Fundamental Vibrational Frequencies Research Articles

Finite Element Analysis of Vortex Induced Responses of Multistory Rectangular Building

High-rise buildings may experience high levels of vibrations under the actions of wind which cause building motions, adversely affecting serviceability and occupant comfort. The paper analyzed the vortex shedding responses of a multistory building with moment resisting frame. It presents a numerical model based on computational wind engineering technique to simulate the wind action over a typical high-rise building using wind speed data of Lagos state Nigeria. The vortex shedding frequency of the vortices and the natural frequency of vibration of the entire high-rise building structural system were calculated by computing fast Fourier transform algorithm (FFT) of the force coefficient and finite element analysis (FEA) of the structural system respectively. From the result obtained, the vortex shedding frequency of the wind vortices was lower than the fundamental frequency of vibration of the typical high-rise building. Hence, vortex shedding was not responsible for the failure of high-rise buildings in the locality being considered due to the reasons stated in the author’s conclusion.

Finite Element Analysis of Vortex Induced Responses of Multistory Rectangular Building

High-rise buildings may experience high levels of vibrations under the actions of wind which cause building motions, adversely affecting serviceability and occupant comfort. The paper analyzed the vortex shedding responses of a multistory building with moment resisting frame. It presents a numerical model based on computational wind engineering technique to simulate the wind action over a typical high-rise building using wind speed data of Lagos state Nigeria. The vortex shedding frequency of the vortices and the natural frequency of vibration of the entire high-rise building structural system were calculated by computing fast Fourier transform algorithm (FFT) of the force coefficient and finite element analysis (FEA) of the structural system respectively. From the result obtained, the vortex shedding frequency of the wind vortices was lower than the fundamental frequency of vibration of the typical high-rise building. Hence, vortex shedding was not responsible for the failure of high-rise buildings in the locality being considered due to the reasons stated in the author’s conclusion.

Evaluation of as-installed properties of transformer bushings

High voltage transformers are essential parts of the electrical distribution grid. Severe failure of entire grids can occur during earthquakes, when transformer bushings fail due to structural dynamic mismatch to the seismic demands. Proper consideration of the fundamental frequency of vibration, which depends on the flexibility of the cover plate of the transformer to which they are connected, is therefore crucial for determining the seismic response of bushings. A simplified method is developed in this work for the evaluation of the “as-installed” fundamental frequency of transformer bushings. Such bushings are modeled as cantilever beams with distributed mass and elasticity, and an additional rotational spring is introduced at the base, to account for the flexibility of the cover plate of the transformer. A simple yet efficient expression is derived for the as-installed frequency, based on the Southwell-Dunkerley method. The solutions require the knowledge of the bending rigidity of the bushing and the (out-of-plane) rotational stiffness of the cover plate. The evaluation of both these quantities is presented. While analytical solutions for the (out-of-plane) rotational stiffness of circular plates are well known, solutions for rectangular plates have not yet been addressed. A semi-empirical-numerical solution is suggested, based on finite element models and analytical expressions derived by force-fitting the “circular plate solution” to the numerical analyses. The results yielded by the proposed method are compared with experiments on real bushings.

Comparing the accuracy of perturbative and variational calculations for predicting fundamental vibrational frequencies of dihalomethanes.

