In-plane Vibrations Research Articles

The Influence of Rotor Adjustment Parameters on the Dynamic Balance of a Scale-Model Rigid Variable Speed Rotor

In this paper, the dynamic balance of a rigid variable speed rotor is tested and analyzed. The vibration acceleration is measured by vibration analyzer instrumentations. The rotor adjustment parameters of counterweight, pitch, and trailing-edge flap are considered. The amplitude and phase of the 1 Ω vibration acceleration are analyzed through an all-phase fast Fourier transform. The experiments are conducted using two rigid rotors with the same geometry. The accelerations of the fuselage in the x, y, and z directions are measured. Through a waterfall diagram of the auto-power spectrum, it is found that the imbalance of counterweight, pitch, and trailing-edge flap causes an obvious increase in 1 Ω and 2 Ω acceleration. The hub counterweight mainly causes the lateral and longitudinal vibration in the disc plane, and the aerodynamic factors such as pitch and trailing-edge flap mainly affect the vertical vibration. In order to achieve dynamic balance for variable speed rotors, the counterweight adjustment should be given the highest priority for the vibration in the disc plane, and the pitch and trailing-edge flap adjustment should be given the highest priority for the vertical vibration. The results obtained from this experiment may be helpful toward reasonable designs of variable speed rotor helicopters.

Emergence of negative-dispersion passbands below the ring frequency of a piezoelectric meta-shell

The local-resonance (LR) mechanism is usually employed to induce bandgaps in the scope of metamaterials. On the contrary, we investigate LR passbands in this paper, which are located below the ring frequency of a piezoelectric meta-shell shunted with resonant circuits. The flexural wave properties of the meta-shell are investigated analytically through dispersion relations, and also verified by numerical results. It is observed that the piezoelectric shunting could induce longitudinal bandgaps above the ring frequency, while passbands below the ring frequency. Interestingly, negative dispersions may appear in this longitudinal passband when negative bending rigidity is induced through the piezoelectric bending effect, implying that the group velocity of flexural wave is opposite to its phase velocity. We demonstrate such rigidity-correlated dispersion behaviors through energy flow analysis based on the Poynting vector. It is also revealed that the curvature of shells impacts the width of negative-dispersion passbands, with the smaller radius leading to narrower passbands. Since the curvature couples in-plane vibrations and out-of-plane vibrations, it facilitates flexural-wave passbands below the ring frequency as well by introducing the piezoelectric tensional effect, but with dispersions maintaining positive. Moreover, we find that if the piezoelectric shunting induces the bending effect and the tensional effect simultaneously, their interplay at the overlap frequency range may create negative-dispersion passbands above the ring frequency, whereas cancels the impacts with each other below the ring frequency. The results in this research break the limitation that flexural wave propagation below ring frequencies of shells is conventionally not allowed in the longitudinal direction. It also offers the opportunity to implement unprecedent wave properties related to negative dispersions, such as negative refraction and superlensing, with single-negative curved metamaterials.

Vibration suppression of a cable under harmonic excitation by a nonlinear energy sink

The application research of nonlinear energy sink (NES) on vibration suppression in many fields is a hot topic. In this paper, the vibration suppression mechanism of a nonlinear energy sink on a cable under a harmonic load is studied novely. First, the dynamic model of the cable-NES system under harmonic excitation is established. The partial differential Equations (PDEs) of motion governing the in-plane vibration of the cable-NES system are derived by Hamilton’s principle. Then, by considering the coupling effect among the first three in-plane modes of the cable, the ordinary differential equations (ODEs) of the coupled system are obtained applying Galerkin integral. The incremental harmonic balance (IHB) method is used to solve the nonlinear ordinary differential equations. Meanwhile, the stability of the solution is determined using Floquet theory. Finally, the primary resonances of the first and third in-plane modes of the cable are explored respectively, and the vibration mitigation performance of the NES and the wavelet transform of the cable displacement response are analyzed. The research results show that the NES has a significant effect on the dynamic behavior and vibration mitigation of the cable, especially, when the NES parameters are the same, the vibration mitigation effect of the NES on the primary resonance of the 3rd mode of the cable is better than that of the 1st mode.

Vibration Energy Conversion Power Supply Based on the Piezoelectric Thin Film Planar Array.

