Vibration Behavior Research Articles

3D coupled vibrations of asymmetric nano-particle mass sensors: Two-phase integral nonlocal strain gradient model and MD simulation

Since it is possible for the nano-particle to have any asymmetric shape and may attach to every position of the resonator-based mass sensors, any type of mass eccentricity and subsequently coupled vibrations are possible. So, in the present work, the 3D coupled axial-torsional-flexural vibrations of the mass nano-sensors are investigated considering both in-plane and out-of-plane bending as well as axial and torsional vibrations. In addition, the integral form of the two-phase local/nonlocal strain gradient (LNSG), as the consistent type of the common nonlocal strain gradient (NSG) elasticity theory, is employed for the first time to consider the size effects in the mass nano-sensors. A quasi-3D coupled FE model is constructed with no shear-locking within the complicated environment of the integral LNSG. The impacts of the LNSG elasticity and diverse types of possible coupling in changing the vibrational behavior of the mass nano-sensor are scrutinized and their crucial role in modeling of the nano-sensors is indicated. Furthermore, molecular dynamic (MD) simulations are implemented to identify and analyze the coupled vibrations of a mass nano-sensor consisting of a fixed-free carbon nanotube. Comparison between the MD results with those of the present coupled FE model reveals that considering the coupling effects reduces the modeling error, especially in the cases in which the coupling influences intensify. The present work can help to provide more accurate models of mechanical resonance-based nanosensors to detect nanoparticles with different shapes, larger sizes, and high mass ratios, which can lead to achieving sensors with higher sensitivity.

A unified nonlinear dynamic model for bolted flange joint disk-drum structures under different interface states: Theory and experiment

Bolted flange joint disk-drum structures (BFJDDSs) are key components in aero-engines, however, bolt looseness inevitably occurs due to extreme service conditions. This can cause the bolted joint interface to exhibit complex contact behaviors, which significantly complicate the vibration characteristics of BFJDDSs. Existing dynamic models for BFJDDSs have not considered the effect of bolt looseness (slip and separation), so their vibration behaviors are not well understood. In this study, a unified nonlinear dynamic model for BFJDDSs considering different interface states (stick, slip, and separation) is proposed, which is effective under both bolt looseness and non-looseness (stick) conditions. The bi-linear hysteretic model combined with the piecewise linear model is used to simultaneously consider different interface states. The Kirchhoff plate theory, the Sanders’ shell theory, and the Euler-Bernoulli beam theory are used to derive the energy functions of the disk, drum, and flange, respectively. Then, the Lagrange equations are employed to derive the governing equations of BFJDDSs. Modal and nonlinear forced vibration experiments are carried out on a BFJDDS to prove the correctness of the proposed mathematical model. Research results show that the proposed mathematical model is able to achieve good predictions of nonlinear dynamic properties of BFJDDSs under both bolt looseness and non-looseness conditions. This model is also able to well predict the jumping phenomenon observed in the experiment.

Investigating the effect of MXene reinforcement on the mechanical and vibrational behaviour of honeycomb core sandwich composite structures

Honeycomb core sandwich composite panels are now being employed in various industries and possess huge potential owing to the fact that they provide almost similar properties as that of traditional metallic materials with substantial reduction in weight and are extremely corrosion resistant. MXene nanosheets have caught attention of the scientific community owing their extraordinary physical, chemical and mechanical properties. In the present work, the effect MXene reinforcement on the bending and vibrational behaviour of honeycomb cored sandwich composite structures has been investigated using experimentation and finite element (FE) modeling. The honeycomb cored sandwich plates were fabricated and samples were tested via three-point bending and vibration test under various testing conditions. The SEM images revealed that the MXene nanosheets were well dispersed within the epoxy matrix when their mixture was prepared and the homogenous dispersion was also maintained in the fabricated honeycomb core. Also, the MXene and glass fibres were found to be well bonded with the matrix. As far as bending behaviour is concerned, the sandwich structure containing MXene reinforced honeycomb core displayed superior load bearing capacity and exhibited higher values of core shear strength and face sheet bending strength at all testing temperatures. Furthermore, the reinforcement of MXene resulted in an increase in the natural frequency for all the considered modes irrespective of the end conditions. For instance, the natural frequency of the honeycomb core sandwich composite plate at first mode increased by 5.5 % and 10.2 % under CFFF and CFCF boundary conditions, respectively, upon addition of MXene.

