Fundamental Vibrations Research Articles

Features of the defect structure of a lithium-gradient nonlinear optical single crystal LiNbO3 and their manifestation in the Raman spectra

LiNbO3 crystal with a lithium composition gradient of Li/Nb = 0.8 wt%/cm (Li0.97..1.01Nb1.03..0.99O3) were obtained. A monotonic change in the edge of the UV absorption edge is observed when scanning the surface of the gradient crystal along the growth direction. Raman spectra from different areas of studied crystal were analyzed in a wide frequency range, which includes the region of fundamental vibrations of the crystal lattice (100–900 cm−1) and the region of overtone processes (900–3000 cm−1). A compositionally homogeneous, congruent LiNbO3 crystal was used as a comparison sample. It was found that in the spectra obtained from different parts of the gradient crystal, there is a significant scatter in the frequency values of the lines corresponding to the fundamental vibrations of the crystal lattice, but at the same time, the number of lines corresponding to the fundamental vibrations of the lattice for the gradient and compositionally homogeneous LiNbO3 crystals is the same. Moreover, in the spectrum of a gradient crystal in the region of overtone processes of fundamental vibrations, significantly more lines (35 lines) are observed than in the spectrum of compositionally homogeneous crystals (15 lines). The data obtained show that the state of the defect structure of compositionally homogeneous crystals and gradient LiNbO3 crystal is significantly different. The discovered differences between the defective structure of a gradient crystal and the defective structure of a compositionally homogeneous crystal may be the reason for compensation (damping) of distortions during nonlinear optical conversion of laser radiation by a gradient crystal due to the uneven temperature distribution along the length of the crystal. In compositionally homogeneous crystals, such temperature distortions significantly limit the efficiency of nonlinear optical conversion.

The sound of porosity: Suitability of the impulse excitation technique (IET) to determine the Young's modulus of 2D macroporous ceramics

The presence of pores in a ceramic leads to a lower Young's modulus compared to dense material. For the development of porous ceramics with tailored elastic properties, an exact determination of the Young's modulus is required, especially for industrial applications. Therefore, we investigated the suitability of the non-destructive impulse excitation technique for measuring the dynamic Young's modulus of two-dimensional ceramics with low porosity (P < 19 %). For rectangular samples it was shown that the measurement results depend on the geometric pore position, as added pores outside the nodal lines of the fundamental flexural vibration had no influence on the result. Pores in the inner part of the sample led to a decrease of the Young's modulus that is in good agreement with empirical and analytical models. For the investigated interval of porosity range, the influence of pore size and geometric position on the reduction of the Young's modulus was determined.

An Investigation into the Impact of Time-Varying Non-Conservative Loads on the Seismic Stability of Concrete-Filled Steel-Tube Arch Bridges

When the arch rib of the mid-bearing through and lower-bearing through arch bridges undergoes out-of-plane deformation, it is usually subject to the resilience force provided by the flexible hanger, which is known as the “non-conservative force effect” of the suspender. In contrast to the static condition, in the dynamic scenario, the time-varying non-conservative force exerted by the flexible suspender becomes more complex due to dynamic changes in external load. Moreover, the difference in fundamental frequency and vibration period between the bridge system and arch rib may influence the stress distribution within the arch rib during ground motion. This paper investigates the impact of time-varying non-conservative forces on the dynamic stability of arch ribs in concrete-filled steel tube (CFST) bridges under seismic loads. Specifically, it examines the influence of different seismic waveforms, frequency disparities between bridge slabs and arch ribs, and suspender stiffness on the non-conservative effect. The results reveal significant disparities in the impact of non-conservative forces exerted by the suspender during seismic events with identical intensity but varying frequency characteristics. The influence of non-conservative forces on the dynamic stability of bridges escalates as deck stiffness increases, while it remains relatively unaffected by changes in suspender stiffness.