Vibration energy harvesting has received much attention as a new type of power solution for low-power micro/nano-devices. However, VEH (vibration energy harvester) based on PVDF (polyvinylidene fluoride) piezoelectric materials have a low output power and energy conversation efficiency due to the relatively low piezoelectric constant, coupling coefficient, and dielectric constant. For this reason, we design a vibration energy conversion power supply, which consists of a VEH with a PVDF piezoelectric thin film planar array vibration structure and an energy harvesting circuit for regulating the electric energy of multiple sources. Furthermore, our solution was validated by simulations of structural dynamics in COMSOL and equivalent circuits model in Multisim. From the circuitry simulation results, the output current and the charging period increase and decrease, doubling, respectively, for each doubling of the number of array groups of films. Moreover, the solid mechanics simulation results show that the planar array structure makes the phase and amplitude of the input vibration waves as consistent as possible so that the same theoretical enhancement effect of the circuitry model is achieved. An identical experimental test was implemented with vibration conditions of 75 Hz-2.198 g. The fabricated harvester quickly charged the 22 V-0.022 F ultracapacitor bank to 5 V in 24 min. The maximum open circuit voltage and output power, respectively, were 10.4 V and 0.304 mW. This maximum charging power was 11.69 times higher than that of a single film. This special power supply can replace batteries to power low-power electronics deployed in vibrating environments, thus reducing the maintenance costs of equipment and environmental pollution rates.

In-plane free vibrations of small-sag inclined cables considering bending stiffness with applications to cable tension identification

This study proposed an analytical model to characterize in-plane free vibration of a cable considering sags, inclined angles, and non-negligible bending stiffness to enhance the accuracy and efficiency of vibration analysis and health monitoring of cable structures under complex engineering environments. The static equilibrium configuration of the cable is derived, and the singularity at boundary regions is elucidated in detail. The analytical solution of the dynamical control equation is obtained using the successive approximation method. The influences of the sags, inclined angles, and bending stiffness on eigenfrequencies and mode shapes are individualy studied via introducing three non-dimensional parameters. The analytical model is further examined through parametric anaysis. As a typical extension, the model is used to establish a cable tension identification method, in which an inverse problem is solved by the trust-region-dogleg technique. The identification method is verified through comparisons with existing methods established based on classical string vibration theory and various numerical methods, e.g., finite element method and finite difference method. Validations are made by using experimental outcomes, on which the data collected from both an experiment in laboratory and a field experiment in the Poyanghu bridge are used for comparison. It is found that the proposed model along with the method is able to capture precise vibration features and identify cable tensions accurately in favor of the improvement of cable condition monitoring and health management in fields such as bridge engineering.

Wave-based in-plane vibration analysis of multiple coupled beam structures with arbitrary connection angle and elastic boundary restraints

Beam structures are widely used in various engineering branches, and the investigation on their dynamic behavior is of fundamental significance for the efficient design and vibration control of complex beam structures. In this work, a unified wave-based model for the in-plane vibration analysis of multiple coupled beams with arbitrary connection angle and boundary conditions is established, in which the vibrations within structures are described as wave propagation along structural elements, accompanying with wave reflection and transmission at some particular positions (such as the boundaries or structural joints). The reflection and transmission matrices corresponding to the incident waves propagating to the angular joint from various directions and the wave reflection matrix at the elastic boundary are derived. The natural and forced in-plane vibrations of multiple coupled beams can be analyzed concisely and systematically by assembling these wave reflection and transmission matrices. The accuracy of this approach is validated by comparing the dynamic characteristics obtained by the current approach with finite element method. Then, the influences of boundary stiffnesses and joint angle on wave reflection and transmission matrices are investigated. The results show that it is possible to know which wave type is dominant in structure at a certain frequency or angle, which shows certain significance for future work of vibration control and power flow analysis. The unified analysis model established in this paper can not only analyze the vibration characteristics of complex coupled beams but also reveal how waves are reflected and transmitted in the structure.

Detecting Defects in Composite Polymers by Using 3D Scanning Laser Doppler Vibrometry.

The technique of 3D scanning laser Doppler vibrometry has recently appeared as a promising tool of nondestructive evaluation of discontinuity-like defects in composite polymers. The use of the phenomenon of local defect resonance (LDR) allows intensifying vibrations in defect zones, which can reliably be detected by means of laser vibrometry. The resonance acoustic stimulation of structural defects in materials causes compression/tension deformations, which are essentially lower than the material tensile strength, thus proving a nondestructive character of the LDR technique. In this study, the propagation of elastic waves in composites and their interaction with structural inhomogeneities were analyzed by performing 3D scanning of vibrations in Fast Fourier Transform mode. At each scanning point, the in-plane (x, y) and out of plane (z) vibration components were analyzed. The acoustic stimulation was fulfilled by generating a frequency-modulated harmonic signal in the range from 50 Hz to 100 kHz. In the case of a reference plate with a flat bottom hole, the resonance frequencies for all (x, y, and z) components were identical. In the case of impact damage in a carbon fiber reinforced plastic sample, the predominant contribution into total vibrations was provided by compression/tension deformations (x, y vibration component) to compare with vibrations by the z coordinate. In general, inspection results were enhanced by analyzing total vibration patterns obtained by averaging results at some resonance frequencies.