Design, fabrication and vibration characteristics of a novel composite auxetic structure embedded with resonators

With the rapid development of shipbuilding and aerospace industries, the mechanical performance requirements for structures are becoming increasingly demanding. Conventional vibration reduction structures cannot meet the requirements for lightweight, high load capacity, low frequency and broadband vibration reduction. Therefore, it is necessary to consider new structural topologies and material systems. Inspired by the lightweight and high strength characteristics of composite materials, the negative Poisson's ratio characteristics and the locally resonating phononic crystal, the carbon fiber composite auxetic structure embedded with resonators is proposed. Embedded resonators within composite auxetic structures can be strategically positioned to introduce gaps, thereby enhancing the vibration damping performance. The basic auxetic structure is prepared by simpler methods including molding and bonding, and the outer shell of resonator is made by 3D printing technology. The method enables the design of appropriate outer shell based on various cavity types within the structure, ensuring a stable connection between resonators and the structure itself. The range of the band gap can be predicted based on the negative effective mass. Vibration behavior and band gap characteristics of the structure are proved through vibration experiments and numerical simulations. It is revealed that the structure can generate local resonant band gaps at lower frequencies. Meanwhile, the coupling relationship between the auxetic structure and the resonator makes an impact to the band gap range. Therefore, the proposed structure can meet the required multi-functional integrated performance requirements. Furthermore, the parametric analysis is carried out, and the relevant conclusions can provide theoretical guidance for designing porous composite structures with effective low-broadband vibration reduction capabilities.

Free vibration of doubly-curved panels reinforced by carbon nanotubes: New analytic solutions under non-Lévy-type boundary conditions

Existing analytic solutions for the free vibration of functionally graded carbon nanotube reinforced doubly-curved panels primarily address the cases with two parallel simply supported boundaries, known as Lévy-type boundary conditions (BCs). However, doubly-curved panels with non-Lévy-type BCs are more commonly encountered in practical engineering applications, yet their analytic solutions are rarely available due to significant mathematical challenges. This gap motivates us to develop new analytic free vibration solutions under these more complex BCs. The nanocomposites’ material properties are first computed according to the rule of mixture. The Hamiltonian-system governing equation for the free vibration of doubly-curved panels is then formulated from the Donnell-Mushtari theory, and is solved by adopting the analytic symplectic superposition method. The obtained analytic solutions are derived without requiring predefined solution forms, and have been thoroughly validated by comparison with the results from the finite element method. By utilizing the accurate analytic solutions, the effects of aspect ratios, BCs, types of CNT distributions, and volume fractions of CNT on the free vibration behaviors are further analyzed. The present solution procedure and the resulting analytic solutions are expected to be useful for dynamic modeling of composite shell panels, supporting both future research and practical applications.

The effect of temperature on the vibration behavior of laminated composite plates

The effect of temperature on the vibration behavior of laminated composite plates

Potential of Non-Contact Dynamic Response Measurements for Predicting Small Size or Hidden Damages in Highly Damped Structures.

Vibration-based structural health monitoring (SHM) is essential for evaluating structural integrity. Traditional methods using contact vibration sensors like accelerometers have limitations in accessibility, coverage, and impact on structural dynamics. Recent digital advancements offer new solutions through high-speed camera-based measurements. This study explores how camera settings (speed and resolution) influence the accuracy of dynamic response measurements for detecting small cracks in damped cantilever beams. Different beam thicknesses affect damping, altering dynamic response parameters such as frequency and amplitude, which are crucial for damage quantification. Experiments were conducted on 3D-printed Acrylonitrile Butadiene Styrene (ABS) cantilever beams with varying crack depth ratios from 0% to 60% of the beam thickness. The study utilised the Canny edge detection technique and Fast Fourier Transform to analyse vibration behaviour captured by cameras at different settings. The results show an optimal set of camera resolutions and frame rates for accurately capturing dynamic responses. Empirical models based on four image resolutions were validated against experimental data, achieving over 98% accuracy for predicting the natural frequency and around 90% for resonance amplitude. The optimal frame rate for measuring natural frequency and amplitude was found to be 2.4 times the beam's natural frequency. The findings provide a method for damage assessment by establishing a relationship between crack depth, beam thickness, and damping ratio.

