Resonant Vibration Research Articles

Logical vibrational resonance in a symmetric bistable system: Numerical and experimental studies

In previous studies, double harmonic signals as external driving forces have been used for inducing logical vibrational resonance to facilitate the control of logic operations. It requires the bias parameter to break the symmetry of the bistable system. In hardware circuits, symmetric bistable system circuits are easy to build and even using few components. To address the problem of maintaining the symmetry of the system while inducing the logical vibrational resonance, we take advantage of the property that an anharmonic signal with a constant component in the Fourier series can replace the bias parameter to induce logical vibrational resonance. We add an anharmonic low-frequency signal to the symmetric bistable system as a slowly-varying signal. In addition, we add another high-frequency signal as a fast-varying signal. Through numerical simulation, we find the optimal logic output region of the system and the logic output region is explained by using bifurcation theory. Then, noise is added to the system to demonstrate its effect on the optimal logic output region. Finally, the simulation results are further verified by a hardware circuit. Both simulation and experimental results prove the occurrence of logical vibrational resonance and its necessary condition in the symmetric bistable system.

A novel approach to reduce fan rotor blades stress in case of resonance due to inlet flow distortion by means of piezoelectric actuators

Resonant vibration condition involves a drop in the life-cycle of the components and is one of the main causes of high cycle fatigue failure (HCF) in turbomachinery blades. As a consequence vibration damping techniques play a key role for turbomachinery designers. Even though resonant vibration conditions can be identified by means of the Singh’s Advanced Frequency Evaluation (SAFE) diagram at the design level, not all resonant conditions can be avoided. Among these methods, systems of piezoelectric (PZT) actuators can be tuned to actively damp the vibrations caused by resonant excitations. In this work, an analytical model was developed to identify the optimal voltage distribution that maximises the reduction in blade stress. The model considers the flexural–torsional–extensional deformations coupling due to the pre-twisting, non-constant cross-section and inertial loads of the rotating blades. A typical case was examined to demonstrate the effectiveness of the proposed method, which involved vibration induced by inlet flow distortion in an axial fan stage coupled with a three-strut front frame. A decoupled approach based on Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) simulations was used to evaluate the aerodynamic loads and to numerically validate the optimal voltage distribution on the PZT actuator pairs. The results show that the proposed method alleviates the effects of the resonant response to an inlet flow distortion on a fan integrally bladed disc (blisk) and the optimal voltage distribution predicted by the model is the one that achieves the highest blade stress mitigation.

Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators.

Although the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonlinear damping to investigate the nonlinear vibrations of the electrostatic resonators in the present paper. We apply the Galerkin method on a nonlinear partial differential equation to obtain the nonlinear ordinary differential equations for the first and third modes. The two equations include constant terms. The multiple-scale method is used to obtain the approximate analytical solutions of the two equations. The approximate analytical solutions discover the effects of driving electric field, small-scale effect, and nonlinear damping on structural vibrations. The results suggest that the small-scale effect, the direct current (DC) voltage, and the alternating current (AC) voltage have some critical effects on the vibrations of microresonators.

Nonlinear Resonance in a Position-Dependent Mass-Duffing Oscillator System with Monostable Potentials Driven by an Amplitude-Modulated Signal

This study examines the phenomenon of vibrational resonance (VR) in a classical positiondependent mass (PDM) system characterized by three types of single-well potentials. These potentials are influenced by an amplitude-modulated (AM) signal with $\Omega\gg\omega$. Our analysis is limited to the following parametric choices: <br> (i) $\omega_0^2$, $\beta$, $m_0$, $\lambda>0$ (type-1 single-well), <br> (ii) $\omega_0^2>0$, $\beta <0$, $2< m_0 <3$, $1< \lambda <2$ (type-2 single-well), <br> (iii) $\omega_0^2>0$, $\beta <0$, $0< m_0 <2$, $0<\lambda<1$ (type-3 single-well). <br> The system presents an intriguing scenario in which the PDM function significantly contributes to the occurrence of VR. In addition to the analytical derivation of the equation for slow motions of the system based on the high-frequency signal’s parameters using the method of direct separation of motion, numerical evidence is presented for VR and its basic dynamical behaviors are investigated. Based on the findings presented in this paper, the weak low-frequency signal within the single-well PDM system can be either attenuated or amplified by manipulating PDM parameters, such as mass amplitude ($m_0$) and mass spatial nonlinearity $\lambda$. The outcomes of the analytical investigations are validated and further supported through numerical simulations.

