Fundamental Vibrational Frequencies Research Articles

On the Use of the H/V Spectral Ratio Method to Estimate the Fundamental Frequency of Tailings Dams

ABSTRACT This paper analyses the feasibility of estimating the fundamental frequency of an 85 m high cycloned-sand tailings dam located in the Central-North area of Chile using the single-station H/V Spectral Ratio Method (HVSR), calculated from seismic ambient noise and earthquakes recorded by a temporal seismic array deployed along the embankment crest, the downstream slope, and the dam toe, directly over the foundation soil. The fundamental vibration frequencies obtained from the HVSRs show consistency with results from the Standard Spectral Ratio method (SSR) calculated between the crest and the toe using the available earthquake records, particularly in the dam central part.

Inharmonicity in plucked guitar strings

We have considered the vibration of various types of pinned guitar strings and have investigated the deviation of the partials from integer multiples of the string's fundamental vibration frequency. We measured the inharmonicity parameter B and compared it to a direct calculation based on a model equation. We generally found very good agreement between the two determinations of B for monofilament strings, but perhaps not surprisingly, we find rather poor agreement for wound strings. Furthermore, we show that the methodology used to carry out this experiment can easily serve as the basis for an upper division physics laboratory on physical acoustics including a more thorough investigation of the classical wave equation in a real-world application.

Infrared bands of formaldehyde dissolved in liquid krypton at cryogenic temperatures and the vibrational modes ν1, ν2, and ν5 of H2CO in comets and interstellar clouds

The infrared spectra of formaldehyde (H2CO) dissolved in liquid krypton between 125 K and 137 K have been obtained using a Fourier transform infrared spectrophotometer and a low temperature cryostat. Backing pressures higher than 1.5 atm were necessary to liquefy Kr above 120 K. Monomeric formaldehyde in gas phase was prepared by thermal decomposition of para-formaldehyde. Peak positions (ν), wavenumber shifts between the gas and liquid solution spectra (Δν), and full widths at half maximum (fwhm) are reported. The H2CO vibrational frequencies in liquid Kr are slightly lower than the gas phase frequencies at room temperature because of the inertness of the solvent. The Gaussian 16 software package is used to determine the geometry and lowest energy of H2CO at room temperature and at the temperature of the experiment. Fundamental harmonic and anharmonic vibrational frequencies and relative intensities are calculated. The influence of the solvent on fundamental vibrational frequencies is studied using the polarizable continuum model (PCM). When used in conjunction with calculated anharmonic frequencies, the PCM model shows qualitative agreement with experimental frequency shifts and relative intensities in liquid Kr. The presence of H2CO in space is discussed in reference to the ν1 and ν5 absorption bands observed in comets, the ν1 and ν2 absorptions in interstellar clouds, and the lack of detection of the ν4 and ν6 bands of H2CO in the atmosphere of Titan. The carbonyl stretching mode ν2 is suggested as a possible candidate for confirmation and identification of H2CO in space due to its larger strength in comparison to the other modes that have been studied at low temperatures and its characteristic frequency that is completely removed from CO2, CO, H2O and CH3OH vibrational modes.

Spectral Signatures of Hydrogen Thioperoxide (HOSH) and Hydrogen Persulfide (HSSH): Possible Molecular Sulfur Sinks in the Dense ISM.

For decades, sulfur has remained underdetected in molecular form within the dense interstellar medium (ISM), and somewhere a molecular sulfur sink exists where it may be hiding. With the discovery of hydrogen peroxide (HOOH) in the ISM in 2011, a natural starting point may be found in sulfur-bearing analogs that are chemically similar to HOOH: hydrogen thioperoxide (HOSH) and hydrogen persulfide (HSSH). The present theoretical study couples the accuracy in the anharmonic fundamental vibrational frequencies from the explicitly correlated coupled cluster theory with the accurate rotational constants provided by canonical high-level coupled cluster theory to produce rovibrational spectra for use in the potential observation of HOSH and HSSH. The mode for HSSH at 886.1 cm is within 0.2 cm of the gas-phase experiment, and the rotational constant for HSSH of 6979.5 MHz is within 9.0 MHz of the experimental benchmarks, implying that the unknown spectral features (such as the first overtones and combination bands) provided herein are similarly accurate. Notably, a previous experimentally-attributed 2 mode, at 7041.8 cm, has been reassigned to the combination band based on the present work’s value at 7034.3 cm. The most intense vibrational transitions for each molecule are the torsions, with HOSH having a more intense transition of 72 km/mol compared to HSSH’s intensity of 14 km/mol. Furthermore, HOSH has a larger net dipole moment of 1.60 D compared to HSSH’s 1.15 D. While HOSH may be the more likely candidate of the two for possible astronomical observation via vibrational spectroscopy due to the notable difference in their intensities, both HSSH and HOSH have large enough net dipole moments to be detectable by rotational spectroscopy to discover the role these molecules may have as possible molecular sulfur sinks in the dense ISM.

