Vibration Research Articles

Three-dimensional vibration suppression of flexible beams via flywheel assembly

For three-dimensional (3-D) vibration suppression of flexible beams, the most commonly used method is the boundary-controlled strategy, which is challenging to employ in general environments. In this study, a novel strategy by employing planned-motion flywheel assembly is designed to suppress 3-D vibration of flexible beams, which is easier to implement and more widely applicable than the boundary-controlled strategy. First, the dynamic equations of flexible beams with flywheel assembly are derived based on the Lagrange equation, where the Euler-Bernoulli beam theory and the geometric nonlinearity are employed. Subsequently, the phase delay method is employed to plan the motion of the flywheel assembly, while the optimal parameters in the expressions of flywheel assembly's motion are derived through the analysis of system energy. Theoretical results suggest that the flywheel assembly with planned motion enables the beam stable rapidly in free vibration and decreases displacement in forced vibration. Experimental results also demonstrate this strategy can enable the beam stable rapidly in free vibration under various initial conditions. The proposed control strategy can provide effective 3-D vibration suppression in flexible beams.

Hygrothermomechanical loading-induced vibration study of multilayer piezoelectric nanoplates with functionally graded porous cores resting on a variable viscoelastic substrate

Harnessing vibrations in multifunctional nanostructured plates is pivotal to next-gen microsystems but necessitates understanding scale effects under multifield loading. Investigated in this work are the forced and unforced vibrations of multilayered piezoelectric nanoplates supported on a variable viscoelastic medium and loaded hygrothermo-electromechanically with functionally graded porous (FGP) cores. The viscoelastic foundation is supposed to demonstrate non-linear changes in both stiffness and damping characteristics in the x-coordinate direction. The goal is to improve the accuracy of the results by using the nonlocal strain gradient theory (NSGT) and the third-order shear deformation assumption (TSDA), which include the effects of hardening and softening materials. The FGP core layer considers four states of porosity distribution patterns. These porosity distributions are expected to change in both the in-plane and thickness directions. The governing partial differential equations resulting from Hamilton's principle can be reduced to a system of algebraic equations by applying the Galerkin method. The parametric studies evaluate the effects of several factors, such as the initial electric voltage, viscoelastic medium parameters, moisture rise, temperature changes, porosity distributions, FG index, nonlocal and strain gradient features, and boundary conditions, on the vibration response. The novelty lies in the incorporation of advanced theories, such as the NSGT and TSDT, which capture size-dependent effects and material hardening/softening phenomena. Additionally, the consideration of four distinct porosity distribution patterns in the FGP core layer provides insights into the influence of porosity gradients on the dynamic response. The proposed model can guide the design and optimization of multifunctional nanostructured plates for applications in next-generation microsystems, energy harvesting devices, and smart structures.

Nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells: Theoretical and experimental investigations

In this study, the nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells (FHSCSs) are investigated theoretically and experimentally. Initially, a time-domain minimum residual (TDMR) method is first adopted for the analysis of nonlinear free and forced vibrations of the FHSCSs, which is based on a dynamical model developed, with the effective material parameters of the foam-filled honeycomb core being obtained by employing the Gibson method and the Hamilton equivalence technique. Based on the high-order shear deformation shell principle and von Karman's theory, the nonlinear natural frequencies and resonant responses are solved using the Broyden iterative approach and TDMR method. Furthermore, several literature results are utilized for the rough verification of such a method. Meanwhile, the FHSCS specimens are made manually and comprehensive tests with various base excitation energies are undertaken to provide a thorough validation of the current method. It can be found that the largest calculation errors of natural frequencies and resonant responses are 4.9 and 12.3%, respectively. Finally, the influences of the core form and base excitation amplitudes on the nonlinear vibration behaviours of the FHSCSs are examined. It can be noticed that the foam-filled FHSCS structure exhibits a more excellent anti-vibration capability compared to the non-foam-filled structure. The solving method, fabrication technique, and valuable findings in the current study highlight the path for the design and implementation of such advanced shells.