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.

An exact analytical method for free vibration analysis of FG-GPLRC sector cylindrical shells under Levy-type boundary conditions

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Variable angle tow-steered fibres based rotating composite beam with rotary oscillations – Parametric excitation/instability analysis

This study is concerned with the stability analysis for various vibrational motions of tow-steered variable angle fibres based composite rotating beam with time varying speed. The formulation combines a higher order theory introducing sine function along with finite element methodology. It satisfies the plane stress condition in width direction of beam. The displacement kinematics are generic in the sense it includes various possible vibrational motions like chord and flap wise motions, torsional and axial vibration behaviours. The equilibrium equations for the proposed problem evolved adopting virtual dynamic work are then transformed into the equations of Mathieu-Hill type considering time varying harmonic rotational speed. Using Bolotin’s procedure coupled with C1 continuity-based beam element, the parametric resonance zones along with boundary limits are numerically evaluated. The eigenvalue type of solution methodology applied for the detailed study is validated for accuracy and computational efficiency against the time domain dynamic response analysis. Based on in-depth analysis, dynamic instability characteristics in terms of resonance range and origin of instability of composite beam subjected to the chord and flap wise, torsional and axial motions are studied considering curvilinear fibre path angles, beam cross section, hub radius, thickness ratio and mean rotary speed.

Vibrational analysis of polyurethane-sandwiched bridge decks with variable skew angles

Bridge decks are the surface of bridges that carry the weight of the vehicles and pedestrians crossing over them. The design of bridge decks varies depending on the span, traffic volume, and material availability. But nowadays, the need for a sustainable approach is required. So, use of a sustainable material for construction and retrofitting purposes is the need of the hour. In the present study, a novel synthetic material polyurethane has been used in bridges. The study deals with the variation in skew angles to determine the response of the bridge deck. The response of natural frequencies on the bridge deck due to the variation in skewness and thickness of steel are analysed under simply supported and clamped boundary conditions. Further, the bridge deck is sandwiched using steel and polyurethane having different thicknesses, and the responses are recorded. Afterwards, a bridge deck is modelled using polyurethane as a special case, to pursue sustainability and justify the RRR (reduce, reuse, and recycle) concept of waste management. A comparative study is also performed between the isotropic steel deck and sandwiched deck by varying the skewness. The skew angle is varied from 0° to 60° with a difference of 10°, i.e., 0°, 10°, 20°, 30°, 40°, 50°, and 60°. The frequencies of the isotropic steel and sandwiched decks are increasing when the skewness is increased. Also, the decks may be modelled in a way to enhances the vibration behaviour by sandwiching the existing steel decks. The free vibration frequencies of the sandwiched decks are comparable to the steel deck of similar thickness, which shows the use of polyurethane as the core material does not affect the vibrational characteristics of the deck, while at the same time reducing the cost significantly. The research lays the groundwork for the creation of engineering recommendations that practitioners can use.

