gervasio et al. In this study, the theoretical analysis has been calculated by using the ab-initio method based on the Density Functional Theory/B3LYP/6-311G(d,p) to characterize the structural, spectroscopy, and electronic properties of the title azo dye. Its molecular geometries are in good agreement with those of available experimental data. 129 vibrational modes have been specified with stretching, in-plane-bending, out-of-plane-bending, and torsion vibration modes by the Potential energy Distribution analysis. The ultraviolet spectra appear in a single peak for six common solvation at 429 nm. The Gauge-Invariant Atomic Orbital approach has been applied to predict the chemical shifts of 1H and 13C NMR only in DMSO solvation. The electronic properties have been investigated such as the energy bandgap (3.34 eV), ionization potential energy (6.24 eV), electron affinity (2.90 eV), electronegativity (4.57 eV), and chemical hardness (1.67 eV) by using the Frontier Molecular Orbital Theory from the energy interaction of the Lowest Unoccupied Molecular Orbital and Highest Occupied Molecular Orbital. The characterization of the title azo dye is conducted theoretically for the first time in this study.

Double Sub-Resonance Mechanism in Torsional–Flexural Vibrations of a Double-Track Short Bridge Under a Moving Train

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ([Formula: see text]) of the bridge, from which we can determine the sub-resonance speed as ([Formula: see text]). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.

An Internal Resonance Based Method for Reducing Torsional Vibration of a Gear System

The gear system is one of the most widely-used transmission systems due to its accurate transmission ratio and high efficiency. However, torsional vibration may severely degrade transmission performance and shorten the gear lifespan. In view of this, a nonlinear interaction principle suitable for vibration energy transfer is researched, and an internal resonance based method is put forward to reduce the torsional vibration of the gear system. According to the coupling relationship between the gear torsional vibration mode and the vibration absorber mode, the 1:1 internal resonance condition is analyzed by the multiple scale method and the sufficient and necessary conditions for establishing internal resonance are obtained. Through stability analysis, the vibration energy transfer channel based on internal resonance is successfully established, by which vibration energy can be transferred to and dissipated by the vibration absorber. Based on numerical and virtual prototyping simulations, vibration reduction performances are examined, including effectiveness, damping characteristics and robustness. The research results show that the proposed internal resonance based method can effectively reduce the torsional vibration of the gear system.

Viscous fluid–structure interaction of micro-resonators in the beam–plate transition

We numerically investigate the fluid–structure interaction of thin elastic cantilever micro-structures in viscous fluids. The Kirchhoff plate equation describes the dynamics of the structure, and a boundary integral formulation represents the fluid flow. We show how the displacement spectrum of the structures changes as the geometry is altered from a narrow beam to a wide plate in a liquid. For narrow beams, the displacement spectrum exhibits only a few resonance frequencies, which correspond to the vibrational modes described by the Euler–Bernoulli equation (Euler–Bernoulli modes). The spectrum of wide plates exhibits several additional resonance frequencies associated with the plate’s torsional and higher-order vibrational modes. Wide plates in Euler–Bernoulli modes exhibit higher damping coefficients, but due to an increased added-mass effect, also higher Q-factors than slender beams. An investigation into the fluid flow reveals that for the Euler–Bernoulli modes of wider plates, the fluid flow and energy dissipation near the plate’s edges increase, resulting in increased damping coefficients. Concomitantly, a region of minimal viscous dissipation near the plate’s center appears for wider plates, resulting in an increased added-mass effect. Higher-order modes of wider plates exhibit lower Q-factor than the Euler–Bernoulli modes due to a decreased fluid flow at the plate’s edges caused by the appearance of circulation zones on both sides of the plate. This decreased flow at the edge reduces the damping and the added-mass effect, yielding lower Q-factors. We anticipate that the results presented here will play a vital role in conceiving novel MEMS resonators for operation in viscous fluids.