Nonlinear forced vibration and detached resonance curves of axially moving functionally graded carbon nanotube reinforced composite plates

Nonlinear forced vibration and detached resonance curves of axially moving functionally graded carbon nanotube reinforced composite plates

Early condition monitoring of circular saw blades with large diameter-to-thickness ratios under high-speed sawing of hard metals

Circular sawblades with large diameter-thickness ratios feature weak stiffness which results in self-excited and forced vibrations in high-speed sawing. The scenario brings uncertainty to the evolution of the multichannel signal features, which sometimes even exhibit contradictions, making it extremely challenging to predict the sawblade lifespan. To fill the gaps, a transverse vibration differential equation was firstly established to elucidate its complex behavior. Then, this study used an artificial intelligence algorithm based on multidomain features to predict the condition of the sawblade. Therefore, a hybrid prediction model was constructed using a BP neural network (BPNN) optimized by a genetic algorithm (GA). Cutting experiments were carried out to prove that the proposed model can effectively predict the sawblade condition. This study not only provides useful insights for the condition monitoring of sawblades, but also offers a solid foundation for monitoring wood, stone, and composite processing.

Down-film as a new non-frame porous material for sound absorption

Down-polyethylene film material has been introduced for the first time as an excellent non-frame sound absorber, showing a distinctively outstanding performance. It contains down fiber adjacent to each other without firm connection in between, forming a structure of elastic fiber network. The unique structure has broadband response to sound wave, showing non-synchronous vibration in low and middle frequency and synchronous vibration in middle and high frequency. The broadband resonance in middle and high frequency allows the structure to achieve complete sound absorption in resonance frequency band. Moreover, down-polyethylene film material possesses forced vibration, corresponding sound absorption coefficient has been obtained based on vibration theory. The down-film sound absorption material has the characteristics of light weight, soft, environment-friendly, and has excellent broadband sound absorption performance.

Analytical solution for forced vibration response of rectangular thin plates attached by straight and curved acoustic black hole beams based on symplectic and impedance method

In recent years, due to the excellent vibration reduction performance of the acoustic black hole (ABH), its application in engineering has become increasingly widespread. This paper proposes an analytical method which combines the symplectic method with the impedance method, for solving the forced response of the rectangular thin plates attached by the straight and curved ABH beams. The ABH beams and plate are connected by a short bar. Firstly, the impedance method is used to obtain the dynamic stiffness of the coupling end of the ABH beam. Secondly, the symplectic method is used to obtain analytical waves of the plates. By utilizing the relationship between force and displacement at plate-beam junction, the dynamic stiffness of the plate at the coupling point can be obtained. Finally, based on wave propagation analysis, the forced vibration response of the hybrid system are obtained. The numerical examples compared the calculation results of this method with the finite element method. The results show that the proposed method can effectively predict the forced response of the hybrid system considered in this paper. Then, the influence of the relative position between the coupling point and the excitation point on the vibration reduction effect was analyzed. This method is analytical, with accurate results and high computational efficiency.

Key structure design and vibration reduction performance analysis of four-tooth unequal pitch end mill based on spectral characteristics

The unequal pitch end mill can effectively suppress the vibration in the cutting process, and it is widely used in the processing of key parts. In this article, the four-tooth unequal pitch end mill is taken as the research object. Combined with the actual working conditions, the key structural parameters and process parameters are optimized from the perspective of spectrum energy distribution and processing efficiency, and the vibration reduction performance of the tool is analyzed and verified. First, the influence of process parameters, inter-tooth angle and helix angle of unequal pitch milling cutter on spectrum amplitude is analyzed. Second, for the milling aluminum alloy AL7075-T6, the most significant parameters affecting the vibration reduction performance of the milling cutter-tooth angle and helix angle and the matching process parameters were optimized. Finally, in order to explore the milling performance of unequal pitch end mills, experiments were carried out on equal pitch and unequal pitch end mills under the same process parameters. The gap between the two tools in milling force and milling vibration was analyzed, and the superiority of unequal pitch end mills in improving milling stability was verified.