Three dihalogenated methane derivatives (CH2F2, CH2FCl, and CH2Cl2) were used as model systems to compare and assess the accuracy of two different approaches for predicting observed fundamental frequencies: canonical operator Van Vleck vibrational perturbation theory (CVPT) and vibrational configuration interaction (VCI). For convenience and consistency, both methods employ the Watson Hamiltonian in rectilinear normal coordinates, expanding the potential energy surface (PES) as a Taylor series about equilibrium and constructing the wavefunction from a harmonic oscillator product basis. At the highest levels of theory considered here, fourth-order CVPT and VCI in a harmonic oscillator basis with up to 10 quanta of vibrational excitation in conjunction with a 4-mode representation sextic force field (SFF-4MR) computed at MP2/cc-pVTZ with replacement CCSD(T)/aug-cc-pVQZ harmonic force constants, the agreement between computed fundamentals is closer to 0.3 cm-1 on average, with a maximum difference of 1.7 cm-1. The major remaining accuracy-limiting factors are the accuracy of the underlying electronic structure model, followed by the incompleteness of the PES expansion. Nonetheless, computed and experimental fundamentals agree to within 5 cm-1, with an average difference of 2 cm-1, confirming the utility and accuracy of both theoretical models. One exception to this rule is the formally IR-inactive but weakly allowed through Coriolis-coupling H-C-H out-of-plane twisting mode of dichloromethane, whose spectrum we therefore revisit and reassign. We also investigate convergence with respect to order of CVPT, VCI excitation level, and order of PES expansion, concluding that premature truncation substantially decreases accuracy, although VCI(6)/SFF-4MR results are still of acceptable accuracy, and some error cancellation is observed with CVPT2 using a quartic force field.

Hybrid Filtered‐x Adaptive Vibration Control with Internal Feedback and Online Identification

Active control is an effective way to suppress low‐frequency mechanical vibration. However, with applications to submarine equipment, there are still some shortcomings due to vibration coupling and multifrequency complex excitation. In this paper, a novel hybrid improved adaptive control strategy, feedback and online identification filtered‐x LMS, namely, FOFxlms, is proposed, which introduces the residual errors to correct variable step‐size, uses the estimated primary path to improve online identification, and applies internal feedback to compensate for the feedforward control. Then the FOFxlms algorithm is applied to a double‐layer vibration isolation system of submarine rotating equipment, and the simulation results show that the normalized variable step‐size with residual error can effectively improve convergence speed, the internal feedback can efficaciously compensate for steady‐state control accuracy, and the online identification can dynamically identify the time‐varying characteristics of the secondary path. The vibration reduction efficiency of Fxlms, FFxlms, and FOFxlms increases for the fundamental frequency vibration; the control effect and convergence speed are also enhanced in turn.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH.

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Vapor Pressures and Thermophysical Properties of Ethylene Carbonate, Propylene Carbonate, γ-Valerolactone, and γ-Butyrolactone

In this work, a thermodynamic study of four important industrial solvents, ethylene carbonate (CAS RN: 96-49-1), propylene carbonate (CAS RN: 108-32-7), γ-valerolactone (CAS RN: 108-29-2), and γ-butyrolactone (CAS RN: 96-48-0), is presented. The vapor pressure measurements were performed by static method using two apparatuses in a combined temperature interval (238–363) K. Heat capacities of condensed phases were measured by Tian–Calvet calorimetry in the temperature interval (262–358) K. The phase behavior of ethylene carbonate and γ-valerolactone was investigated by a heat-flux DSC from 183–303 and 328 K, respectively. Ideal-gas thermodynamic properties were calculated using the methods of statistical thermodynamics based on calculated fundamental vibrational frequencies and molecular structure data. A consistent thermodynamic description of all involved properties (calculated ideal-gas heat capacities and experimental data on vapor pressures, condensed phase heat capacities, and vaporization enthalpies...

Magnesium replacement in formaldehyde: Theoretical rovibrational analysis of [formula omitted] MgCH2

A full, anharmonic set of fundamental vibrational frequencies as well as spectrosocpic constants are provided at high-level for X∼3B1 MgCH2 for the first time. The present data are in line with previous computational and Ar-matrix results, but the anharmonic data show that two brightest frequencies, ν4 and ν5, are nearly coincident with one another at 560 cm−1. Hence, this area is the best spectral region to search for signatures of this molecule. The rotational constants are also provided indicating a near-prolate rotational progression which should aid in microwave/millimeter-wave analysis of this molecule. Magnesium is known to be a significant component of the Earth, and molecules containing it may be more common in the interstellar medium/circumstellar media than previously thought. More spectral characterization of such molecules like MgCH2 should be undertaken, and this work is a step in that direction.

Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error

We investigate the impact of choosing regressors and molecular representations for the construction of fast machine learning (ML) models of 13 electronic ground-state properties of organic molecules. The performance of each regressor/representation/property combination is assessed using learning curves which report out-of-sample errors as a function of training set size with up to ∼118k distinct molecules. Molecular structures and properties at the hybrid density functional theory (DFT) level of theory come from the QM9 database [ Ramakrishnan et al. Sci. Data 2014 , 1 , 140022 ] and include enthalpies and free energies of atomization, HOMO/LUMO energies and gap, dipole moment, polarizability, zero point vibrational energy, heat capacity, and the highest fundamental vibrational frequency. Various molecular representations have been studied (Coulomb matrix, bag of bonds, BAML and ECFP4, molecular graphs (MG)), as well as newly developed distribution based variants including histograms of distances (HD), angles (HDA/MARAD), and dihedrals (HDAD). Regressors include linear models (Bayesian ridge regression (BR) and linear regression with elastic net regularization (EN)), random forest (RF), kernel ridge regression (KRR), and two types of neural networks, graph convolutions (GC) and gated graph networks (GG). Out-of sample errors are strongly dependent on the choice of representation and regressor and molecular property. Electronic properties are typically best accounted for by MG and GC, while energetic properties are better described by HDAD and KRR. The specific combinations with the lowest out-of-sample errors in the ∼118k training set size limit are (free) energies and enthalpies of atomization (HDAD/KRR), HOMO/LUMO eigenvalue and gap (MG/GC), dipole moment (MG/GC), static polarizability (MG/GG), zero point vibrational energy (HDAD/KRR), heat capacity at room temperature (HDAD/KRR), and highest fundamental vibrational frequency (BAML/RF). We present numerical evidence that ML model predictions deviate from DFT (B3LYP) less than DFT (B3LYP) deviates from experiment for all properties. Furthermore, out-of-sample prediction errors with respect to hybrid DFT reference are on par with, or close to, chemical accuracy. The results suggest that ML models could be more accurate than hybrid DFT if explicitly electron correlated quantum (or experimental) data were available.

Fundamental frequency of IsoTruss tubular composite structures

To reveal free vibration modes and fundamental frequency of one-dimensional periodic IsoTruss tubular composite structures (ITTCSs), finite element modeling method and dynamic equivalent models were developed. ITTCS has two typical vibration modes: (a) shell-like modes and (b) beam-like modes. Short ITTCS and large inclinations of helical members easily induce shell-like vibration modes, while long ITTCS and small inclinations easily induce beam-like vibration modes. For shell-like vibration, the fundamental frequency is decided by the inclination, while the length has little influence. For beam-like vibration, the fundamental frequency depends on the column length and the inclination has slight influence. Dynamic continuum beam-like model and shell-like model were developed to predict the fundamental frequency of the IsoTruss structure. The predictions are consistent with the numerical simulations, and these models can be applied in engineering to instruct the dynamic design of the IsoTruss structure.

Free vibration analysis of single-walled boron nitride nanotubes based on a computational mechanics framework

Free vibration behaviors of single-walled boron nitride nanotubes are investigated using a computational mechanics approach. Tersoff-Brenner potential is used to reflect atomic interaction between boron and nitrogen atoms. The higher-order Cauchy-Born rule is employed to establish the constitutive relationship for single-walled boron nitride nanotubes on the basis of higher-order gradient continuum theory. It bridges the gaps between the nanoscale lattice structures with a continuum body. A mesh-free modeling framework is constructed, using the moving Kriging interpolation which automatically satisfies the higher-order continuity, to implement numerical simulation in order to match the higher-order constitutive model. In comparison with conventional atomistic simulation methods, the established atomistic-continuum multi-scale approach possesses advantages in tackling atomic structures with high-accuracy and high-efficiency. Free vibration characteristics of single-walled boron nitride nanotubes with different boundary conditions, tube chiralities, lengths and radii are examined in case studies. In this research, it is pointed out that a critical radius exists for the evaluation of fundamental vibration frequencies of boron nitride nanotubes; opposite trends can be observed prior to and beyond the critical radius. Simulation results are presented and discussed.