Molecular dynamics simulation, DFT calculations and vibrational spectroscopic study of N[sbnd]H•••O bound dimer models for DL-β-phenylalanine and 3-amino-3-(4-chlorophenyl)propionic acid

Zwitterionic NH•••O bonded dimer structures have been proposed one each for DL-β-Phenylalanine and 3-Amino-3-(4-chlorophenyl)propionic acid. Stable zwitterionic monomer possessing NH3+ and COO¯ moieties in implicit aqueous solvation were computed at B3LYP/6-311++G** level and used for classical MD simulations. MD simulations yielded, among many NH•••O bonded transient dimer and trimer species, the two dimer structures with longest lifetime τ in water medium (τ = 111.67 ps for DL-β-Phenylalanine and 111.53 ps for 3-Amino-3-(4-chlorophenyl)propionic acid). The first peaks in radial distribution functions (RDF) confirmed the formation of NH•••O bonded dimer structures, one each for DL-β-Phenylalanine and 3-Amino-3-(4-chlorophenyl)propionic acid; the first minima determined the cut-off values for the inter-molecular H•••O distances. Further, the first minimum-solvation shell also indicated one zwitterionic dimer structure with 10 water molecules as solvent medium. Experimental IR frequencies due to the NH3+ and COO¯ moieties agree within 5% of the computed values for the dimer structures. Low-frequency Raman bands near 100–50 cm−1 are assigned to the torsional vibration modes of zwitterionic NH•••O bonded dimer structures. On the role of Chlorine with respect to all the molecular properties of 3-Amino-3-(4-chlorophenyl)propionic acid vs DL-β-Phenylalanine computed from NBO, AIM and NCI calculations, its influence is not substantial but discernible enough for gaining insights into the two NH•••O bonded zwitterionic dimer species.

Vibration characteristics of axial compressor blade under complex loads

In this study, 3D models of a compressor blade for an aero engine with three different levels of surface accuracy (with 4, 6 and 10 section profiles) were obtained via reverse engineering by fitting point-cloud data. Then, finite element and flow-field models of the blade were established and validated. The vibration characteristics of the blade under typical operating conditions were analyzed by considering the interaction between the aerodynamic load by airflow and the centrifugal load by blade rotating. The results showed that, under complex centrifugal and aerodynamic loads, the three blade models differed significantly in their high-order dynamic frequencies, and the modal frequencies that were dominated by a torsional mode of vibration were sensitive to the aerodynamic load. Hence, considering both the aerodynamic excitation and the centrifugal load increased the accuracy of the numerical computation of the blade vibration characteristics. Moreover, a comparison of the computational results from the three blade models showed that models B6 and B10 differed only insignificantly, and B6 decreased the complexity of the modeling process while satisfying the required computational accuracy. Thus, model B6 is the best option for engineering analysis and computation.

QM/MM Studies on Thermally Activated Delayed Fluorescence of a Dicopper Complex in the Solid State

Dicopper complexes with thermally activated delayed fluorescence (TADF) phenomena are important in enriching the arsenal of organic light-emitting diodes materials. However, the TADF mechanism is still elusive, especially in the solid state. Herein, we chose a TADF dicopper complex and investigated its geometric and electronic structures and absorption and emission spectra using DFT, TD-DFT, and QM/MM methods. On the basis of these results, we further estimate the fluorescence emission rate from the S1 state, phosphorescence emission rate from the T1 state, and forward and reverse intersystem crossing (ISC and rISC) rates between S1 and T1. The present work shows that both the S1 and the T1 states have mixed metal-to-ligand and interligand charge-transfer character. Good spatial separation between the HOMO and the LUMO makes the S1–T1 energy gap small, ca. 2.8 kcal/mol. This small energy gap leads to efficient ISC and rISC processes, whose rates are much larger than the fluorescence and phosphorescence emission rates at 300 K, therefore enabling TADF. In contrast, at 77 K, the rISC process is blocked because its rate is much smaller than the phosphorescence emission. Thus, TADF disappears at 77 K. Further analysis shows that high-frequency deformation and low-frequency torsional vibrational modes make a large contribution to the Huang–Rhys factors, but Duschinsky rotation effects are essentially negligible for both the ISC and the rISC processes.