Arbitrary variable thickness annular piezoelectric ultrasonic transducer based on transfer matrix method

The variable thickness annular radial piezoelectric ultrasonic transducer can realize impedance transformation and energy concentration, has the advantages of large radiation area and full directivity, and is widely used in power ultrasound, underwater acoustic and other fields. Because solving complex variable thickness metal ring radial vibration wave equation is more difficult, in this paper, the radial vibration of metal rings with variable thickness is transformed into the superposition of the radial vibrations of N metal rings with equal thickness by using the transfer matrix method. The equivalent circuit diagram, the resonance frequency equation and the expression of the displacement amplification coefficient of the radial vibration of the metal thin ring with arbitrary thickness are obtained. The relationship between the displacement amplification coefficient and the geometric size of the cone, power function, exponential and catenary metal rings is analyzed. On this basis, the equivalent circuit and resonance frequency equation of radial vibration of piezoelectric ultrasonic transducer which is composed of a metal ring with variable thickness and a piezoelectric ring with equal thickness are derived. In order to verify the correctness of the theoretical results, the finite element software is used in simulation, and the numerical solutions of the first and second order resonance frequency and displacement amplification coefficients are in good agreement with the theoretical solutions. In this paper, the universal solution of radial vibration of metal ring with arbitrary variable thickness is given, which provides theoretical guidance for designing and optimizing the radial piezoelectric ultrasonic transducers.

Experimental validation of impact energy scattering as concept for mitigating resonant vibrations.

The Vibro-Impact Nonlinear Energy Sink (or impact damper) is well-known for its ability to engage into transient resonance captures with arbitrary frequencies and thus has inherent broad-band effectiveness. Its working principle relies on (recurrent) energy localization and local dissipation within the contact region. Dissipative (inelastic) collisions are inevitably associated with damage and challenging to predict. Recently, it has been shown theoretically that the device is effective even for purely elastic collisions when the energy is (almost) irreversibly transferred from the critical low-frequency modes to high frequencies.In that case, the device is more properly termed Impact Energy Scatterer (IES). In the present work, we experimentally validate, for the first time, the working principle of the IES. To this end, we design a test rig consisting of a cantilevered beam, hosting a spherical impactor inside a cavity at its tip. The resonant vibrations of the lowest-frequency bending mode are reduced by a factor of 10-20. Given that the IES weighs less than 1% of the host structure, this corresponds to a paramount vibration mitigation capability. We achieve excellent agreement between the measurements and the numerical predictions obtained by modeling the impacts as perfectly elastic. We also demonstrate that the dissipation in the contact region is negligible, while a substantial amount of energy is scattered to higher frequencies, validating the theoretically proposed working principle.

Two-Dimensional Equivalent Circuit Model of Ultrasonic Wireless Power Transmission

In this article, piezoelectric ceramic is a core device of an ultrasonic wireless power transmission (UWPT) system. The most commonly used piezoelectric ceramic in research and applications of UWPT has a ring-like shape. The piezoelectric ceramic rings usually work in the presence of significant radial and axial vibrations as long as they are not extremely thin. However, in most studies related to the UWPT, only the axial vibration mode is considered. The Mason equivalent circuit model of axial vibration is widely used and the effect of radial vibration on the whole system is ignored. In this article, first, a method to analyze the piezoelectric ceramic ring considering the radial-axial coupled vibration is proposed. Second, the analytical expressions of the constitutive equations of the piezoelectric ceramic ring are derived. Third, a new form of analytical equations is constructed, and a novel two-dimensional equivalent circuit of the UWPT system considering the radial-axial coupled vibration of the piezoelectric ceramic ring is proposed. Fourth, the input and output characteristics of the proposed model and the conventional Mason equivalent circuit model are simulated using MATLAB. Last, the simulation results are compared and verified by experiments. The results demonstrate that the proposed model can describe the system resonance more accurately and comprehensively than the conventional Mason model. As a whole, this study increases the accuracy of the equivalent circuit model of the UWPT system and has important theoretical significance for UWPT research.

Resonant vibrations of a non-ideal gyroscopic rotary system with nonlinear damping and nonlinear stiffness of the elastic support

When motor performance characteristic is unknown, non-linear differential equations of motion of nonideal gyroscopic rigid rotary system with nonlinear cubic damping and nonlinear stiffness of the elastic support turn out to be numerically unsolvable.•In this case, the method uses the motor performance characteristic expression found from the frequency equation of forced stationary oscillations based on assumption that the angular acceleration is many times less than the square of the angular speed of rotation, replacing the stationary rotation angular speed with the shaft rotation angle derivative.•The method correctness is evidenced by a good consistency between the rotor motion equation numerical solution results and the analytical solution results, and by the nonlinear cubic damping of the shaft angular coordinate oscillograms obtained by direct simulation, as well as by comparison with the results of numerical simulation for a straight-line DC motor performance characteristic.•The method limitations are that it is used for the first approximation and weak nonlinear oscillations in the resonance region, where the shaft rotation speed is of the order of the oscillating system natural frequency.