Toward the laboratory identification of the not-so-simple NS2 neutral and anion isomers.

The NS2 radical is a simple arrangement of atoms with a complex electronic structure. This molecule was first reported by Hassanzadeh and Andrew's group [J. Am. Chem. Soc. 114, 83 (1992)] through Ar matrix isolation experiments. In the quarter century since this seminal work was published, almost nothing has been reported about nitrogen disulfide even though NS2 is isovalent with the common NO2. The present study aims to shed new insight into possible challenges with the characterization of this radical. No less than three potential energy surfaces all intersect in the C2v region of the SNS radical isomer. A type-C Renner-Teller molecule is present for the linear 2Πu state where the potential energy surface is fully contained within the 2.05 kcal/mol lower energy X̃ 2A1 state. A C2v, 1 2B1 state is present in this same region, but a double excitation is required to access this state from the X̃ 2A1 state of SNS. Additionally, a 1 2A' NSS isomer is also present but with notable differences in the geometry from the global minimum. Consequently, the rovibronic spectrum of these NS2 isomers is quite complicated. While the present theory and previous Ar matrix experiments agree well on isotopic shifts, they differ notably for the absolute fundamental vibrational frequency transitions. These differences are likely a combination of matrix shifts and issues associated with the neglect of non-adiabatic coupling in the computations. In either case, it is clear that high-resolution gas phase experimental observations will be complicated to sort. The present computations should aid in their analysis.

Vapor Pressures and Thermophysical Properties of Dimethyl Carbonate, Diethyl Carbonate, and Dipropyl Carbonate

In this work, a thermodynamic study of important industrial solvents, dimethyl carbonate (CAS RN: 616-38-6), diethyl carbonate (CAS RN: 105-58-8), and dipropyl carbonate (CAS RN: 623-96-1), is presented. The vapor pressure pressure measurements were performed using the static method in the temperature interval 238–308 K. Heat capacities of condensed phases were measured by Tian–Calvet calorimetry in the temperature interval 260–358 K. The phase behavior was investigated by DSC in the temperature interval 183–300 K. The thermodynamic properties in the ideal gaseous state were calculated using the methods of statistical thermodynamics based on calculated fundamental vibrational frequencies and molecular structure data. Calculated ideal-gas heat capacities and experimental data on vapor pressures, condensed phase heat capacities, and vaporization enthalpies were treated simultaneously to obtain a consistent thermodynamic description.

Growth and characterization of dl-Mandelic acid (C6H5CH(OH)CO2H) single crystal for third-order nonlinear optical applications

An organic conjugated chromophore dl-mandelic acid (DLMA) single crystal was synthesized and grown-up by means of slow evaporation technique. Single crystal X-ray diffraction study proclaimed that the DLMA crystal crystallized in monoclinic system with centrosymmetric space group P21/c. The various characteristic fundamental vibration frequencies were identified by FTIR spectroscopic studies. UV–visible spectral analysis concluded that the lower cut-off wavelength and calculated direct optical band gap of DLMA as 257 nm and 5.40 eV respectively. Thermal property of dl-mandelic acid was established through thermogravimetric and differential scanning calorimetric technique. The electric field response of DLMA crystal was investigated from the dielectric studies at a few selected temperatures and frequencies. The quantum chemical assessments such as HOMO-LUMO, molecular electrostatic potential and NLO activity were calculated and presented. In order to determine mechanical strength of DLMA crystal for various loads using Vickers microhardness tester. The real and imaginary parts of the third-order susceptibility (χ3) were evaluated with the Z-scan technique using closed and open signatures respectively and was found to be Re (χ3) = 4.15 × 10−6 esu and Im (χ3) = 0.47 × 10−6 esu.