Non-linear primary resonance analysis of stiffened FGM conical panels resting on viscoelastic foundation

This article investigates the non-linear forced vibrations and primary resonance analysis of stiffened FGM conical panels (OCPs) resting on a viscoelastic foundation utilizing a semi-analytical method. The classical shells theory and von Kármán nonlinear strain–displacement relations are used to model of OCPs. The equations of motion are derived by applying Hamilton’s principle. Then, the dimensionless equations of motion are established and converted into dimensionless nonlinear ordinary differential equations by applying Galerkin’s method. The solution of the ordinary differential equations is carried out based on the multiple-scale method for analyzing the vibration behavior. In this regard, the necessary relations for the nonlinear primary resonance and internal resonance of stiffened FGM-OCPs are obtained. To validate the suggested methodology, first, the results are verified with various previous research. Second, a numerical method based on the fourth-order Runge-Kutta’s approach is used for verifying the nonlinear vibration analysis. Finally, changes in various parameters such as viscoelastic foundation coefficients, stiffeners, temperature, semi-vertex angle and subtended angle are examined by helping the frequency response plots.

Vertical vibration model for the roll system of a six-high rolling mill based on the Timoshenko beam theory

During the production of cold-rolled strips, the high-speed operation of rolling mills generates vibrations that significantly impact the production efficiency, the strip quality, and the rolling mill service life. Therefore, investigating the vibration characteristics of rolling mills is of paramount importance. Previous studies predominantly treated the rolls as point masses, overlooking variations in the vibrations along the lengths of the rolls. In this study, the working, intermediate, and backup rolls were regarded as continuous elastic bodies, and they were simplified as Timoshenko beams. The modal superposition method was used to solve the vertical vibration equations for the rolls of a six-high rolling mill; thus, the natural frequencies and modal shapes for the rolls were obtained for both free and forced vibrations. A finite-element model validation confirmed that the accuracy of the novel Timoshenko beam six-high rolling mill vibration model introduced in this paper is significantly higher than that of the traditional Euler beam model when the roller length-to-diameter ratio is relatively small. Further analysis based on this model indicates that the forced vibration of the rolls is primarily influenced by fluctuations in rolling force. The amplitude of forced vibration is affected by factors such as the friction coefficient in the deformation zone, rolling speed, and cumulative rolling distance of the work rolls. These findings provide a precise representation of the characteristics of forced vibrations in rolling mills and offer valuable theoretical insight to ensure stable rolling mill operation.

Free and forced vibrations of elastically restrained cantilever with lumped oscillator

The efficiency assessment of cantilever-based energy harvesters relies on vibrational analysis, which necessitates modifications aimed at enhancing efficiency. These modifications involve manipulating the fundamental frequency to lower values and encompassing a wider range of resonances within a specified bandwidth. Consequently, this paper introduces an original analytical-numerical exploration into the vibratory response of a cantilever with a novel boundary condition involving an elastically restrained oscillator-spring arrangement. At the microbeam's tip, an oscillator is elastically confined by a linear spring, resulting in a novel set of coupled governing equations and a distinct shearing boundary condition. Microbeam equations is derived from the modified couple stress theory to capture size dependency. During free vibration analysis, a previously unreported characteristic equation is derived. This nonlinear transcendental equation is numerically solved utilizing root-solver algorithms, such as those available in MATLAB. Significantly, it is discovered that the inclusion of a lumped oscillator with an elastic support induces a minimal (new) natural frequency. Applying the extended Hamilton's principle, the effect of the lumped oscillator emerges both on the governing equations of motion and boundary conditions of the microbeam. Novelty of the paper focuses on the both characteristic equation and transmissibility by adopting the Galerkin’s modal decomposition technique. This finding carries vital implications as the efficiency of cantilever-based energy harvesters is directly contingent upon the resonance frequency. Notably, the oscillator mass and spring constant are two parameters that directly influence the vibratory response of the microbeam. In the context of forced vibrations, harmonic base excitation is considered as the input excitation, and the mechanical frequency response function is provided. The proposed system offers two distinct advantages for energy harvester systems: the creation of minimal resonance at lower values and the potential to manipulate the system's resonance toward a desired frequency spectrum.Article HighlightsModifying the boundary conditions of a cantilever beam with lumped-parameter system, can significantly change the behavior of the vibratory response.The boundary condition directly impact the resonance frequencies; which influences the maximum amount of harvestable voltage in vibration-based energy harvesters.Spring constant and mass of the lumped oscillator, are the key factors to alter the vibratory behavior and bandwidth of frequencies. Optimizing such mentioned parameters can help reaching to the maximum harvesting of energy.