Torsional motions of the free and H-bonded hydroxyl groups of the catechol molecule

Torsional vibrations of free and hydrogen-bonded hydroxyl groups of the 1,2-dihydroxybenzene molecule are analyzed within the harmonic and anharmonic approximations, as well as by constructing a 2D potential energy surface formed by varying the torsional coordinates of the two OH groups. Calculation of the vibrational spectrum of the molecule in the harmonic and anharmonic approximations was performed at the MP2/acc-pVTZ level of theory. Calculations of the 2D potential energy surface were performed at the MP2/acc-pVTZ, MP2/CBS(T,Q), and CCSD(T)/acc-pVDZ levels of theory. Calculations of the 2D surfaces of dipole moment components and kinetic coefficients were performed at the MP2/cc-pVTZ and MP2/acc-pVTZ levels of theory. In the latter case, the formalism of Wilson’s s→ vectors was used. The energies of the first 100 stationary torsional levels are calculated and classified by irreducible representations of the molecular symmetry group C2V(M). Furthermore, the analysis of wave functions allowed us to assign most of the torsional states to the fundamentals, combinations, and overtones of the torsional vibrations of the hydroxyl groups of two conformers that have the point symmetry groups CS (I) and C2V (II). The tunneling frequencies between equivalent configurations of conformer I in the ground and excited torsional states are estimated. The calculated values of the frequencies of fundamental torsional vibrations of two OH groups and the tunneling splitting value of the first excited torsional state of the free hydroxyl group of conformer I are compared with the experimental data presented in a recently published work [J. Bruckhuisen et al., Molecules 26 (2021) 3645]. Torsional IR spectra of the molecule are modeled at different temperatures.

Investigation of Transformer Vibration Characteristics using the Finite Element Method

Understanding the vibrational characteristics of power transformers is significantly important in their design and monitoring. In this contribution, a model with a multi-physics coupling simulation of the electrical circuit, magnetic field, and solid mechanics is developed to investigate the characteristics of the transformer vibration. After describing the model, the harmonic contents of the vibration signals and their variation in the case of mechanical faults are studied. It is shown that under normal operating conditions, the fundamental vibration frequency of 100 Hz has the maximum amplitude, while in the case of mechanical faults, the amplitudes of 200 Hz and 300 Hz harmonics increase dramatically compared to the fundamental harmonic. The influence of vibration sensor position is investigated too, which indicates that the area near the tank bottom is the best position to gather vibration signals. Moreover, the mechanical resonance frequencies of the transformer, along with their mode shapes, are addressed in this paper. Finally, the influence of mechanical changes on the vibration energy distribution in the tank surface is explored. The results of the paper suggest possible diagnosis methods for condition monitoring of transformers, such as using the vibration energy distribution on the tank surface or analyzing the vibration harmonics.

Theoretical study on potential energy surface and bound states of the Kr-CNCN complex: Compared with the Kr-NCCN system

The first ab initio potential energy surface of the Kr-CNCN system is investigated using the single double excitation coupled-cluster theory with noniterative treatment of triple excitation. The mixed basis sets are used with aug-cc-pVTz for the C and N atoms and aug-cc-pVTz-pp for the Kr atom, including an additional midbond function of 3s3p2d1f1g. The computed single point energies at 585 configurations are fitted to an analytical potential model. The potential energy surface of the Kr-CNCN complex has a nearly T-shaped global minimum with the energy of −286.6 cm−1 located at R = 6.88 a0, θ = 89.3°. The interaction of the linear CNCNKr geometry is stronger than that of the linear KrCNCN structure. The whole potential energy surface of the Kr-CNCN presents angular anisotropy. The bound state energies up to J = 9 and the wave functions are calculated by analytically solving the Schrödinger equation based on the ab initio potential energy surface. The calculated fundamental frequencies of bending vibration and stretching vibration of the Kr-CNCN are 24.0 cm−1 and 32.7 cm−1, respectively. The transition frequencies and the spectroscopic constants of the Kr-CNCN system are predicted, and the relevant results are compared with the Kr-NCCN complex. The differences in the PES and bound state energy levels between the Kr-CNCN and Kr-NCCN complexes are clarified. These results will help to further explore the formation causes of CN radical in the interstellar medium and provide a theoretical basis for future experimental spectra research of the Kr-CNCN system.