Bending vibrations of stepped rods

Manufacturing stepped rods with segments of sizes proportional to stresses induced in operation is often used to reduce the material consumption in various fields of technology, for example, in the aircraft industry, where the requirements for the weight of structural elements are high. The vibration problems of continuous systems, i.e. systems which masses are considered distributed, are close to the resistance of materials and elasticity theory problems. They are described by partial differential equations. In this case, we consider a homogeneous isotropic material, obeying Hooke’s law. Of all the vibration problems of continuous systems, the transverse vibration problems of shafts and beams is of greatest practical importance. The simplest examples of vibrations of prismatic rods were studied in the 18th century in works on acoustics. But before solving problems of practical importance, the problems of stepped beams, it had taken another two hundred years and the development of approximate methods of solving differential equations. The paper presents a solution to the problem of determining the fundamental frequencies of bending vibrations of two-stepped rods with various boundary conditions, using the approximate Lagrange-Ritz method. The calculation error does not exceed 2.6 %. The fundamental frequency of vibration is defined considering different lengths and stiffness ratios of stepped rod segments. The obtained results can be used in solving practical problems in various fields of technology.

Symmetry breaking and spectral considerations of the surprisingly floppy c-C3H radical and the related dipole-bound excited state of c-C3H.

The C3H radical is believed to be prevalent throughout the interstellar medium and may be involved in the formation of polycyclic aromatic hydrocarbons. C3H exists as both a linear and a cyclic isomer. The C2v cyclopropenylidenyl radical isomer was detected in the dark molecular cloud TMC-1, and the linear propenylidenyl radical isomer has been observed in various dark molecular clouds. Even though the c-C3H radical has been classified rotationally, the vibrational frequencies of this seemingly important interstellar molecule have never been directly observed. Established, highly accurate quartic force field methodologies are employed here to compute useful geometrical data, spectroscopic constants, and vibrational frequencies. The computed rotational constants are consistent with the experimental results. Consequently, the three a1 (ν1, ν2, and ν3) and one b1 (ν6) anharmonic vibrational frequencies at 3117.7 cm-1, 1564.3 cm-1, 1198.5 cm-1, and 826.7 cm-1, respectively, are reliable predictions for these, as of yet unseen, observables. Unfortunately, the two b2 fundamentals (ν4 and ν5) cannot be treated adequately in the current approach due to a flat and possible double-well potential described in detail herein. The dipole-bound excited state of the anion suffers from the same issues and may not even be bound. However, the trusted fundamental vibrational frequencies described for the neutral radical should not be affected by this deformity and are the first robustly produced for c-C3H. The insights gained here will also be applicable to other structures containing three-membered bare and exposed carbon rings that are surprisingly floppy in nature.

Photoelectron spectroscopy of the thiazate (NSO-) and thionitrite (SNO-) isomer anions.

Anion photoelectron spectra of the thiazate (NSO-) and thionitrite (SNO-) isomers are reported. The NSO- photoelectron spectrum showed several well-resolved vibronic transitions from the anion to the NSO radical neutral. The electron affinity of NSO was determined to be 3.113(1) eV. The fundamental vibrational frequencies of NSO were measured and unambiguously assigned to be 1202(6) cm-1 (ν1, asymmetric stretch), 1010(10) cm-1 (ν2, symmetric stretch), and 300(7) cm-1 (ν3, bend). From the presence of vibrational hot band transitions, the fundamental vibrational frequencies of the NSO- anion were also measured: 1280(30) cm-1 (ν1, asymmetric stretch), 990(20) cm-1 (ν2, symmetric stretch), and 480(10) cm-1 (ν3, bend). Combined with the previously measured ΔacidH298 Ko(HNSO), D0(H-NSO) was found to be 102(5) kcal/mol. Unlike the results from NSO-, the SNO- photoelectron spectrum was broad with little structure, indicative of a large geometry change between the anion and neutral radical. In addition to the spectrally congested spectrum, there was evidence of a competition between photodetachment from SNO- and SNO- photodissociation to form S- + NO. Quantum chemical calculations were used to aid in the interpretation of the experimental data and agree well with the observed photoelectron spectra, particularly for the NSO- isomer.