Simulation of fluid-structure interaction during the phaco-emulsification stage of cataract surgery

During cataract surgery the clouded lens is broken up by phacoemulsification. The iris can become highly mobile and could be entrained by the phacoemulsification probe, under a condition known as intraoperative floppy iris syndrome (IFIS). In this study we explore the mechanism of IFIS during phacoemulsification-based cataract surgery using fluid-structure interaction (FSI) simulations. As the first study of its kind, we developed a simplified two-dimensional simulation framework and utilized it to elucidate the dynamics of the iris and surrounding aqueous humor during phaco-emulsification. Three types of iris dynamics were observed when the phaco probe was operated in the torsional vibration mode and placed at various locations in the anterior chamber, which we termed as the repulsion (where the iris is repelled by the probe), attraction (where the iris is drawn toward the probe) and adhesion mode (where the iris is adhered to the probe at some point along its length), respectively. The anterior chamber is partitioned into different zones which exhibit each of these three modes. Furthermore, the effects of iris stiffness and length as well as the power and frequency of the probe operation were investigated. It was found that IFIS could be mitigated by increasing the iris stiffness, shortening the iris length (i.e., pupil dilation), decreasing the power of the emulsification probe, and maintaining the probe operation frequency in a range around the frequency of the iris’ fundamental bending mode. This study provides new physical insights into the dynamics of fluid-iris interaction during phaco-emulsification, which may guide clinicians to optimize their surgical protocol.

Flexural–Torsional Free Vibration Analysis of a Double-Cantilever Structure

Abstract This paper aims to investigate the free coupled flexural–torsional vibrations of a double-cantilever structure. The structure consists of two identical Euler–Bernoulli cantilever beams with a piezoelectric layer on top. The beams are connected by a rigid tip connection at their free ends. The double-cantilever structure in this study vibrates in two distinct modes: flexural mode or coupled flexural–torsional mode. The flexural mode refers to the in-phase flexural vibrations of the two cantilever beams resulting in translation of the tip connection, while the coupled flexural–torsional mode refers to the coupled flexural–torsional vibrations of the cantilever beams resulting in rotation of the tip connection. The latter is the main interest of this research. The governing equations of motion and boundary conditions are developed using Hamilton’s principle. Two uncoupled equations are realized for each beam: one corresponding to the flexural vibrations and the other one corresponding to the torsional vibrations. The characteristic equations for both the flexural and the coupled flexural–torsional vibration modes are derived and solved to find the natural frequencies corresponding to each mode of vibration. The orthogonality condition among the mode shapes is derived and utilized to determine the modal coefficients corresponding to each mode of vibration. Moreover, the analytical and experimental investigations show that the coupled flexural–torsional fundamental frequency of the structure is dependent on dimensional parameters including the length of the cantilever beams and the length of the tip connection.

Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

Out-of-plane free vibration analysis of three-layer sandwich beams using dynamic stiffness matrix

This paper has been devoted to exact calculation of the natural frequencies for out-of-plane free vibration of three-layer symmetric sandwich beams by using dynamic stiffness matrix method. Governing differential equations of motion have been derived using Euler-Bernoulli beam theory and St. Venant’s torsion theory, so that the effects of shear deformation in the face layers and rotary inertia are not taken into account and the cross-section is allowed to warp without restraint. Wittrick-Williams algorithm has been used to calculate the natural frequencies. Accuracy and ability of the dynamic stiffness matrix method have been illustrated in form of several examples. Results are verified through comparison with the natural frequencies obtained from ABAQUS software. Full independence of out-of-plane bending and torsional modes of vibration for three-layer symmetric sandwich beams has been proven.

Influence of soil flexibility and plan asymmetry on seismic behaviour of soil-piled raft-structure system

Ever-increasing scarcity of land and demand for high-rise structures has significantly contributed to the use of combined piled raft foundations (CPRF) in soft ground. However, utility, design constraints and aesthetic considerations bring asymmetry to superstructures, making structures more vulnerable during seismic excitations. Traditional design practices involve designing superstructure elements and foundation considering fixity at the base of the superstructure and ignoring soil-structure interaction (SSI) which may result in under-estimation of forces and displacement in the system. Hence, the present study aims at developing new seismic design guideline pertaining to asymmetric single and multi-storied structure supported on CPRF embedded in soft clay. Some important parameters, such as torsional coupling mode of vibration and multi-storey idealisation involving the effect of higher modes are investigated incorporating seismic SSI effect. The study broadly reveals that the torsional to lateral period ratio considerably influence the seismic response of asymmetric structural system on the piled raft foundation due to the incorporation of SSI. Furthermore, multi-storey building idealisation gives a higher estimation of response compared to single storey idealization in superstructure and pile head which may be due to the effect of higher modes of vibration and SSI