Bernstein polynomials in analyzing nonlinear forced vibration of curved fractional viscoelastic beam with viscoelastic boundaries

Bernstein polynomials in analyzing nonlinear forced vibration of curved fractional viscoelastic beam with viscoelastic boundaries

The masking technique for forced nonlinear oscillator stability behavior analysis using the non-perturbative approach

The study utilized the masking technique to explore the stability behavior of a forced nonlinear oscillator through the non-perturbative approach, with a particular focus on a Van der Pol oscillator subjected to external force, characterized by both cubic and quadratic nonlinearities. The application of the non-perturbative method (NPM) in conjunction with the masking technique was a pivotal aspect of this research, transforming the inherently non-homogeneous, nonlinear system into a homogeneous linear system. This transformation was crucial as it simplified the complex dynamics of the system, rendering it more amenable to analysis. Through this method, the research successfully established the system’s overall frequency, meticulously accounting for the impact of the periodic external force. The study also identified a distinct type of resonance response, where the system’s frequency incorporates the excited frequency in a nonlinear relationship. The masking technique proved to be an invaluable tool for examining the stability behavior of forced vibrations in oscillators via the NPM, providing profound insights into stability under external forces and enhancing the understanding and control of oscillatory behaviors in nonlinear dynamical systems. A critical confirmation of the current methodology is provided by the remarkable agreement found between the numerical solution and the provided analytical solution. This agreement shows that the analytical method produces trustworthy predictions and appropriately describes the system’s behavior. The plotted stability diagrams, which demonstrate that the model’s simulation of stability behavior is consistent with observed events, particularly resonance phenomena, offer further validity for the findings. In the resonance case, the effects of the damping coefficient and the external force’s magnitude are significant. The results of the analysis show that an increase in the damping coefficient has a destabilizing effect that causes unstable zones to expand. In contrast, in the resonance state, the quadratic and cubic nonlinearity factors both contribute to stabilization. Understanding how various system factors impact stability dynamics particularly in relation to resonance phenomena is made easier with the help of this insight.

Minimal Conditioned Stiffness Matrices with Frequency-Dependent Path Following for Arbitrary Elastic Layers over Half-Spaces

This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow dispersion curves and flag up possible singularities are investigated. While there are inherent limitations in terms of computational accuracy and capacity, this methodology is straightforward to implement for studying free or forced vibrations and obtaining relevant response data. We present computations of wavenumber dispersion diagrams, phase velocity plots, and response data in both the frequency and time domains. These computational results are provided for two example cases: plane strain and axisymmetry. Our methodology is grounded in a well-conditioned dynamic stiffness approach specifically tailored for deep-layered strata analysis. We introduce an innovative method for efficiently computing wavenumber dispersion curves. By tracking the slope of these curves, users can effectively manage continuation parameters. We illustrate this technique through numerical evidence of a layer resonance in a real-life case study characterized by a fold in the dispersion curves. Furthermore, this framework is particularly advantageous for engineers addressing problems related to ground-borne vibrations. It enables the analysis of phenomena such as zero group velocity (ZGV), where a singularity occurs, both in the frequency and time domains, shedding light on the unique characteristics of such cases. Given the reduced dimension of the problem, this formulation can considerably aid geophysicists and engineers in areas such as MASW or SASW techniques.

Electroacoustic evaluation of the bone conduction transducer B250 for vestibular and hearing diagnostics in comparison with Radioear B71 and B81

Objective The objective is to evaluate the electroacoustic performance of the B250 transducer and to compare it with the two most widely used audiometric transducers B71 and B81. Design The electroacoustic performance was evaluated in terms of sensitivity level, distortion, maximum hearing level and electrical impedance. Study sample Six B250 prototype transducers were evaluated and compared with published data of B71 and B81 together with complementary measurements of maximum hearing level at 125 Hz and phase of electrical impedance. Differences in reference equivalent threshold vibratory force levels were estimated by comparing hearing threshold measurements of 60 healthy ears using B81 and B250. Results B250 has approximately 27 dB higher sensitivity levels than both B71 and B81 at 250 Hz and can generate higher maximum hearing level at low frequencies: 11.8 to 35.8 dB (125–1000 Hz) higher than B71, and 1.4 to 18.6 dB (125–750 Hz) higher than B81. The maximum average difference in reference threshold force levels was 13.5 ± 8.7 dB higher for B250 at 250 Hz compared to B81. Conclusions B250 can produce higher output force with less distortion than B71 and B81, especially at 125 and 250 Hz, which could possibly improve low frequency investigations of the audio-vestibular system.