Влияние эффекта медленной динамики на упругие релаксационные свойства поликристаллических металлических стержней

A theoretical model for the formation of ultrasonic signals in metallic microcrystalline rods taking into account the metastable behavior of their defective states is proposed. The influence of metastable states of the defective structure of samples on the features of changes in their resonant frequencies in ultrasonic experiments of fast dynamics is analyzed. The increase in the Young's modulus and the dynamics of changes in resonant vibrations of rods made of aluminum alloy D16T under conditions of free relaxation are explained. Based on the results obtained, the concentration of metastable defects was estimated.

Numerical simulation of deformations of a specimen of a composite helicopter blade as part of a resonant vibration set-up

To determine the fatigue life of the tail rotor blade of a helicopter made of polymer composite materials (CM), a method of fatigue testing of the specimens of the blade with accompanied numerical modeling of the deformed state has been developed. The tests are carried out on a resonant vibration set-up, with simultaneous reproduction of a forcing harmonic transverse force and a constant longitudinal tensile force. The tests are carried out by a vibration loading mode equivalent in fatigue damage, which includes one level of variable load in the thrust plane and in the plane of rotation. The equivalent mode is formed based on the variable loading spectrum of the blade, which is obtained from the results of flight measurements of the loads on the tail rotor, as well as the repeatability of the expected operating conditions of the helicopter. The tests are accompanied by computational and experimental studies, which include finite element calculation of the stress state and modal analysis of the standard blade and the test specimen, as well as the strain measuring of the structure. According to the results of the research, the vibration loading modes are corrected.

Nonlinear vibrations of earth structures

This article offers a detailed analysis of the current state of plane structure dynamics, addressing the complexities posed by non-homogeneous materials exhibiting nonlinear elastic and viscoelastic properties during real-life operations. The study proposes a comprehensive mathematical model and algorithm to investigate the dynamic behavior of such structures, employing the non-linear hereditary Boltzmann-Volterra theory to describe viscoelastic material properties accurately. Nonlinear oscillatory systems are analyzed using Lagrange equations based on the d’Alembert principle. The problem is approached through a multi-step process. Initially, the linear elastic problem of the structure’s natural oscillations is solved to determine its natural frequencies and modes of oscillations. Subsequently, these eigenmodes are employed as coordinate functions to address forced nonlinear oscillations in viscoelastic non-homogeneous systems. The complexity of the problem necessitates solving a Cauchy problem comprising a system of nonlinear integrodifferential equations. To illustrate the methodology, the study examines the Gissarak earth dam, considering real operational conditions and nonlinear, viscoelastic material properties near resonant modes of vibrations. Utilizing numerical methods, the dynamic behavior of the structure is analyzed, assessing displacements and stress components at different time points under non-stationary kinematic action. Stress concentration regions within the structure are identified for resonant vibrations, allowing the evaluation of its strength. Furthermore, the impact of nonlinear elasticity and viscoelasticity on the structural dynamics is quantified. This research provides valuable insights into the behavior of plane non-homogeneous structures, considering real-world scenarios and material complexities, ultimately contributing to an improved understanding of structural dynamics and facilitating the identification and mitigation of potential structural challenges.

Modelling and simulation of the energy regenerative system for active horizontal seat suspension driven by an induction motor

The paper investigates the design and performance of an active horizontal seat suspension driven by an induction motor, with the aim of reducing harmful vibrations and enhancing energy efficiency. The physical model employs a permanent magnet synchronous motor (PMSM) as a modern actuator to generate the active force. Both passive and active seat suspensions are examined, revealing that the active system significantly reduces resonant vibration by applying electromagnetic torque from an induction motor. The motoring/braking principle is explored, where braking an induction motor returns electric energy to the servo drive system, and regenerative braking is utilized to charge batteries. However, the current regenerative braking system recovers only 3% of power. A novel control design methodology is proposed for the subsequent project to enhance suspension dynamics, attenuate vibrations transmitted to the human body, and minimize energy consumption during operation. The proposed energy-regenerative electromagnetic actuator model, in conjunction with advanced programmable micro-controller algorithms and inverter switching schemes, aims to optimize energy recuperation and vibration energy harvesting in the vibration reduction system.