Magnetostrictive assisted free and forced vibration response of layered functionally graded circular plate with effect of prestress

One of the optimization requirements for improving the performance of magnetostrictive materials is prestress, which improves the magnetostriction coefficient. The influence of prestress on the fundamental frequencies and vibration suppression of a smart functionally graded circular plate is examined in the current work. The coupled differential equations regulating the motion are derived using Hamilton’s principle. This paper proposes using Kerr’s foundation as a flexible support structure for the disc braking system assembly. The Dirac-delta function and differential quadrature technique have been used to quantitatively simulate the forced vibration behaviour of a circular plate under moving loads. The accuracy and validity of the method used are tested by comparing numerical results to those that have already been published.

Study on the structural, magnetic, and magnetodielectric properties of M-type BaFe12O19 and SrFe12O19 hexaferrite nanoparticles

This study addresses the synthesis and characterization of hexagonal barium hexaferrite (BaFe12O19) and strontium hexaferrite (SrFe12O19) nanoparticles, aiming to enhance their structural and magnetic properties for potential applications. Using the sol–gel method, nanoparticles were synthesized and calcinated at 1000 °C, 1100 °C, and 1200 °C for 5 h. A comprehensive analysis was conducted on the prepared nanoparticles' structural, functional, morphological, and magnetic properties. X-ray diffraction confirmed the hexagonal structure and single-crystal phase for BaFe12O19 and SrFe12O19 across all calcination temperatures. The Rietveld analysis of XRD patterns of all the samples have been carried. Fourier transform infrared spectroscopy identified fundamental vibrations at octahedral and tetrahedral sites, verifying the presence of characteristic functional groups. Morphological studies revealed that at an annealing temperature of 1100 °C, the average nanoparticle diameters were 335 nm for BaFe12O19 and 302 nm for SrFe12O19. The elemental analysis and distribution of elements of hexaferrites were studies using Energy Dispersive X-ray Analysis with color mapping method. Magnetic properties were extensively analyzed, including saturation magnetization (Ms), coercivity (Hc), retentivity (Mr), anisotropy field (Ha), squareness ratio (Mr/Ms), and magnetocrystalline anisotropy (K1). At 1100 °C, the magnetic properties of BaFe12O19 are Ms = 55.96 emu/g, Hc = 4308 G, Mr/Ms = 0.51, Ha = 31.30 kG, and K1 = 5.65 × 105 erg/cm3. For SrFe12O19, these values are Ms = 50.80 emu/g, Hc = 3507 G, Mr/Ms = 0.52, Ha = 21.20 kG, and K1 = 5.65 × 105 erg/cm3. Additionally, the study explored the magnetodielectric properties of BaFe12O19 and SrFe12O19 nanoparticles. At a magnetic field of 6000 G, the magnetocapacitance percentage (MC%) and magnetotangent loss percentage (ML%) for BaFe12O19 are −6.23 % and −8.85 %, respectively, while for SrFe12O19, these values are −4.38 % and −1.0 %. The findings indicate that the synthesized hexaferrite BaFe12O19 and SrFe12O19 nanoparticles exhibit significant potential for applications in sensors, permanent magnets, and data recording, with optimized structural and magnetic properties achieved at specific calcination temperatures.

Symmetry properties, tunneling splittings of some vibrational energy levels and torsional IR spectra of the trans – and cis – conformers of hydroquinone molecule