An experimental and numerical effort on the vibration behavior of additively manufactured recycled polyethylene terephthalate glycol components

AbstractThe importance of recycling engineering components and thus obtaining low‐cost production solutions has become prominent in today's world. In this study, the mechanical and dynamic behaviors of three‐dimensional‐printed recycled polyethylene terephthalate glycol (RePET‐G) beams were investigated numerically and experimentally for the first time in the literature. Initially, the governing equations of the beams were determined according to the Bernoulli–Euler beam theory, and these equations were numerically solved using the differential quadrature method and ANSYS program. Subsequently, to validate the accuracy of the numerical models, the obtained natural frequencies were compared with experimental results. It was observed that the numerical results showed good agreement with the experimental results. Finally, the effects of beam length, infill rate, and building direction on the natural frequencies of RePET‐G beams were investigated. The outcomes showed that as the beam length changed, natural frequencies were significantly affected. Increasing the infill rate, especially for beams with vertical building direction, from 20% to 100% led to a slight decrease in the natural frequency values of the structure. Moreover, it was found that for beams with an infill rate of 100%, the natural frequency values obtained in the horizontal building direction were higher than those obtained in the vertical building direction.Highlights Printable recycled filaments have great potential for vibration applications. Sample length affects the first natural frequency value of RePETG parts. Differential quadrature and ANSYS methods can be utilized for the vibration. For the 3D‐printed samples, rising infill rate causes a natural frequency drop.

Kink effect on the lattice properties of one-dimensional carbyne nanocrystals under high temperature

Carbyne nanocrystal (CN), as a kind of one-dimensional (1D) sp-hybridized carbon allotrope, has attracted much attention due to its excellent optical and transport properties. However, the lattice properties of 1D CNs under high temperature remain unclear. In our work, we investigate the stability and lattice properties of 1DCNs based on the atomic-bond-relaxation (ABR) approach and first-principles calculations. We find the change of transverse vibration frequencies and bond kinks induced by the thermal effect plays a significant role in the mechanical properties of 1D CNs. We establish a relationship between kink angle and phonon vibration modes, giving a deep inside into high frequency and low-frequency vibration behavior of 1D CNs. Our results indicate the phonon vibration modes modulated by kinks under applied temperatures can lead to a negative thermal expansion behavior in the axial direction of 1D CNs, suggesting an effective way to control the thermal properties of 1D CNs for practical applications.

A numerical study on locomotive wheel wear on curved track subjected to adhesion control

The wheel wear of heavy-duty locomotives is more complicated than that of other vehicles when it affects tractive force and adhesion control. The purpose of this article is to calculate wheel wear on a curved track using a co-simulation dynamic model of a heavy-duty locomotive with adhesion control. Additionally, the effect of creep threshold, decline slope, curve radius, and passing speed on wheel wear is further investigated. The findings demonstrate that wheel wear can be successfully decreased by adjusting the creep threshold and decline slope of adhesion control parameters. The wheel-rail stick-slip vibration behavior on the curve track can be eliminated by increasing the curve’s radius and passing speed, but the vertical wear at the left wheel’s flange will rise sharply with the increase of passing speed on right hand curve.

Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations

Abstract In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies.

Prediction of rail wear band evolution under excitation by periodic track irregularities and its influence on vehicle dynamic performance

Periodic track irregularities (PTIs) are an important and sensitive source of vehicle vibration and have attracted considerable attention from railway researchers. However, previous studies have mainly focused on the irregularities themselves, with limited investigation of how the rail wear band (RWB) generated by PTIs excitation affects vehicle responses. To assess this, a three-dimensional rail wear prediction model is developed in this study to simulate the evolution of the RWB under PTIs conditions and then the effect of RWB excitation on the vehicle dynamic performance is investigated. The results show that the spatial trace of the rail contact points generated by the PTIs also exhibits clear periodic characteristics. Accordingly, the distribution pattern of the RWB also reflects these periodic features. The excitation of the periodic rail wear band (PRWB) has a negative effect on the vehicle running stability, especially when the vehicle is traveling at speeds that induce coupling resonance, which exacerbates the consequences. As the wear level of the PRWB increases, there is also an escalation in the vibration of the carbody. Furthermore, the amplitude of the change in the wheelset balance position resulting from variations in rail profile is found to serve as an effective descriptor for characterizing the wear intensity of PRWB, and the vibration amplitude of the carbody exhibits a clear linear correlation with PRWB excitation. The research results are helpful for understanding the relationship between PRWB excitation and vehicle vibration behavior and serve as a theoretical basis for track maintenance and profile optimization.

