Symmetric Vibrations Research Articles

Analytical models of movement of wires of air high-voltage power transmission lines

The article PURPOSE with the problem of monitoring the state of high-voltage overhead power lines in order to ensure uninterrupted and reliable supply of consumers with electricity. METHODS. As parameters of the state, the sag, the tensile force and the mass per unit length of the wire hanging in the span are defined. IT IS STRESSED that a complete picture of the state of an overhead line can be established by determining the spectral composition of the wire vibrations using mounted automated multi-parameter sensors with accelerometers as sensors. It is shown that the currently used dynamic models for describing the motion of a wire as a pendulum and as a tightly stretched string are not complete enough to represent the vibrations of the wire in all three spatial coordinates, do not cover vibrations with odd harmonics and symmetrical vibrations. A system of equations has been OBTAINED that makes it possible to describe the spatial oscillations of the wire along all three axes, taking into account the difference in heights of the wire suspension points. IT IS SHOWN that the analysis of the higher harmonics of the spectrum of vibrations of the wire makes it possible to determine all the main mechanical parameters of the wires of overhead power lines.

Raman vibration, bond chemistry and enhanced microwave dielectric properties of Li3Mg2NbO6 ceramics under an oxygen atmosphere

An effective synthesis provides a significant influence on microwave dielectric ceramics for commercial production. In this work, single-phase Li3Mg2NbO6 ceramics were synthesized under an oxygen atmosphere to depress oxygen vacancies. Raman vibration, bond characteristics and crystal structure were analyzed to calculate the inherent features of the Li3Mg2NbO6 ceramics. The Raman spectra and group theory indicated that the mode at 772 cm−1 reflected the symmetric vibrations of Nb–O bonds in NbO6 octahedra and dominated the Raman vibrations. XRD patterns and Rietveld refinement indicated an orthorhombic rock-salt phase under an oxygen assisted sintering process. Well-distributed and homogeneous microstructures were obtained through SEM and grain distribution. From the chemical theory calculation, Nb–O bonds dominated the dielectric properties in consideration of their largest bond ionicity, lattice energy, and bond energy. The Li3Mg2NbO6 ceramics sintered at 1100 °C with an oxygen atmosphere exhibited remarkable performance: εr = 15.3, Q × f = 109,600 GHz and τf = −17.3 ppm/°C, providing enormous potential for communication applications.

Lamb waves in elastic–plastic plate containing voids

Abstract Propagation of Lamb waves has been studied in an infinite plate of finite thickness and composed of elastic–plastic material containing void pores. The plastic deformation in the plate material is considered through a single-plane and direction. Assuming a linear relation between the elastic and plastic parts of the change in void volume fraction and using the stress-free boundary surfaces of the plate, the dispersion relations corresponding to the symmetric and antisymmetric vibrations with respect to the mid-plane of the plate are derived. The corresponding dispersion relations of Lamb modes in the elastic–plastic plate have been reduced by neglecting the presence of voids. Some earlier known results are recovered from the present formulation under particular cases. The behaviour of symmetric and antisymmetric family of Lamb modes are depicted pictorially against the frequency, slip-angle, thickness of the plate and void parameters in a specific plate material. It is found that the plasticity and the presence of the voids in the plate material affect the propagation of Lamb modes. In particular, at the slip-angle $45^o$, the $S_0$- and $A_0$- modes exhibit symmetry, but $S_0$ is bell shaped and $A_0$ is parabolic.

Ultrafast Carrier-Coupled Interlayer Contraction, Coherent Intralayer Motions, and Phonon Thermalization Dynamics of Black Phosphorus.

Black phosphorus (bP) exhibits highly anisotropic properties and dynamical behavior that are unique even among two-dimensional and van der Waals (vdW) layered materials. Here, we show that an interlayer lattice contraction and concerted, symmetric intralayer vibrations occur concurrently within few picoseconds following the photoinjection and relaxation of carriers, using ultrafast electron diffraction in the reflection geometry to probe the out-of-plane motions. A strong coupling between the photocarriers and bP's puckered structure, with the alignment of the electronic band structure, is at work for such directional atomic motions without a photoinduced phase transition. Three temporal regimes can be identified for the phonon thermalization dynamics where a quasi-equilibrium without anisotropy is reached in about 50 ps, followed by propagation of coherent acoustic phonons and heat diffusion into the bulk. The early time out-of-plane dynamics reported here have important implications for single- and few-layer bP and other vdW materials with strong electronic-lattice correlations.