Peculiarities of the Influence of hydraulic vibration damper failures upon the dynamics of a passenger car

When the car is moving along periodic irregularities of the track at a speed when the frequencies of forced and natural oscillations are close in magnitude, large amplitudes of vibrations of the body on the springs may occur, if there are no or small resistance forces in the spring suspension system. To dampen resonant vibrations, special dampers are introduced into the spring suspension system, which make it possible to reduce the amplitudes and accelerations of the driving motion, and, consequently, to reduce the impact of dynamic forces on the elements of the bogie car with different load capacity (passenger, mail and baggage cars and restaurant cars). Hydraulic vibration dampers of viscous resistance, which, despite the complication of manufacturing, repair and maintenance, are used in the bogies of passenger cars, elastic elements that do not have internal friction are used. Vertical and inclined hydraulic vibration dampers used in wagon bogies have a telescopic piston design. They are easy to operate and have a low weight.

Dynamic behavior of earth dams under different kinematic impacts

The paper provides a detailed analysis of the current state of the problem. A mathematical model is presented to determine the dynamic behavior of earth dams, considering the viscoelastic properties of soil, using the hereditary Boltzmann-Volterra theory with the A.R. Rzhanitsyn kernel under periodic kinematic impacts. To solve the problems considered, the finite element method and complex arithmetics were used to reduce integrodifferential equations to a high-order complex algebraic equation. The accuracy of the methods was verified by solving test problems. Steadystate forced vibrations of the Pskem earth dam 195 m high are studied considering the real geometry and soil properties under resonant vibration modes. It was stated that the largest stress amplitudes in the body of the dam occur not only under the first resonance, but they can occur under other dense spectra of the eigenfrequencies of the dam, due to the interaction between close natural modes of vibration. The strength of various sections of the dam body was tested under kinematic impact using the Coulomb- Mohr theory of strength; the most dangerous sections of the dam were identified in terms of the highest stress.

Free in-plane vibration of thin-walled rings with elastic supports

Free in-plane vibration of thin-walled rings with elastic supports

Opportunities for Ivory Nut Residue Valorization as a Source of Nanocellulose Colloidal Suspensions.

Ivory nut seeds have been traditionally exploited in Central and South America for obtaining vegetable ivory. The residues from this industry are susceptible to valorization as a source of fatty acids (by organic extraction) and mannans (by alkaline dissolution and regeneration). Nonetheless, cellulose may also be recovered at the end of this fractionation process by acid hydrolysis and functionalization, with associated advantages over other lignocellulosic sources due to the absence of lignin in the endospermic tissue. In this work, various experimental parameters (sulfuric acid concentration, temperature, and hydrolysis time) were investigated to optimize the processing conditions for preparing stable nanocellulose suspensions after ultrasonication. The most stable nanocellulose gel (1 wt% solid content) was obtained after 4-h hydrolysis at 60 °C with 8 M H2SO4 and was characterized by using complementary tech-niques, including dynamic light scattering (DLS), transmission electron microscopy (TEM), X-ray powder diffraction (XRD), nano-fibril sulfation measurements, vibrational and solid-state nuclear magnetic resonance (CP/MAS 13C-NMR) spectroscopies, and thermal analysis. This nanocellulose hydrogel is susceptible to further utilization in various applications and fields, e.g., in agricul-ture for controlling the release of agrochemicals, in pharmaceutics for developing new dosage forms, and in the treatment of wastewater from the textile and paper industries.

Investigating the alkaline treatment of fiber coconut (Cocos nucifera L) for cellulosic ethanol generation

The coconut husk of Cocos nucifera L. species has a high potential for use in industry and agriculture, and many studies on the use of this biomass are being developed for the production of biofuels. Sodium hydroxide solution (NaOH) is one of the oldest and economically viable treatments for reducing the lignin content and improving energy efficiency in biomass. Thus, the objective of this research was to analyze the solubility of the fibers biomass in the mesocarp of Cocos nucifera with different concentrations of sodium hydroxide (NaOH). The fibers were separated from the bark, which had their extractives removed, and were subjected to the solubility procedure in 1, 2, 3, and 4% NaOH. The Klason lignin and holocellulose were determined. Changes in functional groups of Klason lignin were observed by infrared spectroscopy (FTIR). There was a decrease in Klason lignin content due to alkaline treatment. Infrared spectra indicated structural changes between the treatments analyzed, especially when the following bands: 3 433 cm-1 (stretching of OH), 1 271-1 220 cm-1 (vibration of the guaiacyl ring with the contribution of the C=O stretch), and 1 116-1 165 cm-1 (stretching of CO of acid and/or ester). Coconut fibers treated with 4% NaOH maintained the integrity of holocellulose and presented high lignin degradation.