Torsional vibrational states of trans − and cis − conformers belonging to point symmetry groups C2H and C2V, respectively, of hydroquinone molecules are classified according to the irreducible representations of the molecular symmetry group D2H(M). A correspondence has been established between the symmetry elements of the D2H(M) group and the symmetry elements on the torsional coordinate plane for two-dimensional surfaces of potential energy, wave functions, kinetic coefficients and dipole moment projections. A correspondence has been established between the symmetry species of the point symmetry groups C2H, C2V and the symmetry species of the molecular symmetry group D2H(M). Conformational states, barriers to internal rotation and the above-mentioned characteristics of the hydroquinone molecule were calculated at the MP2/Aug-cc-pVDZ, MP2/Aug-cc-pVQZ, MP2/Aug-cc-pVTZ, MP2/CBS(aD,aT,aQ), and CCSD(T)/dAug-cc-pVDZ levels of theory. The calculated data sets were approximated using symmetry-adapted sets of basis functions. Using a numerical solution of the vibrational Schrödinger equation of restricted dimensionality, the energies and wave functions of 50 stationary torsional states of the hydroquinone molecule were determined for the first time. The values of tunneling splittings of the ground vibrational and a number of excited torsional states of trans − and cis − conformers were determined. In particular, when calculating at the MP2/CBS(aD,aT,aQ) level of theory, the values of tunneling splittings of the ground vibrational states of trans − and cis − conformers turned were 1.32*10-6 and 1.62*10-6 cm−1, which is consistent with the experimentally established upper limit for this value in the cis − conformer by authors of [W. Caminati, S. Melandri, L. B. Favero, J.Chem.Phys., 100 (1994) 8569 – 8572] (0.2 MHz or 6.67*10-6 cm−1). The calculations of the matrix elements of the dipole moment operator and the partition function made it possible to simulate the torsional IR spectra of the molecule’s conformers at different temperatures. The frequencies of fundamental torsional vibrations in the trans – (267.1 and 269.0 cm−1) and cis – (269.5 and 270.9 cm−1) conformers, calculated at the MP2/CBS(aD,aT,aQ) level of theory, are in good agreement with the experimental value of frequency of this vibration (266 cm−1), established in [W.G. Fateley, G.L. Carlson, F.F. Bentley, J.Phys.Chem., 79 (1975) 199–204.].

Symmetric and asymmetric vibration and buckling of a thermal rotating annular-plate with Pasternak foundation

This paper studies the symmetric and asymmetric vibration and buckling modes of a rotating thermal annular plate resting on a Pasternak foundation. With considering the von Kármán geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are established via Hamilton's principle, and then solved by using the differential quadrature method. With both inner and outer boundaries constrained, the modes of the rotating system vary differently depending on the mode symmetry. The symmetric modes are mainly affected by the generated centrifugal force, while the asymmetric ones are affected by both centrifugal and Coriolis forces. The additional Coriolis, with mainly two directions, strengthens the forward travelling parts of the asymmetric modes, but makes the backward counterparts buckled more easily. Also, the thermal effect, as well as boundary elasticity and foundation coefficients, are also investigated from the viewpoint of mode symmetry. Results show that the temperature rise can shift the fundamental vibration mode from the symmetric one to the asymmetric one and backward travelling waves for rotation, which also adds to the complexity of mode variation with joint parameters. For the joint effect of the temperature rise and rotating, the annular plate tends to buckle more readily while the effects of the two factors are linearly superimposed.

Vibration behaviours of composite conical–cylindrical shells with damping coating: Theory and experiment

This study presents the theoretical and experimental investigations on vibration behaviours of carbon fiber/ resin composite conical-cylindrical shells (or CC shells) with damping coating. First, an analytical model of such a combined shell with coating material considers the effects of base harmonic excitation load under arbitrary boundary conditions is proposed using the first-order shear deformation theory, virtual artificial spring technique, modal superposition approach, the Rayleigh-Ritz method, etc. Subsequently, the solutions of fundamental frequencies, mode shapes, and vibration displacements in the frequency domain are acquired by deriving the corresponding energy expressions and motion equations. Convergence analysis is utilized to determine the virtual spring stiffness value and the appropriate truncation numbers. Both literature and experimental results are conducted to give an adequate validation of the current model, in which the continuous 3D printing technology is adapted to fabricate two CC shell specimens with one of the outside surfaces being sprayed by coating material using an atomization deposition approach. Finally, the effects of the coating thickness ratio, Young's modulus ratio of the coating and the substrate shell, the semi-vertex angle, and the fiber laying angle on the free vibration and forced vibrations of the coated structure are discussed, with some practical recommendations being provided to improve the vibration suppression of such a coated structure.

