Resonant Vibration Research Articles

Ballistic and delayed photodissociation channels in the B̃ 2A11 state of water studied with resonant inelastic x-ray scattering

Photodissociation is one of the most important photoinduced chemical reactions. It occurs when the potential energy curve along a chemical bond is repulsive in an excited state. Typically, “ballistic” ultrafast dissociation leads to the broadening of absorption resonances and the smearing out of vibrational fine-structure. We report on the photodissociation of H2O in the B̃ 2A11 electronic state, characterized by a |3a1−14a11〉 configuration, which can be reached via resonant inelastic x-ray scattering or direct ultraviolet absorption. In both cases the spectra show narrow vibrational resonances, in spite of the dissociative character of the state. We find that “delayed” dissociation pathways, caused by reflection of the nuclear wave packet, are responsible for this effect. In spite of the analogous topology of the potential energy surfaces of the core- and valence-excited states, the reflection of the wave packet takes place only in the latter. The two-dimensional wave packet of the O-H stretching coordinates becomes trapped in a “cavity” near the Franck-Condon region, resulting from a mismatch between the OH vibrational frequency in the cavity and the one at the dissociation limit. Published by the American Physical Society 2024

Crisis-induced vibrational resonance in a phase-modulated periodic structure.

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation. We identify two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyze these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

Application of a vibration resonance-assisted enhanced feedforward cascaded stochastic resonance system in bearing diagnostics

Extracting fault features from strong background noise is a key challenge in bearing diagnostics. Stochastic resonance (SR) has been widely applied in bearing diagnostics by utilizing noise to enhance useful signals. This paper proposes a feedforward cascaded system based on vibration resonance (VR) to assist in enhancing SR from the perspective of multi-system synergy, aiming to improve the performance of the SR system. Firstly, a matching steady-state potential function is designed to effectively alleviate the output saturation phenomenon. Then, by introducing a feedback term and VR, a feedforward cascaded system with band-pass characteristics is constructed, significantly enhancing the ability to suppress low-frequency interference. Finally, the proposed system is analyzed in the detection of simulated signals and actual bearing fault signals from the German PADERBORN dataset. The results demonstrate that the system outperforms two other SR systems and the Fast-Kurtogram method (FK), validating its performance and practicality.

A variable-thickness-arch based nonlinear vibration absorber for rotor-bearing systems

There are complex nonlinear vibrations in rotating machinery and their suppression is essential. This study aims to design a nonlinear vibration absorber to suppress the nonlinear vibration of rotor-bearing systems. The nonlinear vibration absorber is composed of a mass ring and circumferentially arranged multiple variable thickness arches mounted on the rotor and rotated synchronously. The absorber provides the nonlinear stiffness through the bending deformation of the arches under concentrated loads and the nonlinear stiffness is adjustable by designing variable thickness in the arches. The dynamic model of a rotor-bearing system coupled with the nonlinear vibration absorber is established. An efficient Galerkin averaging incremental harmonic balance (EGA-IHB) method is developed to analyze the vibration reduction performance of the absorber. The results indicate that the centrifugal force produced by the rotation of the absorber provides negative stiffness depends on the mass and the rotational speed of the absorber. When the absorber has a linear stiffness near the negative stiffness, the absorber demonstrates outstanding capability in suppressing the nonlinear vibrations of rotor-bearing systems. The absorber effectively suppresses both the primary resonance and harmonic resonance of the rotor system. The analysis demonstrated detailed the effects of the absorber parameters on vibration reduction. Increasing absorber damping can decrease both the primary resonance and harmonic resonance of the rotor system slightly. Appropriately increasing the absorber mass and reducing the cubic nonlinear stiffness can enhance the absorber performance in reducing primary resonance vibrations without affecting the vibration characteristics of the rotor system.

Nonlinear resonance in an overdamped Duffing oscillator as a model of paleoclimate oscillations.