Ultra-compact displacement and vibration sensor with a sub-nanometric resolution based on Talbot effect of optical microgratings.

Based on Talbot effect of optical microgratings, we report an ultra-compact sensor for displacement and vibration measurement with resolution down to sub-nanometer level. With no need of optical components such as reflectors, splitters, polarizers, and wave plates, the proposed sensor based on a common-path structure shows a high compactness. Using gratings with period of 3 µm, displacement measurement within a range of 1 mm is demonstrated experimentally. Associated with an interpolation circuit with subdividing factor of 4096, a resolution of 0.73 nm is obtained. The experimental results also show the ability for the sensor to detect in-plane vibration with frequency below 900 Hz. With a sub-nanometer resolution and an ultra-compact structure, the miniature sensor shows potential in applications such as high-precision machinery manufacturing and semiconductor processing.

Experimental and Numerical Study on Flow-Induced Vibration of PWR Steam Generator U-Tubes

The flow-induced vibration (FIV) of steam generators (SGs) in pressurized water reactors (PWRs) is a significant problem in the design process. This problem contains issues such as two-phase flow, nonlinear dynamics and fretting wear. In this paper, an experimental setup was established to study the FIV of a newly designed U-tube SG. Numerical simulations, including computational fluid dynamics (CFD) and vibration studies were performed to reveal the detailed mechanisms of FIV. To study the U-bend region of the tube bundles, the experiments were carried out under 23 experimental conditions containing void fractions of 70%, 80%, 90 and 95%. The flow fields of the tested model in each condition were calculated to reveal the causes of the vibration phenomenon, and the vibration results were calculated through structure dynamics. The experimental results showed that the vibration amplitudes of the U-tube increased with increasing inlet velocity, flow rate and bending radius. It decreased with increasing void fraction under the same inlet velocity, while it increased with increasing void fraction under the same flow rate. Along with the out-of-plane vibration, the in-plane vibration also featured high amplitude vibration of the U-tubes due to lack of support by the anti-vibration bars (AVBs). The simulation results show the same variation trends of the vibration responses as the above experiments. The prototype SG can be fluid-elastic stable in given working conditions, and the main vibration mechanism of this model is turbulence buffeting. The experiment and simulation methods and data can be used in the design process of new SGs similar to this prototype.

NORMAL VIBRATIONS OF SAGGING CONDUCTORS OF OVERHEAD POWER LINES

The phenomenon of self-excitation of thermomechanical vibrations of current-carrying conductors, experimentally discovered by academician A.F. Ioffe, is of practical interest as a possible explanation of the phenomenon of galloping conductors of overhead power transmission lines (OHL) – low-frequency vibrations with frequencies of ~ 1 Hz and with amplitudes of the order of the static conductor sagging. To build the theoretical foundations of this phenomenon, as a special class of self-oscillating systems, it is necessary, first of all, a model of conductor vibrations in the OHL span. With regard to the most studied type of conductor vibrations, high-frequency aeolian vibration, excited by sign-alternating aerodynamic forces from the Karman vortex street, the classical model of a straight string is reasonably applied. However, to study low-frequency vibrations of the galloping type, it is necessary to take into account the effect of sagging of the conductor, the associated elastic tension and, in some cases, the nonlinear nature of the vibrations. The article presents two models for calculating the natural vibrations of sagging conductors (cables) within the framework of the technical theory of flexible threads, assuming the constancy of the tension force along the length. The first model describes linear oscillations of an elastic conductor in the sagging plane. For a system of equations with respect to the displacement components given in natural coordinates, an exact solution of the Sturm-Liouville problem with estimates of the frequency ranges arising is obtained. The second model describes nonlinear vibrations of an elastic conductor in the sagging plane and pendulum vibrations accompanied by an exit from it. The solution of the problem is based on the principle of possible displacements using the Ritz method. The structure of the frequency spectrum and the natural forms of transverse vibrations are studied. The developed models are intended for further investigation of thermomechanical vibrations of conductor and flexible cable systems.