Fourier-transform infrared spectroscopy with undetected photons from high-gain spontaneous parametric down-conversion

Fourier-transform infrared spectroscopy (FTIR) is an indispensable analytical method that allows label-free identification of substances via fundamental molecular vibrations. However, traditional FTIR spectrometers require mid-infrared (MIR) elements, including low-efficiency MIR photodetectors. SU(1,1) interferometry has previously enabled FTIR with undetected MIR photons via spontaneous parametric down-conversion in the low-parametric-gain regime, where the number of photons per mode is much less than one and sensitive photodetectors are needed. In this work, we develop a high-parametric-gain SU(1,1) interferometer for MIR-range FTIR with undetected photons. Using our method, we demonstrate three major advantages: a high photon number at the interferometer output, a considerably lower photon number at the sample, and improved interference contrast. In addition, we broaden the spectral range of the interferometer by aperiodic poling in the gain medium. Exploiting the broadband SU(1,1) interferometer, we measure and evaluate the MIR absorption spectra of polymers in the 3-μm region.

Optimization of column-in-column system based on non-conventional TMD concept

Previous studies showed that the non-conventional tuned mass damper (TMD) with large mass ratio outperforms the traditional one in respect to the structural vibration control efficiency and robustness. The authors recently proposed a novel control system based on the non-conventional TMD concept, namely the column-in-column (CIC) system, which was composed of a primary column, a secondary column and a series of interconnected springs/dashpots. In this novel system, the secondary column connected to the primary one with springs/dashpots could act as a large TMD to attenuate adverse vibration of the primary structure, and its control effectiveness was preliminarily verified through numerical investigations. However, the control robustness was found not sufficient based on the existing optimal formulae in the literature for CIC optimization. This paper presents a new design method for optimizing the CIC system for better harnessing its control effectiveness and robustness in reducing structural response. The CIC system consists of two columns with distributed mass and uniform flexural rigidity, connected by springs along the column height. The effective modal mass and modal stiffness of a specific vibration mode of the system can be straightforwardly calculated by using the Euler-Bernoulli beam theory. Considering the fundamental vibration mode of the system as the target response mode for vibration control, the multiple degree-of-freedom (DOF) CIC is simplified into a two DOF with three springs (2DOF3S) structural model, the design parameters, i.e., the optimal tuning frequency ratio and damping ratio of this system are derived to minimize the displacement response of the primary structure. To demonstrate the proposed design method, the effectiveness and robustness of the CIC system in controlling seismic induced structural vibrations are assessed in both the frequency and time domains. Results show that the derived optimum formulae are applicable for optimizing the TMD system with consideration of the distributed mass and deformation of the mass damper, i.e., a column in this study. The optimized CIC system has good control robustness even if the CIC is mistuned with its design parameters deviate from the optimal values by ±50 %. The conventional TMD system with lumped mass as the mass damper is a special case of the proposed CIC system. The optimized CIC system has favorable control efficiency in mitigating the seismic responses of structures with reduction ratios averagely varying within the range of 15 % ∼ 55 % with a probability of 92.67 %. It is concluded that the proposed method is reliable and can be used for the optimum design and control of the CIC system.

Derivation of the Formula for the Power Line Tower Fundamental Vibration Frequency

Derivation of the Formula for the Power Line Tower Fundamental Vibration Frequency

Vibration behavior prediction of submerged nanobeams with axially traveling supports: numerical, analytical, and machine learning approaches