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models. Subsequently, we demonstrate the existence of vibrational resonance (VR) and nonlinear resonance phenomena at the combination tones of the driving frequencies in a simple bistable potential without self-sustained oscillations. We find that periodic forcing by the obliquity and frequencies similar tothose of the precession cycle can generate output dominated by 100-kyr cycles, thereby offering a mechanism for explaining the observations in geological data. While previous studies of VR have assumed one periodic driver to have a frequency much higher than the other, we show that for a range of amplitudes, both phenomena can occur at the orbital cycle frequencies. We find that the nonlinear resonance phenomenon is more robust to noise than VR between eccentricity and obliquity and emerges within a much larger range of amplitudes of forcing. Finally, we conclude that it is conceivable that nonlinear resonance between obliquity and precession might explain the spectral frequencies observed in the late Pleistocene.

Analytical Spectral Semi-quantitative Dating Method of Printed Text Toner Using Raman Spectroscopy and the Fluorescence signal of Paper Sheet Cellulose

Abstract: The chemical processes that occur during the surface degradation of document paper under the influence of external factors were studied by Raman spectroscopy. The possibility of comparing the same processes occurring on clean free paper and under printed text toner letters is of interest. It is assumed that the transformation of cellulose can occur at different rates in the areas of paper exposed to direct atmospheric and light exposure and in the areas containing an intermediate layer of the toner. The most stable temporal changes occur in the region of C–C–C and C– C–O vibrations of glycosidic rings in the short-wavelength region of the Raman spectrum. Background: The main areas of research in the field of document dating, mainly focused on chromatographic methods. These methods are based on studying the dynamics of evaporation of volatile ink components. There is also a variety of chromatography techniques, including gas chromatography, ion chromatography, high performance liquid chromatography, thin layer chromatography and gas chromatography-mass spectrometry. This indicates the wide range of approaches and techniques used to determine the age of written materials. However, all these methods are used mainly during the first two years after writing the document details, which does not allow examining documents that are more than two years old. Methods: Raman spectroscopy was used as the main research method. The object of the study was sheets of white A4 paper with printed text printed on them, produced on a laser printer. The subject of the study was areas of paper free of text, as well as areas of paper under toner. The integrated fluorescence of a paper optical brightener based on stilbene was studied in the wavelength range of 400–500 nm. Also, all objects were studied using optical microscopy. Results: The comparison of peak intensity values averaged over 10 brands over the years made it possible to reveal the following regularities: – the ratio of peaks in the paper spectra from which the toner was removed is greater than in the blank paper spectra, and the difference becomes less noticeable as the age of the paper decreases. The ratio of the intensity of the 330 cm-1 peak to the intensity of the 1603 cm-1 peak: the older the document becomes, the lower the average ratios of these peaks in both the blank paper spectra and in the spectra of paper from which the toner has been removed. –the intensity of the peak in the region of 280 cm-1 and 1 086 cm-1 of the Raman shift increases with decreasing the age of the toner-free paper.– a gradual increase in the intensity of the 380 cm-1 peak is observed when comparing the paper samples from which the toner was removed for 2016, 2018, 2020, and 2022. Regularity was also found in the change in the ratio of the average statistical values of the peak at 280 cm-1 in the spectra of the paper under the toner to a similar peak in the spectra of the paper free from text: the value of this ratio decreases with decreasing the paper age. At the same time, the paper fluorescence signal is an informative parameter that makes it possible to establish some facts from the document’s history. With artificial document aging, a significant broadening of the dispersion region and the appearance of its “splitting” into two or three strata are observed in the distribution of the fluorescence signal level of a paper sheet relative to the average value. The average fluorescence signal of a naturally aged sheet decreases with the age of the document. Conclusion: As a result of research, it has been established that Raman spectroscopy can be successfully used as a method for dating documents. When comparing the degree of degradation of the surface of open areas of paper and areas protected by toner of printed text, different effects of external factors on these areas were established, leading to different rates of degradation processes. The use of Raman peak intensity ratios for paper components in exposed areas compared to peaks under printed text further expands the methodology. The emphasis on spectral methods, in particular fluorescence signal distribution and Raman spectroscopy, to detect surface changes is well justified. It demonstrates a holistic approach to document analysis, taking into account both the chemical changes observed using Raman spectroscopy and the fluorescence signal distribution that may indicate signs of artificial aging through light exposure. This combination of methods appears to be reliable for assessing the age of documents and can make significant contributions to the field of forensic document examination.