Generating various motion paths of single-mass vibratory system equipped with symmetric planetary-type vibration exciter

Vibration exciters are of the most important parts of vibratory technological equipment. Among a great variety of exciters, the inertial ones are currently the most widely used due to their design simplicity, well-studied control techniques, and relatively large efficiency. The present paper deals with a prospective type of inertial exciters based on a planetary mechanism. The main purpose of this research consists in substantiating the possibilities of providing triangular, rectangular, hexagonal, and other paths of oscillations of a single-mass vibratory system driven by a symmetric planetary-type vibration exciter. The mathematical model of the system motion is developed using the Euler-Lagrange equations, and the following numerical modeling is carried out with the help of the Runge-Kutta methods integrated in the Mathematica software. Virtual experiments are conducted in the SolidWorks software using the 3D-model of the vibratory system. The obtained results are presented in the form of time response curves and motion paths of the oscillating body under different operational conditions. The major scientific novelty of the paper consists in substantiating the parameters of the symmetric planetary-type vibration exciter allowing for generating triangular, rectangular, hexagonal oscillations of the single-mass vibratory system. The obtained results can be effectively used while designing new and improving existent vibratory technological equipment, e.g., conveyors, screens, feeders, sieves, etc.

Classical Intermolecular Hydrogen Bonding Motifs of Heterocyclic rac-2-Amino-3-carbonitrile Derivatives: Linking Hirshfeld Surface Analysis, CT-DNA Binding Affinity, and Molecular Docking

Four 2-amino-4-(aryl)-7,7-dimethyl-5-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitrile (Series I) and three 2-amino-1-phenyl-7,7-dimethyl-5-oxo-4-(aryl)-1,4,5,6,7,8-hexahydroquinoline-3-carbonitrile (Series II) derivatives were formed via multicomponent microwave reactions as racemic mixtures. The solid-state IR spectra revealed bands in the region between 3190 and 3414 cm–1 attributed to the amino functional group’s asymmetric, symmetric, and bending overtone vibration modes. Furthermore, the IR spectra of some of the compounds in each series were similar and this served as an indication of similar structural features in the solid state. This was confirmed via single-crystal X-ray diffraction. A detailed survey of the related 2-amino-3-carbonitrile derivatives in the Cambridge Structural Database revealed 12 classical intermolecular hydrogen-bonding motifs involving the amino functional group. The vast variation in the hydrogen bonding motifs was found to be caused by the type of group bonded to the 4H-pyran (in Series I) or dihydropyridine (in Series II) moiety. In this work, an unprecedented hydrogen bonding motif comprising a non-classical hydrogen bond acceptor was found in one instance. For both Series I and II, the N–H···N and N–H···O hydrogen bonds were investigated using noncovalent interaction (NCI) plots and molecular pairwise energy calculations. The contributions of reciprocal N···H and O···H contacts (attributed to N–H···N and N–H···O, respectively) toward the Hirshfeld surface range between 9.9 and 15.3% in Series I and between 10.8 and 15.0% in Series II. In addition, the compounds showed moderate to good binding affinity to calf thymus DNA (CT-DNA) with intrinsic binding constants (Kb) between 8.00 × 104 and 5.00 × 105 M–1 for Series I compounds and between 6.60 × 104 and 1.45 × 105 M–1 for Series II. A relationship was established between the reciprocal N···H to O···H contributions ratio from the Hirshfeld surface analysis and Kb. Molecular docking studies of each compound’s respective enantiomers into DNA were done using canonical–DNA dodecamer (B-DNA) as a model for CT-DNA. The compounds were found to interact with DNA via a minor groove-binding mode. The S-enantiomer for most of the compounds bound favorably compared to their respective R-enantiomers. The ratio of calculated ΔG for the DNA binding of the R-enantiomer to that of the S-enantiomer (ΔGR/ΔGS) follows the same positive trend as the experimental Kb value for each compound in Series I while a negative trend was observed for Series II. Finally, a relationship between the Hirshfeld surface analysis and calculated ΔG values was also established in this work.