Transfer matrix model and experimental validation for a radial-torsional ultrasonic motor

Traditional traveling-wave rotary ultrasonic motors have been widely used in many applications due to their excellent output performances. However, the structure optimization have be hindered by the specific requirements on the piezoelectric ceramics with complex polarizations and shapes. To address such issues, a compact type ultrasonic motor operating at radial-torsional conversion mode is proposed in this paper, which is simply excited by one ring type piezoelectric wafer with a single polarization. This motor basically consists of one rotor and one disk type stator, which can be divided into an outer ring, four connection beams and an inner ring. A ring type piezoelectric wafer is bonded to the bottom face of the outer ring. Upon an excitation signal at resonance frequency, the proposed motor is able to rotate, driven by the torsional vibration mode of the inner ring converted from the radial vibration mode of the outer ring via the connecting beams An electromechanical model utilizing the transfer matrix method is built to analyze the dynamic behavior of the motor. This transfer matrix model of the system could provide an effective approach for simulating the coupled mechanical and electrical properties. Based on the proposed model, the dynamic process for converting the radial vibration mode into the torsional mode is quantatively assessed. Last, the vibration characteristics of the prototype motor is tested by using a 3D laser Doppler vibrometer and the experimental results are in good agreement with the calculations, confirming the validity of the transfer matrix model and the feasibility of the motor design.

Analysis of Modal Characteristics of Long-Span Suspension Bridges with Ruled Surface Spatial Cables

In this paper, new concepts of single-leaf hyperboloid spatial cable suspension bridges and hyperbolic parabolic spatial cable suspension bridges are proposed. Combined with the 4000 m long-span Messina Strait Bridge, dynamic modal analyses of the spatial cable suspension bridges are carried out. The results show that the spatial suspension bridges have a torsional vibration mode appearing much later, a torsional-bending frequency ratio greatly improved, a critical wind speed for flutter greatly improved, and better wind stability, as compared with the parallel suspension bridge.

Excitation method and electromechanical coupling dynamic model of a novel torsional piezoelectric actuator

Torsional piezoelectric actuators have been widely applied in many fields due to their specific vibration mode. However, the conventional torsional vibration piezoelectric actuators require circumferentially polarized piezoelectric ceramics or special structural designs, increasing manufacturing difficulty and processing costs, and seriously limiting their applications. In order to solve these problems, a novel excitation method of torsional vibration is proposed in this study through the arrangement of the regular piezoelectric ceramic plates polarized along their thickness direction, and then two surface-bonded type torsional piezoelectric actuators are constructed to stimulate the odd and even order torsional vibration modes, respectively. A novel transfer matrix model of describing the torsional vibration, which involves in the mechanical and electrical properties, is created first for the piezoelectric composite beam element. Then a general electromechanical coupling dynamic model is developed to reveal dynamic behaviors of the proposed surface-bonded type torsional piezoelectric actuators. In addition, the finite element simulation and experimental investigations are carried out to confirm the validation of the proposed excitation method of torsional vibration and to verify the correctness of the developed electromechanical coupling dynamic model. The comparisons showed that the results calculated by the developed theoretical model, simulated by the finite element method, and tested by the experiments matched well, indicating that the developed electromechanical coupling dynamic model is correctness and the excitation method of torsional vibration is effective. Finally, the output characteristics of the two proposed actuator prototypes are measured, further confirming the feasibility of the proposed torsional vibration excitation method.

Prediction of stability against subsonic flutter for axial turbine machine compressor blade assemblies

The developed method for prediction of their dynamic stability limit is described for the first flexural and torsional modes of vibrations against subsonic flutter. It involves the use of the database of the critical reduced frequencies of the blade vibrations as a dynamic stability limit within the wide range of variations of the following characteristics: phase angle of flexural, torsional and flexural-torsional vibrations of the adjacent blades; attack angle; reduced vibration frequency; geometric parameters for the airfoil and cascade; law of motion for blade airfoils. The algorithm realized as the numerical software assumes the determination of the critical reduced frequencies in the most loaded section of the full-scale blade assembly via the analysis of the distribution of the relative flow rate, attack angle, amplitudes of vibrations over the blade height and the subsequent comparison with the functional defining its critical value for different attack angles. The results of practical implementation of the developed procedure are given for the assessment of the stability of the blade assemblies of axial compressors in some modern aircraft gas-turbine engine at the first flexural mode of vibrations. It is implied that the proposed method allows one to select the optimal reduced frequency of vibrations of the blade assembly for the specified geometry of its peripheral sections and attack angle of the mainstream flow upon the condition of subsonic flutter at the engine design state.