A Comprehensive Review on the Viscoelastic Parameters Used for Engineering Materials, Including Soft Materials, and the Relationships between Different Damping Parameters.

Although the physical properties of a structure, such as stiffness, can be determined using some statical tests, the identification of damping parameters requires a dynamic test. In general, both theoretical prediction and experimental identification of damping are quite difficult. There are many different techniques available for damping identification, and each method gives a different damping parameter. The dynamic indentation method, rheometry, atomic force microscopy, and resonant vibration tests are commonly used to identify the damping of materials, including soft materials. While the viscous damping ratio, loss factor, complex modulus, and viscosity are quite common to describe the damping of materials, there are also other parameters, such as the specific damping capacity, loss angle, half-power bandwidth, and logarithmic decrement, to describe the damping of various materials. Often, one of these parameters is measured, and the measured parameter needs to be converted into another damping parameter for comparison purposes. In this review, the theoretical derivations of different parameters for the description and quantification of damping and their relationships are presented. The expressions for both high damping and low damping are included and evaluated. This study is considered as the first comprehensive review article presenting the theoretical derivations of a large number of damping parameters and the relationships among many damping parameters, with a quantitative evaluation of accurate and approximate formulas. This paper could be a primary resource for damping research and teaching.

Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential.

For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, H_{2},N_{2},Cl_{2},I_{2},O_{2}, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation.

Forced Response of Rotating Blisks: Prediction and Correlation to Blade Tip-Timing Measurements

Abstract This paper explores two different blisk dynamic models for resonant vibration prediction of a rotating blisk test piece, i.e., the Model-BDTID and geometrically mistuned models (GMM). The former represents a mistuned blisk model with blade mistuning pattern experimentally retrieved by a recently proposed blade mistuning identification method based on blade detuning tests (BDTID). It falls into the scope of the frequency-mistuning modeling approach. The latter refers to a geometrically mistuned model constructed upon high-precision blisk geometry data by leveraging the advanced optical geometry measurement technology. A specifically developed “Sector Mode Assembling Reduction Technique” is exploited for efficient dynamic analyses of the large-sized GMM. Forced response tests are performed in a spinning rig under well-controlled laboratory condition. The blade tip-timing (BTT) technique is employed to give all-blade vibration measurements of the rotating blisk. Correlation results between the forced response predictions to BTT measurements demonstrate that both the Model-BDTID constructed upon the identified blade mistuning of the blisk at rest and the GMM, can predict the resonant vibration of the rotating blisk with satisfactory accuracy.

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

Focus control of a concave–convex ultrasonic gel lens in the radial direction

Optical image stabilization (OIS) systems maintain the three-dimensional focal position of a lens through mechanical actuation systems. This paper examines an optical lens for OIS that utilizes ultrasound vibration to alter the focal position, not only in the depth direction but also in the radial direction. The lens has a simple structure with no mechanical moving parts and consists of an ultrasound transducer divided into four pieces, a glass disk, and a transparent viscoelastic gel film that functions as a lens. The acoustic radiation force generated by the resonant flexural vibration of the glass disk can alter the surface profile of the gel film, allowing for a variable-focus function. The concave and convex lenses can be interchanged using two resonant vibration modes: the standing-wave mode, in which the vibration loop appears at the center, and the traveling-wave mode, in which the vibration node appears at the center. The positions of ultrasound vibrations on the lens can be controlled in a two-dimensional plane by adjusting the driving amplitudes of each channel, thereby achieving focus control in the radial direction. The focusing characteristics of the lens are evaluated through ray-tracing simulation.