A Disturbance Compensation Control Strategy for Rotational Speed Standard Device Based on AMB System.

The rotational speed standard device that can carry loads is the key device for calibrating passive rotational speed sensors. The rotor of the passive rotational speed sensor is connected to the rotor of the standard speed device through a coupling, and the standard reference speed is provided by the standard device. Due to the rotor eccentricity, the unbalanced force of the rotor occurs, and it can not only affect the rotational speed accuracy but can also damage the mechanical bearings of the standard speed device. To solve this issue, a method for suppressing the unbalanced force of the speed standard device based on an active magnetic bearing (AMB) force compensation system is proposed. First, the overall structure of the system is briefly introduced. Then, the force feedback control system model with the AMB as the force actuator is established, and a PI controller is designed to achieve the disturbed force control. Finally, a semi-physical simulation experimental platform is built to verify the effectiveness of the proposed method. The experimental results show that the AMB force compensation system can reduce 84.4%, 81.6%, and 79.8% of the unbalanced vibration force at the frequency of 30 Hz, 90 Hz, and 150 Hz, respectively.

A node-based smoothed finite element method (NS-FEM) for free and forced vibration analysis of three-dimensional (3D) structures

A node-based smoothed finite element method (NS-FEM) for free and forced vibration analysis of three-dimensional (3D) structures

Near-Field Radiative Heat Transfer between Layered β-GeSe Slabs: First-Principles Approach.

The group-IV monochalcogenide monolayers, GeSe, are interesting and novel two-dimensional (2D) semiconductor materials due to their highly anisotropic physical properties. Monolayers of the different GeSe polymorphs have already had their physical properties and potential applications extensively investigated. However, few-layer homostructures, which can also be approximated as 2D systems in many cases, have not received the same attention. For this reason, in this work, we investigate the optical properties of a free-standing few-layer β-GeSe system and use this information to investigate their performance in the near-field radiative heat transfer (NFRHT). The required optical conductivity of the few-layer 2D material is calculated by using density functional theory (DFT), including spin-orbit coupling. The band structure is investigated for up to five layers, and the effective electron masses are calculated correspondingly. Using this information, both the intraband transitions due to the presence of free electrons introduced by doping and the interband transitions are considered. The contribution of the ionic vibrations is also included in calculating the optical properties because of its relevance to NFRHT through the resulting active optical phonons. With all these contributions included, more realistic predictions of the NFRHT between the layered 2D β-GeSe materials can be obtained. It is found that the heat transfer attainable with the layered system is similar to that of a single layer of β-GeSe we have obtained previously.

Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures

This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

Nonlinear dynamics and forced vibrations of simply-supported fractional viscoelastic microbeams using a fractional differential quadrature method

In this paper, free and forced nonlinear vibrations of fractional viscoelastic microbeams are modeled based on Euler-Bernoulli theory, the Von Karman’s nonlinear strain relations, the modified couple stress theory (MCST), and the fractional Kelvin-Voigt viscoelastic model. In the present work, the nonlinear-fractional order governing equations are discretized in the space domain by Galerkin’s method. Two different approaches are introduced to solve the resulting nonlinear fractional-order Duffing equation in the time domain. In the first approach, a time marching fractional finite difference method is presented to compute the transient time response starting from the initial conditions. This approach is time consuming if the frequency-amplitude curves of steady state response are required since it provides just one point on the frequency-amplitude curve. More importantly, this approach usually converges only for the stable branch with smallest amplitude of frequency-amplitude curve. In the second approach, we introduce a novel fractional differential quadrature method (FDQM) to discretize the fractional Duffing equation and apply a pseudo-arc length algorithm to directly construct the frequency-amplitude curves. Effects of the fractional-order, linear and nonlinear viscoelasticity coefficients, viscous damping parameter, microstructure parameters, and the micro-beam thickness on the nonlinear dynamics of the viscoelastic micro-beam are analyzed numerically. Numerical results show that each of these parameters can change natural frequency and/or the damping behavior of the structure. The present model can be used for designing and analyzing the nonlinear microstructure viscoelastic beam under dynamic loads.