Coupling vibration mechanism of rotating shaft–disc–blade system with blade crack—A systematical investigation on the effect of crack, condition, and structure parameters

Rotating shaft–disc–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine, and power plant. Understating and revealing the coupling vibration mechanism of RSDB system is significant for blade health monitoring and blade crack detection. However, the multi-structure, multi-vibration source, and multi-stress coupling makes it a very tough task. This study aims to reveal the coupling vibration mechanism of RSDB system by systematically investigating the steady-state vibration responses under the influences of different blade crack, operation condition, and structure parameters. First and foremost, a coupling vibration model of RSDB system that comprehensively considers the multi-structure, multi-vibration source, and multi-stress coupling effects is presented. And then, a novel condition indicator for blade health monitoring, called blade–blade distance, is proposed to better characterize and analyse the coupling vibration of RSDB system with blade crack. At last, the comprehensive effects of blade crack, operating condition, and structure parameters on the coupling vibration mechanism of the RSDB system with blade crack are systematically studied. The comparative results demonstrate the effectiveness of blade–blade distance and super-harmonic components of shaft torsional vibration and blade bending vibration for indicating the presence of blade crack and tracking the crack severity. Another observation should be noted is that the vibration behaviour including the blade–blade distance, super-harmonic components of shaft torsional vibration and blade bending vibration, the combination frequency components of shaft bending vibration are co-affected by blade crack, operating condition, and structure parameters. It is indicated that the blade health monitoring and crack detection of rotating blade should comprehensively consider different indicators to obtain a more robust and accurate results.

Energy Element Method for Three-Dimensional Vibration Analysis of Stiffened Plates with Complex Geometries

A novel numerical method, the energy element method, is proposed for the three-dimensional vibration analysis of stiffened plates with complex geometries. The problem is modeled in a cuboidal domain, and a cuboidal energy element is developed for the simulation of the structural components. To simulate the energy distribution of the structure, stiffened plates are treated as discrete energy systems, where variable stiffness is used to characterize their energy distribution in a cuboidal domain and a global admissible function is used to approximate their vibrational behavior. With extended interval integral, Gauss quadrature, variable stiffness, and Legendre polynomials used for numerical integration in the cuboidal domain, the cuboidal energy element can offer sufficient precision with sufficient Gauss points for simulating the strain energy of stiffened plates with complex geometries. The Gauss–Legendre quadrature will provide accurate integration results if the integral domain is cuboidal. Otherwise, small cuboidal energy elements are generated with denser Gauss points to capture the geometric boundaries. As the numerical model is constructed on a standard geometric domain, all energy functionals and computational procedures are standard. Three-dimensional vibration problems are investigated for variously shaped stiffened plates with straight or curvilinear stiffeners. The present results are compared with analytical, numerical, and experimental results published in the literature.

The novel Vogel's approximation method integrated with a random forest algorithm in the vibration analysis of a two-directional functionally graded taper porous beam: Assessment

A functionally graded material is a class of composite materials characterized by gradual variations in composition and microstructure, which further induces the respective changes in the material properties. This study focuses on evaluating the vibration behavior of two directional functionally graded taper porous beams (FGTPB). This approach adopts a rectangular cross-section in order to deal with the challenges related to fluctuating material characteristics and geometric tapering in both thickness and width dimensions. The research employs a novel approach that merges Vogel's approximation technique with the Random Forest algorithm, an approach that has not been used in analyzing structural vibrations, establish boundary conditions and solve equations of motion. Comparative results of the suggested beam theory with the existing literature on FGTPB materials such as alumina and SUS304 at various taper, porosity, gradient and width ratios verified it. The material gradation and porosity developed a uniform pattern in the first three modes of fundamental frequencies. Higher gradient indices increased the rigidity and natural frequencies of the beams whereas the porosity index decreased the rigidity, resulting in lower natural frequencies. By combining Vogel's approximation method with machine learning techniques, the study improved vibration behavior analysis in FGTPB. The disciplines of materials and structural engineering are significantly impacted by this.