Nonlinear characteristics and radial-bending-torsional vibration of a blade with breathing crack

Rotor failures due to cracked blades are frequently observed in rotating machinery. The identification of cracking state of rotating blade based on vibration characteristics has garnered a lot of attention. However, nonlinear characteristics and vibration combining in radial, bending and torsional directions of a rotating blade induced by the crack breathing is yet not clear. This paper proposes a radial-bending-torsional dynamic model of rotating blade with breathing crack. A time-varying integration method is proposed for determining the crack state based on the strain energy release rate. The crack breathing behavior is described by Boolean operation and the numerical integration are applied to open or close the crack. The model is validated through modal analysis, vibration responses and contact state of crack surface. Frequency veering is changed between the 2nd flap and 1st edgewise frequency due to the existence of crack. Strong nonlinear behaviors are found in the radial and torsional vibrations because of the crack breathing. Nonlinearities are also found in the combined vibrations between the radial-bending and the bending-torsional directions. Radial and torsional vibration amplitude levels can be used as an indication of blade crack failure, but the applicability depends on the absolute response decided by the aerodynamic excitation and resonant vibration. These findings can serve as guidance in crack identification and cracking state monitoring of rotating blades.

Investigating resonance frequency in advanced composite structures as the main part of bridge construction: a multi-physics simulation approach

This paper investigates the nonlinear vibration characteristics and resonance frequencies of a graphene oxide powders (GOP) reinforced beam structure, which is in contact with fluid, serving as a crucial component in bridge construction. Utilizing a multi-physics simulation approach, this study integrates both mathematical modeling and COMSOL simulations to analyze the behavior of the GOP-reinforced beam. The fluid in the analysis is modeled as incompressible, non-viscous, and irrotational, contributing to the interaction with the beam structure. The isogeometric approach, coupled with the harmonic balance method and the arc-length technique, is employed to solve the complex nonlinear partial differential equations (PDEs). This coupled method ensures the accurate capture of the nonlinear response and resonance frequencies of the beam, which are critical for the safe design and performance of bridge structures. The findings reveal the significant influence of GOP reinforcement on the vibration and stability characteristics of the beam, highlighting its potential to enhance structural performance under dynamic loading conditions. The study also emphasizes the importance of considering fluid-structure interactions in the design process, as the fluid’s presence substantially affects the vibration behavior. This research contributes to the understanding of the dynamic behavior of advanced composite structures in fluid environments, offering valuable insights for the design and analysis of bridge components. The results demonstrate the efficacy of the proposed simulation approach in addressing the complexities of nonlinear vibrations in fluid-structure interaction systems, paving the way for future developments in civil engineering applications.

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

Investigating the role of solvents in modulating glass transition and dynamic mechanical characteristics of polystyrene film

This study investigates how different solvents impact the glass transition and dynamic mechanical properties of polystyrene (PS) films. Using FTIR spectroscopy, it analyzes solvent-induced variations in molecular vibrations, particularly in the phenyl ring region. Results show solvent-specific effects on the 750 cm-1 peak, associated with the "meta-substituted aromatic ring," influencing phenyl ring vibrations. DSC analysis highlights solvent effects on the glass transition temperature (Tg), revealing complexities in PS films prepared with chloroform, tetrahydrofuran (THF), and toluene. Varied Tg behavior suggests solvent-driven structural modifications and gradual solvent removal. Dynamic Mechanical Analysis (DMA) demonstrates solvent-dependent changes in storage modulus, loss modulus, and tan δ, indicating solvent polarity role in polymer chain dynamics. Toluene-induced plasticization reduces Tg and increases creep compliance, revealing PS film sensitivity to solvents. These findings stress solvent selection importance in tailoring thermal and mechanical properties of polymer films for specific applications.

Finite element analysis of a Helmholtz transducer jointly driven by a trilaminar ring and a piezoelectric circular tube

Abstract Crosswell seismic survey can image the crosswell geological anomalies with high resolution in 3D. To effectively conduct crosswell seismic survey, it is necessary to use a seismic source capable of transmitting low-frequency and high-power signals in a compact size. In this paper, a novel Helmholtz transducer is proposed, which utilizes both the bending vibrations of the trilaminar ring and the radial vibrations of the piezoelectric circular tube to simultaneously drive the vibration of the Helmholtz liquid cavity. This design reduces the resonant frequency of the liquid cavity while enhancing the transmitting voltage response at the liquid cavity resonant frequency. The influence of the inner radius of the trilaminar ring, the outer radius of the ceramic ring and the length of the piezoelectric circular tube on the liquid cavity resonant frequency and the transmitting voltage response at the liquid cavity resonant frequency is simulated using the finite element method. The simulation results provide a theoretical foundation for optimizing the design of such transducers.