Identifying Key Descriptors for the Single-Atom Catalyzed CO Oxidation

Identifying Key Descriptors for the Single-Atom Catalyzed CO Oxidation

FTIR Spectroscopy Reveals Molecular Changes in BPC 157 Treated Blood Vessels

From the rats treated with stable gastric pentadecapeptide BPC 157 (10ng/kg ip) or saline (5ml/kg ip) at 5 min before sacrifice, the spectra of thoracic aorta tissue samples were compared. From each rat, 20 samples were cut and FTIR spectra were recorded.Vibrational spectra of the samples were recorded with a Perkin‐Elmer Spectrum GX spectrometer equipped with liquid N2 refrigerated Mercury Cadmium Telluride (MCT) detector. Data were acquired in 450 ‐ 4000 cm‐1 spectral range, in transmission mode with a resolution of 4 cm‐1.First, all recorded spectra were baseline corrected and normalized. Then we utilized the principal component analysis (PCA) to examine the possibility of separating BPC treated and control samples on a PCA score‐score graph. Using 100 spectra of BPC treated and 100 spectra of control samples, a PCA model was made. As seen in Figure 1, there is a clear distinction, mostly due to the PC1 score, between spectra of BPC treated (red) from the control group (green).To identify the parts of FTIR spectra that contributed the most to the separation between BPC treated and the control group of spectra differential spectrum was calculated and compared with PC1 loadings.Differential spectrum and PC loadings show that main bands responsible for separation of the BPC treated and control sample spectra are in the range from 930‐1200 cm‐1, then vibrational bands at 1660 cm‐1,1730 cm‐1, 1120 cm‐1 and in the range from 2840 – 3090 cm‐1. In the first range, there are three vibrational bands at 968 cm‐1, 1087 cm‐1 and 1240 cm‐1 that belong to P‐O symmetric and asymmetric vibrations in nucleic acids respectably, and vibrational band 1170 cm‐1 that belongs to C‐O and C‐O‐C stretching vibrations of carbohydrate. The vibrational band at 1660cm‐1 belongs to amid I stretching vibrations of proteins, and the last range of spectral lines belongs to C‐H symmetric and asymmetric C‐H, C‐H2 and C‐H3 vibrations in lipids. The line at 1730 cm‐1 that is very pronounced in control group spectra is C‐O symmetric vibration in fatty acids. Most prominent difference between BPC treated and control group was observed region of C‐H vibrations of lipids and vibrational line at 1730 cm‐1 of fatty acids.Thus, different FTIR spectra evidenced that BPC treatment causes changes of the tissue at molecular level.

Dipole switching dynamics in P(VDF-TrFE) film revealed by in-situ polarization switching and infrared spectroscopy measurements with high-time resolution

Although P(VDF-TrFE) is an important ferroelectric material, its polarization switching details, especially at the nucleation site of the polarized domain, are unknown. Herein, a setup combining a ferroelectricity evaluation system and a Fourier-transform infrared spectrometer with a 70 ms time resolution was developed to simultaneously monitor polarization-switching current and absorption changes associated with the molecular chain rotation of P(VDF-TrFE) under an electric field. Time variations of absorbance associated with CF 2 symmetric vibration in response to the applied electric field served as an indicator of dipole rotation. The onsets and peaks of the polarization-switching current, which appeared before the dynamic molecular orientation, changed across the material. The complementary characterization revealed that the P(VDF-TrFE) polarized domain first nucleates at the interface and grows toward the inner side of film to achieve a completely polarized state of the film. • Molecular rotation of P(VDF-TrFE) associated with its polarization reversal was monitored by IR. • Drastic absorbance changes occur beyond coercive electric field of P(VDF-TrFE). • Polarized domain first nucleates at interface, then grows toward film interior. • As a result, a completely polarized state of film is achieved.

Laser induced fluorescence spectra of the [formula omitted][formula omitted] – [formula omitted][formula omitted] transition of jet cooled [formula omitted]NO3 and [formula omitted]NO3 I: [formula omitted] progressions in the ground [formula omitted][formula omitted] state

14NO3 and 15NO3 were generated in a supersonic free jet, and their laser excitation spectra and dispersed laser induced fluorescence (LIF) spectra of the B∼2E′ – X∼2A2′ transitions from the vibrationless B∼2E′ state were observed. Because of the cooling of the gas in the supersonic jet, the observed spectra are with resolution an order of magnitude higher than those previously reported and allowed us to resolve, for example, the splitting between the a1′ and e′ components of the 2ν4 state. The spectra of 14NO3 and 15NO3 are similar but small isotope shift in the latter allowed us to separate the ν1 band from the 3ν4 (a1′) band which were overlapped in the former.The high resolution dispersed LIF spectra revealed panoramic views of the vibrational level structures in the X∼2A2′ ground electronic states of the two isotopomers. Although the accuracies of the measurement of energy levels are much less than those obtained from the direct high resolution infrared spectroscopy, the obtained patterns are more complete because totally symmetric (a1′) vibrations such as ν1,2ν2,2ν1,ν1 + 2ν2 etc. are also observed. Such clear and complete spectra have revealed remarkable ν4 progressions with detailed vibrational structures in the ground X∼2A2′ state. Near complete progressions of nν4 overtone bands, nν4 with n = 1 ∼ 5, ν1 + nν4 bands with n = 1 ∼ 4, some 2ν2 + nν4 and ν3 + nν4 have been assigned leaving few lines unassigned. There is no evidence of anomaly in the degenerate ν4 bending progression of the B∼2E′ – X∼2A2′ electronic transition of NO3.