Sugar moiety driven adsorption of nucleic acid on graphene quantum dots: Photophysical, thermodynamic and theoretical evidence

Integration of biologically important molecules with graphene quantum dots (GQDs) as a new class of luminescent water-soluble carbon materials, has drawn considerable attention for recent exciting progress on its biomedical applications. In order to avoid toxic semiconductor QDs, GQDs have shown great promise in detection of DNA and other biological applications and hence, fundamental understanding of processes of interactions is important and necessary. The present work establishes the significant role of sugar residue of nucleic acids in adsorption of graphene materials through experimental estimation of binding thermodynamics concomitant with density functional theoretical (DFT) simulation and a detailed evaluation of photophysical parameters. Maximum quenching efficiency of adenosine moiety coupled with the shift in the vibrations of the five-member ring of D-ribose demonstrates the adsorption of DNA on GQDs framework through sugar moieties. The observed experimental results are consistent with the favorable Gibb’s free energy calculated through theoretical simulation. DFT presenting orbital interactions and bonding mechanism of DNAs on GQDs confirms that adsorption on GQDs surface involves charge transfer from nucleobases to GQDs and adenosine, in particular, binds strongly through charge transfer of 0.032e from nitrogen atom to carbon of GQDs. The present investigation will provide insights in understanding the possible role of GQDs in cellular imaging, biosensing and as carriers in targeted drug delivery.

Study on the spatio-temporal variation of arabinoxylan and alkylresorcinol in wheat grains

The purpose of this study was to clarify the spatio-temporal variation of arabinoxylan (AX) and alkylresorcinol (AR) in wheat. The total arabinoxylan (TOT-AX), water-extractable arabinoxylan (WE-AX), and AR contents of wheat from the main wheat producing areas of China were investigated. The effects of the geographical origin, variety, harvest year, their interactions, and irrigation frequency on the content and structure vibrations of AX and AR in wheat grains were studied based on the field experiment combined with one-way and multi-way analysis of variance. The results showed that the TOT-AX, WE-AX, and AR contents of wheat from the main wheat producing areas of China were 27.03–64.16 mg/g, 3.81–9.70 mg/g and 275.6–661.7 µg/g, respectively. Except for the irrigation, other factors had significant effects on the AX and AR contents of wheat, and the variety had the greatest effect. Xiaoyan 22, Xinmai 18, and Hengguan 35 had the highest TOT-AX, WE-AX and AR contents, respectively. The O-H stretching vibration of AX and AR and the skeleton vibrations of the aromatic ring of AR was mainly affected by the variety. This study indicated that Xiaoyan 22, Xinmai 18, and Hengguan 35 can be used for producing foods with high TOT-AX, WE-AX, and AR contents, respectively.

Improving the dimensional stability of round bamboo by environment-friendly modified rosin

Round bamboo is an environment-friendly and sustainable building, construction, and furniture material. It presents several advantages, such as high strength-to-weight ratio, pliability, and simple processing technology. However, natural round bamboo has inferior dimensional stability and is difficult to modify because of the hydrophobic substance on its outer layer. In this study, we designed a simple and efficient alkali pretreatment method (6 % NaOH treatment), which could effectively remove the hydrophobic layer from the bamboo surface, as well as significantly improve its permeability for the subsequent impregnation treatment. Round bamboo was impregnated with epoxy-modified rosin and natural rosin with different concentrations. Results showed that parts of the epoxy-modified rosin occupied the cell lumens of the bamboo, even filling the nanopores of cell walls and intercellular spaces (the pore volume of the round bamboo decreased by 84.76 % in 10–140 nm compared with the natural rosin) to exhibit improved dimensional stability (anti-swelling efficiency increased by 33.74 %) and hydrophobicity (contact angle increased, and water absorption decreased by 24.73 %). After impregnating the round bamboo, the modified rosin was physically filled into the vessels, parenchyma cells, and other structures. Meanwhile, the peak at 908 cm−1 indicates the disappearance of the the CO stretching vibration of the epoxy ring, confirming the occurrence of a reaction between the modified rosin and hydrophilic groups in the round bamboo. Therefore, impregnation with modified rosin can markedly improve the dimensional stability of round bamboo. The modified round bamboo exhibits considerable potential for application as a green structural material in an outdoor environment or a special environment with highly variable humidity.