Thickness-Stretch Vibration of an Infinite Piezoelectric Plate with Flexoelectricity

In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future.

Enhancement of structural seismic performance of low-rise buildings using displacement-dependent tuned mass damper

Tuned mass dampers are used to reduce vibrations of high-rise buildings due to wind disturbance. Specifically, the displacement-dependent tuned mass damper (DTMD) is an effective vibration energy absorber that is connected to a primary structure to reduce the vibration response of the structure under harmonic and external force disturbances. Its natural frequency is adjusted to be close to the fundamental vibration frequency of the primary structure; this leads to an antiphase resonance that dissipates the external force-induced disturbance energy. Several studies have proposed different optimization design objective functions and developed active and semi-active tuned mass damping systems to improve control efficiency significantly. Therefore, in this study, a reasonable mass and an objective function were considered using a simplified degree-of-freedom structural model (DTMD and primary structure) to derive an optimized design method and evaluate the feasibility of structural reinforcement through numerical analysis of the tuned mass damper and shaking table tests. The fundamental retrofit design process used in this study can facilitate the development of a specialized tuning mass damper that can be used in practical engineering applications, such as improving the seismic resistance of ancient and low-rise buildings.

(Sub-)millimeter-wave spectroscopy of gauche-propanal

A detailed analysis of (sub-)millimeter-wave spectra of the vibrational ground state (υ=0) combined with the energetically lowest excited vibrational state (υ24=1; aldehyde torsion) of gauche-propanal (g-C2H5CHO) up to 500GHz is presented. Both vibrational states, υ=0 and υ24=1, are treated with tunneling rotation interactions between their two respective tunneling states, which originate from two stable degenerate gauche-conformers; left- and right-handed configurations separated by a small potential barrier. Thanks to double-modulation double-resonance (DM-DR) measurements, important but weak c-type transitions connecting the tunneling states could be unambiguously assigned. In addition, Coriolis interaction as well as Fermi resonance between the two vibrational states needed to be taken into account to derive fits with experimental accuracy using Pickett’s SPFIT program in a reduced axis system (RAS). Based on the rotational analysis, the fundamental vibrational frequency ν24 of gauche-propanal is redetermined to 68.75037(30)cm−1.

Molecular Bonding in an Orbital-Free-Related Density Functional Theory.

A density functional theory based on polymer self-consistent field theory is applied to systems of two atoms in order to show that this approach is capable of predicted molecular bonding. Periodic table elements from hydrogen up to neon are examined and homonuclear diatomic molecules are found to form for H2, N2, O2, and F2, in agreement with known results. The heteronuclear molecules CO and HF, which are known to exist under ambient conditions, are also found to be stable. Bond lengths for most of these molecules agree with experimental results to within less than 8%, with the exception of O2 and F2 which deviate more significantly. The bonding energy for H2 is given and is within 16% of the known value, but fundamental vibrational frequencies do not agree well with experiment. The main approximations of the theory are very simple and include a Fermi-Amaldi correction to the electron-electron interaction to account for self-interactions and a basic expression for the Pauli potential to account for the exclusion principle. The self-consistent equations are solved in terms of basis functions that encode the cylindrical symmetry of diatomic molecules. Since orbitals are not used, the approach is related to orbital-free density functional theory.

Theoretical study of the stability and reactivity of salicylic acid isomers by the DFT method

The FT-IR spectrum of salicylic acid (SA) was studied in the region 10-4000 cm-1. The optimized molecular geometry and fundamental vibration frequencies are interpreted using structural optimizations based on the Functional Density Theory (DFT) method. Additionally, we used B3LYP / 6-311G (d, p) to determine the chemical descriptor, the ionization potential (I), the electron affinity (A), the chemical potential (μ), the chemical hardness (η). Nonlinear optical descriptors (NLO) such as dipole moment (μ), polarizability (α), first hyperpolarizability (β) and second hyperpolarizability (γ), 3D maps of HOMO and LUMO orbitals, lengths and Bond angles of salicylic acid isomers are also determined by both DFT and MP2 (The Møller-Plesset theory of order 2 perturbation) methods. The overall descriptors and the non-linear optical properties confirmed that salicylic acid is the reactive molecule and para-hydroxybenzoic acid is the stable molecule. An electrostatic molecular potential (MEP) study was also performed to determine the reactivity of molecules.