This work surveyed the vibration behavior and stability analysis of an underwater moving flexible nanosize beam, implementing numerical and analytical methods as well as tree-based machine learning (ML) algorithms. Dynamic modeling is performed based on the nonlocal stress-strain gradient theory (NSSGT), incorporating variable environmental conditions, surface energy, and rotational inertia effects. The natural frequencies and instability threshold are computed numerically. The exact closed-form mathematical expression for the critical towing velocity of the nanosize beam is determined analytically. Also, decision tree regression and least-squares boosting tree (LSBT) regression algorithms are exploited to predict stability boundaries and the fundamental vibration frequency, and their efficiency is surveyed accordingly. Comparative studies and parametric investigations are conducted. The impressions of geometry, added mass coefficient, scale ratio parameter, surface layer characteristics, fluid mass ratio, humidity, temperature rise, and external magnetic field intensity on the nanosystem dynamics are examined and illuminated. It is detected that the results of the analytical method and ML-based approaches are consistent with those reported by the numerical technique and literature. The results asserted that the proposed ML algorithms have acceptable performance and excellent effectiveness in computational time and cost. It is comprehended that the dynamic features of submerged traveling nanobeams drastically depend on the rotational inertia effects and thickness-dependent scale effects. The stability of the immersed movable nanoscale beams is perceived to improve by increasing the scale ratio parameter and the added mass coefficient. From the perspective of the optimal design of engineering instrumentation tools, the outcomes of the current article can be applied as an inclusive benchmark.

The effect of superstructure properties on the re-centering capability of Friction Pendulum (PS) isolator

The re-centering capability after the seismic excitation is one of the fundamental properties of a seismic isolation system. This study examines the effects of superstructure properties on the re-centering capability of the Friction Pendulum (FP) isolator. To this end, a comprehensive parametric study is conducted using a two-degree-of-freedom (2DOF) model that accounts for the nonlinear behavior of the superstructure and isolator. This study evaluates the re-centering capability of the FP isolator by calculating the ratio of residual displacement (dres) to the maximum displacement (dmax). The effect of superstructure properties, including strength reduction ratio R, fundamental vibration period Ts, post-yield stiffness ratio αs, superstructure damping ratio ξs, and the ratio of superstructure mass to total mass of the system γm on the dres/dmax ratios is thoroughly analyzed. The findings suggest that while estimating the residual displacement of isolation systems, it is important to consider the impact of superstructure parameters. An analytical equation is proposed to predict dres/dmax ratio based on effective superstructure and isolator parameters.

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers.

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Prediction of BLEVE loading on structures

In a previous study by the authors, rigid structure assumption, as commonly used in analysing blast wave interaction with structures, was adapted in investigating the Boiling Liquid Expanding Vapour Explosion (BLEVE) pressure wave interaction with structures to predict BLEVE loads on structures. However, real structures are not rigid and the duration of BLEVE wave is much longer than that from high explosives and may be in the order of structural natural vibration period. Neglecting structural deformation, therefore, may lead to inaccurate predictions of BLEVE loads acting on the structure because structural deformation during the action of BLEVE wave would change the wave and the structure interaction. In this study, intensive numerical simulations are carried out using a validated computer model to investigate the influences of structural stiffness and BLEVE wave duration on the reflected BLEVE pressure on the structure. Based on the numerical results, prediction charts are proposed as a function of the BLEVE wave duration and structural fundamental vibration period for reliable predictions of BLEVE loads on structures. The findings of this study can be used to predict explosion loads in structural design against BLEVE.

Novel third order nonlinear optical stilbazolium crystal replaced with 3-methoxy benzaldehyde as donor for optical device applications

A novel organic nonlinear optical stilbazolium group single crystal of 1-methyl-2-[2-(3-methoxystyryl)]-pyridinium iodide (subsequently referred to as MSMI) was grown by the solution growth technique using the method of slow evaporation at ambient temperature. The Single-crystal XRD investigation indicates that the MSMI crystal belongs to a monoclinic crystal system with a centrosymmetric space group. CHN elemental analyser confirms the weight percentage of carbon (C = 51.00 %) hydrogen (H = 4.55 %) and nitrogen (N = 3.94 %) in the MSMI crystal structure. The presence of 16 hydrogen atoms and 15 carbon atoms in the MSMI was affirmed by the Nuclear Magnetic Resonance (NMR) spectroscopic analysis. Fourier Transform Infrared (FTIR) studies confirmed the fundamental vibrations for different functional groups found in the MSMI crystal. The Hirsfeld surface analysis figured out the hydrogen bond interaction and π…π interaction which supports the stability of the crystal structure. The crystal is found to exhibit transmittance of wavelength above 400 nm and has a band gap of 3.05 eV ascertained from UV–Vis-NIR spectroscopic analysis. Photoluminescence (PL) studies reveal that the title crystal has an emission wavelength of 572 nm. The surface characteristics of the title crystal were examined by Atomic Force Microscopy (AFM), and etching studies. The value of Meyer's number is n = 1.8 which is determined by the Vickers microhardness studies. The value of the third-order nonlinear refractive index (n2) is 4.662×10−8 cm2/W, the nonlinear absorption coefficient (β) is 1.305×10−3 cm/W, nonlinear susceptibility (χ(3)) is 9.297×10−5 esu and the optical limiting threshold is 11.43 J/cm2 was ascertained form the Z-scan technique. The results indicate that the MSMI crystal is a potential optical limiter and has promising applications in nonlinear optical devices.