Coupled Double Closed-Loop Control for an MEMS Resonant Accelerometer.

There is mutual coupling between amplitude control and frequency tracking control in the closed-loop control of micromechanical resonant sensors, which restricts sensor performance. This paper introduces the principle of an in-plane vibration micromechanical resonant accelerometer with electrostatic stiffness. The characteristic parameters of the microaccelerometer were obtained through computer-aided dimension measurement and an open-loop frequency sweep test of the fabricated microstructure. An accurate numerical model was established based on the accelerometer’s dynamic principle and characteristic parameters. We established the double closed-loop driving analysis model of amplitude automatic gain control and resonant frequency phase-locked tracking. We used the averaging method to analyze the steady-state equilibrium point and the stable condition. We concluded that the integral coefficient can improve the startup overshoot when the amplitude automatic gain control loop satisfies the stability condition. Under the constraint of frequency tracking, the sizeable coefficient of the integrator can improve the system instability of the amplitude control loop. The theoretical analysis and simulation were helpful in the design and debugging of the system circuit.

First-principles prediction of the lattice thermal conductivity of two-dimensional (2D) h-BX (X = P, As, Sb) considering the effects of fourth-order and all-order scattering

Recently, cubic boron arsenide (c-BAs) has attracted global attention due to its higher lattice thermal conductivity (κL), which is comparable to diamond, and excellent thermal properties. Can c-BAs achieve the leap in κL after transforming its structure from three-dimensional (3D) to two-dimensional (2D) like diamond to graphene? Previous studies have only investigated the κL considering three-phonon scattering and isotope scattering, and the calculated results are diverse. In this study, we first calculate second-order interatomic force constants (IFCs) and third-order IFCs to iteratively solve the Boltzmann transport equation (BTE) and to obtain the κL3 of monolayer hexagonal BX (X = P, As, Sb), h-BX (X = P, As, Sb), considering only three-phonon and isotope scattering. The corresponding κL3 of h-BX are 278.2, 205.7, and 20.2 W/mK at room temperature, and we explain the monotonous change that κL3 decreases with the increase of average atomic mass (mavg) different from previous studies. Subsequently we use regular residual analysis (RRA) to determine the necessity of including four-phonon scattering when calculating the κL of monolayer h-BX. By calculating the fourth-order IFCs, we obtain the κL3+4 of monolayer h-BX including four-phonon scattering. The values of κL3+4 at room temperature are 61.12, 37.99, and 5.73 W/mK, which are highly consistent with the κL∞ of monolayer h-BX as predicted by the phonon spectral energy density (SED) method. The phonon SED method considers all-order scattering and gives values of 54.05 ± 21.48 W/mK (h-BP), 18.20 ± 4.47 W/mK (h-BAs), and 2.46 ± 0.34 W/mK (h-BSb), respectively. Our results show that the influence of four-phonon scattering on the κL of monolayer h-BX is significant, and the κL3+4 and κL∞ still undergo monotonic changes after including four-phonon scattering. The main factors that determine the low (ultra-low) κL of monolayer h-BAs (h-BSb) are large mavg and weaker bonding strength, the existence of intermediate frequency ZO and scattered acoustic branches, the strong anharmonicity caused by the in-plane vibrations of As (Sb) atoms, and four-phonon scattering. This study aims to end the variance within monolayer h-BAs κL numerical simulation and demonstrate the potential of monolayer h-BSb in thermoelectric field applications.

Benchmark analytic in-plane vibration frequencies of orthotropic rectangular plates

The in-plane vibrations of rectangular plates is classic problem in mechanics. It involves the solution of two coupled differential equations with many combinations of possible edge restraints. Exact solution, for some cases, and high accuracy solution for few more cases, have been obtained along the years. In this work a new high accuracy solution, that covers all the possible combinations is presented. It is obtained by using carefully chosen series that solve the coupled partial differential equations of motion, for all possible combinations of edge conditions. Examples of the new solutions are given and compared with other known solutions and with approximate solutions for these cases. Benchmark results are given for square orthotropic plates with all possible combinations of boundary conditions.