Molecular docking, spectroscopic studies and simulation of the dopamine molecule by the DFT and MP2 methods

The FTIR and Raman spectra of dopamine were also recorded in the spectral region 20 - 4000 cm-1 and 400 - 4000 cm-1 respectively. The optimized molecular geometry and fundamental vibration frequencies are interpreted using structural optimizations based on the DFT method. The B3LYP / 6-311G (d, p) was used to determine the calculations of the chemical descriptor. The dopamine (DA) molecule can acquire a maximum charge of 0.513 eV from its environment. To understand the molecular interactions of Dopamine, the MEP is a crucial tool. Nonlinear optical descriptors (NLO) and the lengths, bond angles are also determined by DFT and MP2 methods. The DFT method was used to determine the chemical shifts of 1H and 13C of the product. These constants have been calculated by employing the GIAO (Gauge-Including-Atomic-Orbit), CSGT (Continuous Set of Gauge Transformations) and IGAIM (Individual Gauges for Atoms In Molecules) methods at the B3LYP/6-311G (d, p). The comparison of the theoretical chemical shifts with the experimental ones shows that the CSGT method is the best.

A hybrid artificial bee colony algorithm for transformer vibration fundamental frequency amplitude prediction

The fundamental frequency amplitude of transformer surface vibration signal is an important basis for judging transformer status. It is very important to predict the amplitude of fundamental frequency quickly and accurately. In this paper, a method is proposed to optimize the prediction of the transformer vibration fundamental frequency amplitude by modifying the artificial bee colony algorithm. An opposition-based learning mechanism is introduced and the search formula of each bee species is improved at the initial stage of the artificial bee colony algorithm. The performance of the proposed method is evaluated by five standard test functions and transformer vibration fundamental frequency amplitude prediction. Experimental results show that the proposed method is much better than the original artificial bee colony algorithm in search accuracy, convergence speed, and robustness, and improve the prediction accuracy.

Semi-Experimental Determination of the Linear Clamped Electro-Optical Coefficients of Polar Crystals from Vibrational Spectroscopic Data

The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations are based on the formula analog to that of the Lyddane–Sachs–Teller relation, which is systematically used for the calculations of the clamped linear electro-optical coefficient of oxide ferroelectric crystals such as LiNbO3, LiTaO3, BaTiO3, PbTiO3, and KNbO3. The computed electro-optical coefficients are in good agreement with those obtained from direct measurements and the first-principles calculations or other semi-empirical models. In addition, the famous r51 or r42 coefficients of the tetragonal BaTiO3, PbTiO3, and KNbO3 crystals are finally calculated with high accuracy and discussed in connection with the soft mode behavior.

Wave propagation in a doubly tapered shear beam: Model and application to a pyramid‐shaped skyscraper

AbstractOne dimensional wave propagation is studied in a cantilever conical structure deforming in shear. The structure has rectangular cross‐section both dimensions of which decrease linearly along the polar axis (hence, doubly tapered). The equation motion is derived and solved in terms of spherical Bessel functions, which can be expressed exactly as finite algebraic expressions in terms of powers and sine and cosine functions of the polar coordinate. The transfer‐matrix for a truncated pyramid element is then derived and generalized to a chain of elements. The model is used to represent a 48‐story pyramid‐shaped steel‐frame skyscraper, the Transamerica Tower in San Francisco, California, in which the Loma Prieta, 1989 earthquake (, epicentral distance, km) was recorded by an array of accelerometers. The building is modeled by homogeneous and layered truncated pyramids. Wave propagation through the building is studied by analysis of impulse response functions computed from the observed earthquake accelerations. In addition, its equivalent homogeneous beam shear‐wave velocity is identified solely from its geometry and observed fundamental frequency of vibration. Further, the variation of wave velocity along is height is identified by least squares fit of a layered pyramid model in the observed impulse response functions. The results reveal equivalent homogeneous pyramid wave velocity of about 150–160 m/s in both directions, which is similar to other steel‐frame structures. The identified wave velocity profiles are consistent with the structural design. The identified parameters can be used as reference in future structural health monitoring of this structure.

Anharmonic Vibrational Frequencies of Water Borane and Associated Molecules.