Investigation of Fourier transform infrared spectroscopy potential in cotton fiber micronaire measurement and distribution

Cotton micronaire is an essential fiber quality attribute that characterizes both fiber maturity and fineness components. Micronaire and other attributes are measured on fiber lint routinely in laboratories under controlled environmental conditions following a well-established high-volume instrument protocol. In this study, the attenuated total reflection Fourier transform infrared spectroscopy, characterizing fundamental group vibrations in fiber cellulose from 4000 to 400 cm−1, and using an attenuated total reflection device, was explored for fiber micronaire assessment, especially for seed cotton locule fibers that were mingled with nonlint materials, and varied in fiber maturity within a naturally variable sample. Partial least squares multivariate regression models and the algorithmic infrared maturity approach were developed and then applied to predict micronaire values of validation samples and independent seed cotton samples for comparison. Unlike partial least squares models that showed worse in the coefficient of determination, bias, and percentage of samples within the 95% agreement range for independent samples than for validation samples, the algorithmic infrared maturity approach indicated a similarity in the coefficient of determination, bias, and percentage of samples within the 95% agreement range between the validation samples and independent samples. In particular, the algorithmic infrared maturity approach avoided the need to re-calibrate the model with new samples. Therefore, the development of a robust and effective Fourier transform infrared technique combined with the infrared maturity approach for rapid laboratory micronaire assessment and distribution demonstrated a great potential for its extension to the early micronaire testing in remote/breeding locations, and also to regular cotton fibers, processed cotton yarns and fabrics.

Vibration Mitigation via Tuned Mass Damper for Adjacent Stay Cables Interconnected with Rigid Cross-Tie

The characteristics of low damping and closely spaced natural frequencies make stay cables susceptible to wind-induced vibrations. This work proposed a novel damping device consisting of tuned mass damper (TMD) and rigid cross-tie (RCT) to mitigate the vibration of stay cables effectively. Two adjacent stay cables interconnected with RCTs can provide installation locations for TMDs, thus making the novel TMD-RCT control system feasible. Experimental control tests were carried out on a two-cable model of adjacent stay cables built in laboratory, where one TMD was designed based on the fundamental vibration mode of the stay cable. The effects of CT stiffness, number of RCTs, mass ratio, and installation position on the vibration reduction effect of the device were studied. To validate the efficacy of the proposed TMD-RCT device in vibration mitigation of stay cables under different loading cases, simulation tests and corresponding control performance evaluation were conducted.

Spectra of the D2O dimer in the O-D fundamental stretch region: The acceptor symmetric stretch fundamental and new combination bands.

The O-D stretch fundamental region of the deuterated water dimer, (D2O)2, is further studied using a pulsed supersonic slit jet and a tunable optical parametric oscillator infrared source. The previously unobserved acceptor symmetric O-D stretch fundamental vibration is detected, with Ka = 0 ← 0 and 1 ← 0 sub-bands at about 2669 and 2674cm-1, respectively. The analysis indicates that the various water dimer tunneling splittings generally decrease in the excited vibrational state, similar to the three other previously observed O-D stretch fundamentals. Two new (D2O)2 combination bands are observed, giving information on intermolecular vibrations in the excited O-D stretch states. The likely vibrational assignments for these and a previously observed combination band are discussed.

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