Influence Mechanism of a New-Style Resonator on Band Gap of Locally Resonant Phononic Crystal Double Panel Structure

Based on the previous studies on the stubbed-on locally resonant phononic crystal (LRPC) double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower plates, the stubbed-on LRPC DPS with soft shell surrounded and simplified model with additional springs surrounded are proposed. According to the changes in structural form, the wider band gap is opened, and the novel formation mechanism of the band gap is revealed. Finite element method (FEM) is applied to calculate the band structures. Numerical results and further analysis demonstrate that the soft shell only affects the bands corresponding to symmetric vibration mode and makes the bands shift up. In addition, the influences of density and Poisson’s ratio of soft shell on the band gap can be ignored, but the starting frequency keeps still, and band gap width increases first and then keeps constant with the increase of elasticity modulus. All the results provide a theoretical basis for the study of vibration and noise resistance in engineering.

Second-Order Raman Scattering in Ferroelectric Ceramic Solid Solutions LiNbxTa1−xO3

In the second-order Raman spectra of ceramic solid solutions, LiNbxTa1−xO3 weak overtone bands of fully symmetric fundamental polar excitations were observed for the first time. The frequencies of the two bands exceeded the value of the overtone frequency corresponding to the fully symmetrical vibration 4A1(z). The possibility of the existence of phonon bound states of the antipolar type in the vibrational spectrum of LiNbxTa1−xO3 ceramics is predicted.

Vibration sorting of small droplets on hydrophilic surface by asymmetric contact-line friction.

Droplet spreading and transport phenomenon is ubiquitous and has been studied by engineered surfaces with a variety of topographic features. To obtain a directional bias in dynamic wetting, hydrophobic surfaces with a geometrical asymmetry are generally used, attributing the directionality to one-sided pinning. Although the pinning may be useful for directional wetting, it usually limits the droplet mobility, especially for small volumes and over wettable surfaces. Here, we demonstrate a pinning-less approach to rapidly transport millimeter sized droplets on a partially wetting surface. Placing droplets on an asymmetrically structured surfaces with micron-scale roughness and applying symmetric horizontal vibration, they travel rapidly in one direction without pinning. The key, here, is to generate capillary-driven rapid contact-line motion within the time-scale of period of vibration. At the right regime where a friction factor local at the contact line dominates the rapid capillary motion, the asymmetric surface geometry can induce smooth and continuous contact-line movement back and forth at different speed, realizing directional motion of droplets even with small volumes over the wettable surface. We found that the translational speed is selective and strongly dependent on the droplet volume, oscillation frequency, and surface pattern properties, and thus droplets with a specific volume can be efficiently sorted out.

Dynamic balancing of mechanisms with flexible links

The dynamic balancing of flexible mechanisms, that is, the reduction or elimination of shaking forces and shaking moments on the support structure, is considered. Two approaches are pursued: one uses similarity and the other modal balancing. A single rotating link can be balanced by a properly scaled countermass, for which balancing criteria are given. If all balancing conditions are satisfied, shaking force balance can even be achieved if geometric non-linearities are taken into account. This single link can be extended to a translator. Owing to the unscaled pitch of the translator and the asymmetric driving motor, no perfect shaking force balance is achieved, but the results can be considered satisfactory. Then, the dynamic balancing of a four-bar mechanism with a flexible coupler by means of modal balancing is shown. If the coupler is supported at the nodes of the first free vibration mode, this mode can be suppressed in the shaking force and shaking moment response. By supporting the coupler at four points with two whippletree mechanisms, the contribution of the first three symmetric vibration modes can be significantly reduced.