On the spectroscopic constants, first electronic state, vibrational frequencies, and isomerization of hydroxymethylene (HCOH[formula omitted

The hydroxymethylene cation (HCOH+) is believed to be chemically independent of the more stable formaldehyde cation isomer in interstellar chemistry and may likely be a precursor to methanol in chemical reaction networks. Previous work is corroborated here showing that the trans conformer of HCOH+ is 3.48 kcal/mol lower than the cis on the potential energy surface. The small energy difference between the conformers and the much larger dipole moment of cis-HCOH+ (2.73 D) make this conformer more likely to be observed than trans-HCOH+ via telescopic rotational spectroscopy. A strong adiabatic shift is also predicted in the first electronic excitation into the 1 2A′′/2 2A state out of either conformer into a C1 structure reducing the excitation wavelength from the near-ultraviolet all the way into the near-infrared. The full set of fundamental vibrational frequencies are also computed here at high-level. The 3306.0 cm−1 and 3225.3 cm−1 hydroxide stretches, respective of bare trans- and cis-HCOH+, are in agreement with previous theory but are significantly higher than the frequencies determined from previous experiment utilizing argon tagging techniques. This shift is likely because the proton-bound complex created with the argon tag reduces the experimental frequencies. Lower-level computations including the argon tag bring the hydroxide stretches much closer to the experimental frequencies indicating that the predicted frequencies for bare HCOH+ are likely well-described.

Non-invasive measurement of acoustic coupling between the clarinet bore and its player’s vocal tract

As acoustically coupled resonators, the bore of a clarinet or other woodwind instrument and the vocal tract of the player interact in ways that affect timbre and pitch. Pitch in particular is strongly dependent on vocal tract acoustics when the bore-tract coupling is strong, such as when a tract impedance maximum is close in frequency and amplitude to a bore impedance maximum. Direct investigation of bore-tract coupling requires invasive measurement of bore and tract input acoustic pressures (or impedances), and one particular technique makes us of the ratio of these pressures (in the frequency domain, Pt/Pb) at harmonics of the reed vibration fundamental frequency. A non-invasive, model-based approach to investigating bore-tract coupling has been developed, which depends on a free-field microphone recording the sound produced by the instrument (P1), and an accelerometer placed against the skin of the neck recording skin vibrations (P2) related to intra-tract acoustic pressures. An additional, model-based calibration step is required. The ratio of these two signals (in the frequency domain, P2/P1) following calibration is qualitatively similar to the ratio Pt/Pb, and approaches quantitative identity as the model-based calibration step improves.

Vibrational analysis of dibenzo-18-crown-6. Effect of dispersion correction on the calculated vibrational spectra

We report for the first time a detailed vibrational analysis of dibenzo-18-crown-6, db18c6. The experimental IR and Raman spectra of db18c6 were measured. The assignment of the fundamental vibrational frequencies of db18c6 was aided by using scaled quantum mechanical force fields calculated at the B3LYP/6-311G** and CAM-B3LYP/6-311G** levels. Comparison between the experimental and calculated spectra of some of the important conformations of db18c6 led to the conclusion that db18c6 in the solid phase exists in a C2 conformation that is similar to that predicted by X-ray, for also the solid phase. The effect of inclusion of the atom pair-wise dispersion correction to the B3LYP method, known as the B3LYP-D3 method, on the calculated IR and Raman spectra of db18c6 at the B3LYP level was also investigated. It was concluded that the effect of inclusion of the dispersion correction on the calculated vibrational frequencies and intensities is negligible.