Study on the global and nano-scale characterization of heat-induced changes in ordinary Portland cement paste

Cement-based composite materials can be damaged by distributed micro-cracking and degradation of hydration products when exposed to sustained high temperatures. In this study, a nano-scale characterization tool (dynamic nanoindentation) and global mechanical methods (vibration resonance frequency and damping) are employed to better understand the degradation of ordinary Portland cement paste subjected to high temperature exposures. A connection between the methods is demonstrated.

Convenient Size Analysis of Polystyrene Nanoplastics via Regulating the Radiative Transition Efficiency.

Developing a convenient method to efficiently determine the size of nanoplastics in the environment is urgent in terms of ecological or human health protection. In this work, a novel strategy for discriminating the size of polystyrene (PS)-based nanoplastics was reported via regulating the radiative transition efficiency of NH2-UIO-66 (NU) with benzoic acid (BA) as the auxiliary ligand. The elaborately doped BA capped the defect sites and triggered nonradiative transition efficiency of NU. As a result, the formed composite (denoted as BA-NU) was more sensitive to interaction among neighboring NU and nanoplastics. The interaction between particles limited the rotation and vibration of the benzene ring within the BA-NU molecule, thus increasing the BA-NU fluorescence. The sensitivity of BA-NU on nanoplastics was well controlled by manipulating the doping contents of BA, leading to precisely tunable physicochemical properties for this structure. Deriving from the exquisitely designed nanostructures, the composite of BA-NU was successfully used to discriminate different size PS as an ultrasensitive turn-on probe. This work highlights the possibility of boosting the detection performance by regulating the main structure with guest molecules at the molecular level.

Bifurcation boundaries analysis of the thin-walled internal resonance energy harvester

The dynamic instability of the thin-walled 1: 2 internal resonant piezoelectric vibration energy harvester is investigated. Previously work (Nie et al., 2019) derived the nonlinear electromechanical-coupled governing equations and validated them experimentally. The modulation equations are performed by the method of multiple scales. The system stability is obtained from the eigenvalues of the Jacobi matrix. Then, three types of bifurcation boundaries of the system are determined analytically and simulated numerically via Routh–Hurwitz criterion. Results show that internal resonance complicates the dynamic properties of the bifurcation region. For a large external excitation, new saddle node bifurcation regions appear in the stability diagram. Moreover, the new saddle node and Hopf bifurcation regions may intertwine. Furthermore, as the acceleration excitation increases, the system can be observed to transition to stable–unstable–stable states. The system’s high and low branch responses are fed back by the system’s large and small initial conditions. The system’s periodic and quasi-periodic motions are characterized by time response, FFT, phase trajectory, and Poincaré map. The study of the stability boundary of the piezoelectric energy harvester contributes to the harvesting of energy from ambient vibrations over a broader frequency range.

A high-static-low-dynamic-stiffness delayed resonator vibration absorber

Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the nonlinear HSLDS characteristics, thus creating a nonlinear DR (NDR). Three unexplored topics are considered: (1). To address the nonlinear dynamics that are made complicated by the introduction of delay and the nonlinearity coupled between the NDR and the primary structure; (2). To tune the control parameters to seek possible complete vibration suppression in the nonlinear case, and accordingly, to determine the operable frequency band; (3). To evaluate how the HSLDS characteristics can enhance the performance of the linear DR (LDR) and how to design an NDR to maximize its benefits. Without loss of generality, a classic nonlinear HSLDS structure with three springs and two links is considered, and mathematical tools and computational algorithms are introduced or proposed to efficiently address theoretical analysis. Using the parameters of an experimental setup, we show that a properly tuned NDR suppresses the vibrations on the primary structure to a sufficiently low level. Besides, the HSLDS characteristics extend the operable frequency band compared with the LDR, while strong nonlinearity limits such extension. The proposed analysis procedures for delay-coupled nonlinear dynamics, alongside the control parameter tuning, determination of operable frequency bands, and structural design rules, establish a basic theoretical framework for the NDR design.