Symmetric vibrations of higher dimensional nonlinear wave equations

Symmetric vibrations of higher dimensional nonlinear wave equations

The complex mechanism of Ti4+ incorporation into litidionite from the Somma–Vesuvius volcano, Italy

AbstractFor this study, the rare Cu-bearing silicate fumarolic assemblages from the Somma–Vesuvius volcano, Italy, characterised by the rare mineral litidionite, CuKNaSi4O10, were investigated. We report new data about Cu- and Ti-bearing phases found in these mineralisations, in which Ti-bearing litidionite occurs together with kamenevite, perovskite and rutile. Ti-bearing litidionite appears on the latest stages of partial crystallisation of Ti-bearing silica glass. Incorporation of Ti4+ into the litidionite crystal structure was investigated in detail. The Raman spectra of Ti-bearing litidionite contains an intense band at 597 cm−1 related to anti-symmetric bending vibrations of Si‒O bonds or overlapping stretching vibrations of Ti‒O bonds. The bands in the range 350‒500 cm−1 correspond to symmetric bending vibrations of O‒Si‒O bonds and overlapping stretching vibrations of Ti‒O bonds. The crystal structure of Ti-litidionite has been refined in the P$\bar{1}$ space group, a = 6.9699(7), b = 7.9953(10), c = 9.8227(10) Å, α = 105.186(9), β = 99.458(8) and γ = 114.489(10) to R1 = 0.064 for 1726 unique observed reflections. The refinement of the site-occupation factors confirmed the presence of Ti at a five-coordinated M site. The mean bond distance of 2.125 Å for the M site agrees with its refined occupancy (Ti0.32Cu0.30Ca0.29Fe0.09)1.00. The incorporation of Ti into the litidionite structure is accompanied by the complex heteropolyhedral substitution according to the scheme VTi4+ + VII–VIII□ + IVAl3+ ↔ VCu2+ + VII-VIII(Na,K)+ + IVSi4+. Two possible configurations for the phase with maximal TiO2 content (12.06 wt.% or 0.56 Ti apfu) CuTiK□Na2Si7AlO20 (Z = 1) or CuTiK2Na□Si7AlO20 (Z = 1) have been proposed.

Axially Symmetric Vibration of a Complete Conic Shell

We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with vertex. The procedure of construction of systems of basis functions for the approximation of displacements of the shell is based on the account of the formal structure of the fundamental system of integrals of the original equations established as a result of the asymptotic integration of a singularly perturbed system of equations with regular singular point. We present examples of numerical analyses of specific conic shells illustrating the efficiency of the proposed algorithm for the solution of the problem.

Flexural wave bandgap properties in metamaterial dual-beam structure

In this paper, a metamaterial dual-beam structure is firstly constructed by periodically adding pillars between two identical homogeneous beams. By simplifying the pillar as an equivalent spring-mass-spring system, another metamaterial dual-beam structure carrying periodic spring-mass-spring resonators is then established. This equivalent representation method is validated through both a vibration transmission analysis and a band structure analysis. Two bands corresponding to the antisymmetric and symmetric flexural vibration modes respectively open a flexural narrow bandgap in the low frequency range. Then, the improved structure with high-static-low-dynamic stiffness (HSLDS) resonators is proposed in the need of widening the bandgap and lowering the beginning frequency. Results show that with the decrease of the proportion of the residual stiffness, the beginning frequency of the bandgap can be reduced, while the ending frequency keeps unchanged. This results in a relative bandgap as high as 1.465, which is about 4.4 times of the original structure.

Charge and Spin Delocalization in Mixed-Valent Vinylruthenium–Triarylamine-Conjugates with Planarized Triarylamines

We report on three new vinylruthenium–triarylamine (TA) conjugates with planarized TA substituents. The neutral, mono-, and dioxidized forms of the complexes were scrutinized by UV/vis/NIR, IR, and EPR spectroscopies as well as by quantum chemical calculations. By analyzing the intervalence charge-transfer (IVCT) transitions of the mixed-valent radical cations, we obtain information on the extent of electronic coupling between the chemically different redox sites. Completely delocalized Ru-MeTA+ shows a vibrationally structured, non-solvatochromic IVCT band. Decreased blueshifts of the indicative Ru(CO) stretching vibration during the first oxidation and larger A(14N) EPR hyperfine splitting constants in concert with smaller g-values indicate enhanced TA contributions to the singly occupied molecular orbital of the other two complexes Ru-TOTA•+ and Ru-DOTA•+ and hence less symmetrical charge and spin density distributions. This is also reflected by the solvatochromism and the asymmetric shape of the IVCT band with a smaller bandwidth at the low-energy side. Temperature-dependent UV/vis/NIR spectroscopy of mixed-valent Ru-TOTA•+ and Ru-DOTA•+ revealed that the band skewing is due to the vibrational coupling of the IVCT transition to symmetrical vibrations, placing these radical cations near or at the class II/III borderline according to Robin and Day.

Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.