Water borane (BHOH) and borinic acid (BHOH) have been proposed as intermediates along the pathway of hydrogen generation from simple reactants: water and borane. However, the vibrational spectra for neither water borane nor borinic acid has been investigaged experimentally due to the difficulty of isolating them in the gas phase, making accurate quantum chemical predictions for such properties the most viable means of their determination. This work presents theoretical predictions of the full rotational and fundamental vibrational spectra of these two potentially application-rich molecules using quartic force fields at the CCSD(T)-F12b/cc-pCVTZ-F12 level with additional corrections included for the effects of scalar relativity. This computational scheme is further benchmarked against the available gas-phase experimental data for the related borane and HBO molecules. The differences are found to be within 3 cm for the fundamental vibrational frequencies and as close as 15 MHz in the and principal rotational constants. Both BHOH and BHOH have multiple vibrational modes with intensities greater than 100 km mol, namely and in BHOH, and , , , , and in BHOH. Finally, BHOH has a large dipole moment of 4.24 D, which should enable it to be observable by rotational spectroscopy, as well.

Dynamic characteristics assessment of the Denis‐Perron dam (SM‐3) based on ambient noise measurements

AbstractStanding at a height of 171 m in a narrow valley, the Denis‐Perron dam is the highest embankment dam in Québec, Canada. Between 1998 and 2002, the structure was equipped with three‐component digital strong‐motion accelerometers. The seismic data recorded during three small earthquakes allowed for the estimation of the fundamental vibration frequency (fn) values of the dam in three directions. As part of the present research study, 10 sets of ambient noise measurements were acquired at the dam using six velocimeters, aiming to evaluate the possible 3D site effects and determine the fn values. The first analyses of these experimental data consisted of processing the individual signals with the simple “reference‐dependent spectral” and “ambient vibration horizontal‐to‐vertical spectral ratio (HVSR)” methods. A more advanced modal analysis combining synchronized measurements led to the establishment of additional higher vibration frequency modes and modal shapes. The consistency between the fn values obtained using the simple methods and those from the advanced modal analysis was noticeable. The seismic data provided an exceptional opportunity to validate the experimental data. A comprehensive analysis was thus conducted to compare the dynamic parameters calculated from the processed experimental data with those resulting from the seismic data and proved the values to be similar. In addition, a numerical modal analysis of the 3D valley‐dam system corroborated the plausibility of the vibration modes obtained from the experimental synchronized ambient noise modal analysis. All of these analyses demonstrate the potential of the ambient noise technique for identifying the dynamic characteristics of large rockfill dams built in narrow valleys, without the need for the costly installation and maintenance of accelerometers in low‐seismicity areas.

A new permutation-symmetry-adapted machine learning diabatization procedure and its application in MgH2 system.

This work introduces a new permutation-symmetry-adapted machine learning diabatization procedure, termed the diabatization by equivariant neural network (DENN). In this approach, the permutation symmetric and anti-symmetric elements in diabatic potential energy metrics (DPEMs) were simultaneously simulated by the equivariant neural network. The diabatization by deep neural network scheme was adopted for machine learning diabatization, and non-zero diabatic coupling was included to increase accuracy in the near degenerate region. Based on DENN, the global DPEMs for 11A' and 21A' states of MgH2 have been constructed. To the best of our knowledge, these are the first global DPEMs for the MgH2 system. The root-mean-square-errors (RMSEs) for diagonal elements (H11 and H22) and the off-diagonal element (H12) around the conical intersection region were 5.824, 5.307, and 5.796meV, respectively. The RMSEs of global adiabatic energies for two adiabatic states were 4.613 and 12.755meV, respectively. The spectroscopic calculations of the 11A' state in the linear HMgH region are in good agreement with the experiment and previous theoretical results. The differences between calculated frequencies and corresponding experiment values are 1.38 and 1.08 cm-1 for anti-symmetric stretching fundamental vibrational frequency and first overtone. The global DPEMs obtained in this work should be useful for further quantum mechanics dynamic simulations on the MgH2 system.

Dynamic behavior of soil-foundation-structure systems subjected to scour

Earthquake and scouring are the leading causes of bridge failure worldwide, resulting not only in casualties and fatalities but also in enormous societal and economic losses. A great number of bridges in earthquake-prone countries cross rivers and have shallow foundations, which renders them highly vulnerable to the combined effects of earthquake and flood-induced scour. Thus, the research on the dynamic response of bridges with shallow foundations under scour and earthquake hazards is timely and imperative. This study investigates the problem through the development of a numerical model for evaluating the effect of scour on the impedance functions of a massless rigid strip foundation resting on a homogenous elastic half-space. The developed impedance functions are then used in an extensive parametric study analyzing the changes of the fundamental frequency of bridge piers for different combinations of the geometrical and mechanical properties of the soil-structure-foundation system. The study results shed light on the effects of scour on the dynamic properties and fundamental frequency of vibration of bridges with shallow foundations and have important implications on the development of inverse techniques for scour identification based on the evaluation of the changes in the bridge modal properties.