The seismic performance of tunnel-form buildings with a non-uniform in-plan mass distribution

The specific operating conditions in concrete box-type (tunnel-form) buildings would lead to the concentration of walls in the interior parts of the plan and lack of structural walls in the perimeter of the plan. In this situation, due to the considerable reduction in torsional stiffness, usually torsional vibration modes prevail over translational vibration modes, therefore the building behaves as a torsionally flexible structure. Torsionally flexible buildings are often more sensitive to the eccentricities of mass and stiffness as well as the intensity of the torsional component of an earthquake, in which, an increase in these parameters results in both increased forces and displacements. In this study, the effect of mass eccentricity in the plan on the behavior of box-type (tunnel-form) concrete buildings with 5 and 10 stories is scrutinized. The performance level of these buildings under the Design Basis Earthquake (475 years return period) for different values of mass eccentricity has been determined. In the framework of reliability studies, fragility curves were extracted based on the IM-Based method. Ratio estimation of the uncoupled frequencies for the studied models is another achievement of this research. The results prove that the studied system has high seismic reliability under torsions due to the asymmetric distribution of mass in the plan. In the studied buildings, while moving the center of mass up to 20% of the plan, there was no drop in performance level in Design Basis Earthquake (DBE) and all of the models stayed in the immediate occupancy performance level.

Triple resonances involving two frequencies in the motor frequency conversion start phase

A rigid body model of torsional vibration of stator and rotor coupling system excited by electromagnetic force of motor is established in this paper. Energy method is introduced to solve the nonlinear vibration of the coupling system. Based on the linear part of the kinetic energy, potential energy and air gap magnetic field energy, the Lagrange function is obtained. And then, the Lagrange-Maxwell equation is used to solve natural characteristics. The nonlinear part is used to derive the nonlinear vibration equations of coupling system in torsional vibration modes. With numerical calculation, considering the triple resonances involving two natural frequencies, the influences of tuning parameters, damping coefficient and magnetic flux-density on resonance characteristics are illustrated and analyzed by the frequency-response curves. The results provide a theoretical basis for the subsequent calculation.

Shear Moduli of Metal Specimens Using Resonant Column Tests

Abstract The shear moduli of cylindrical metal specimens were determined by performing resonant column tests in a torsional mode of vibration. The tests were performed on four different metals, namely (i) aluminum, (ii) brass, (iii) copper, and (iv) mild steel. Keeping the length (L) of the specimens the same, different diameters (d) were chosen to vary the torsional stiffness and, thereby, the resonant frequency. Additional circular plates were attached to the top of the drive mechanism to have different resonant frequencies with the same torsional stiffness (KT). The shear moduli (G) were established by two different methods, namely (i) from the evaluation of KT and (ii) by first determining the mass moment of inertia (Jd) of the drive mechanism and then finding G from the measured circular resonant frequency (ωn). Both the methods provide exactly the same answer(s). For aluminum and brass, the measurement of the shear modulus was found to be much more accurate; the maximum variation of the shear modulus with diameter (8–12 mm/15 mm) for the same driving input voltage (torque) was around 3.3 % for aluminum and 1.2 % for brass. On the other hand, in the case of mild steel and copper, the variation of shear modulus was around 9.2 % and 7.2 %, respectively. The measured values of the shear moduli were found to compare well with the data reported from literature for the different chosen metals.

Five-dimensional cooling and nonlinear dynamics of an optically levitated nanodumbbell

This paper reports five-dimensional cooling and the nonlinear dynamics of a levitated nanoparticle in a vacuum. Three center-of-mass motion modes and two torsional vibration modes of a levitated nanodumbbell in a linearly polarized laser are cooled simultaneously.