Temperature-dependent Raman spectroscopy and thermal conductivity of TiS2 hexagonal nanodiscs

Transition metal dichalcogenides (TMDC) possess a unique combination of properties well-suited for the creation of novel optoelectronic and photonic devices. The titanium disulphide (TiS2) outstands among those as the lightest of TMDCs besides allowing low production cost and high stability. In this work, we present a comprehensive study of electron-phonon interaction induced vibrational properties of suspended TiS2 hexagonal nanodisks for an extended and elevated temperature range from 88 K to 538 K and a variety of laser powers. Our study reveals a stronger temperature dependence for out-of-plane vibrational mode (A1g) in comparison to that of in-plane vibration mode (Eg) which is attributed to a significant difference between strong intralayer covalent bonds and weak interlayer van der Waals bonds within the material. Furthermore, we observed that both Eg and A1g modes linearly undergo a red shift at higher temperatures, and in addition, a broadening at higher in-laser powers. On the basis of the present study, we propose that the thermal conductivity of the material is 5.049 W/mK.

Prediction of Surface Roughness in Turning Applying the Model of Nonlinear Oscillator with Complex Deflection

This paper deals with prediction of the roughness of a cutting surface in the turning process, applying the vibration data of the system. A new type of dynamic model for a workpiece-cutting tool system, appropriate for vibration simulation, is developed. The workpiece is modelled as a mass-spring system with nonlinear elastic property. The cutting tool acts on the workpiece with the cutting force which causes strong in-plane vibration. Based on the experimentally measured values, the cutting force is analytically described as the function of feed ratio and cutting speed. The mathematical model of the vibrating system is a non-homogenous strong nonlinear differential equation with complex function. A new approximate solution for the nonlinear equation is derived and analytic description of vibration is obtained. The solution depends on parameters of the excitation force, velocity of rotation and nonlinear properties of the system. Increasing the feed ratio at a constant velocity of the working piece, the frequency of vibration decreases and the amplitude of vibration increases; increasing the velocity of working piece for constant feed ratio causes an increase of the frequency and a decrease of the amplitude of vibration. Experiments demonstrate that the analytical solution of the nonlinear vibration model in turning process is in direct correlation with the cutting surface roughness. The predicted surface roughness is approximately (1–2) × 10−3 times smaller than the amplitude of vibration of the nonlinear model considered in this paper.

Experimental and Computational Analysis of Free In-Plane Vibration of Curved Beams

Experimental and Computational Analysis of Free In-Plane Vibration of Curved Beams

Chaotic vibration analysis of auxetic nanocomposite structures

The present work deals with the study of nonlinear vibration behaviours of the carbon nanotube reinforced composite structures having negative Poisson’s ratio (CNTRC-NPR). Such types of flexible auxetic structures have many applications in various engineering fields. Based on classical laminated theory, auxetic structures can be designed by some special stacking sequence of layers in the laminated composites. A mathematical model is formulated for nonlinear vibration analysis of the clamped-clamped CNTRC-NPR beam under the time varying uniformly distributed transverse load. The present formulation is based on the Reddy’s third-order shear deformation theory and the governing equation of motion of such beam is derived by using the Hamilton’s principle. Based on the Galerkin’s method, the obtained governing partial differential equations are converted to an ordinary nonlinear second-order differential equation for the analysis of out plane vibration. The obtained vibrations of such auxetic structures are discussed using time series waveforms, phase portraits and Poincare maps, and the route of chaotic vibration of such structures is found and reported based on the bifurcation diagrams. The jump phenomena associated with the dynamics have also been characterized. Nonlinear vibrations of without and with auxetic nanocomposite structures have also been compared. It is found that the amplitude of transverse force of excitation is the controlling parameter of nonlinear dynamics of such CNTRC-NPR structures.

Strain effects on the interfacial thermal conductance of graphene/h-BN heterostructure

Previous experimental and computational results have confirmed that the thermal conductivity of a two-dimensional (2D) material can be considerably affected by strain. Numerous attention has been paid to explore the relevant mechanisms. However, the strain effects on the interfacial thermal conductance (ITC) of 2D heterostructure have attracted little attention. Herein, the non-equilibrium molecular dynamics (NEMD) simulations were conducted to the graphene/hexagonal boron nitride (GR/h-BN) heterostructure to investigate the strain effects on the ITC. Three types of strains were considered, i.e., tensile strain, compressive strain, and shear strain. The results indicate that the strain can adjust the ITC for the GR/h-BN heterostructure effectively, and the strain loading direction also influences the ITC. Generally, the tensile strain reduces the ITC of the heterostructure, in addition to the BN-C system at small tensile strain; both the compressive strain and shear strain increase the ITC, especially at a small strain. For the NB-C system, it is more sensitive to the strain loading direction and the yx shear strain of 0.06 is the most effective way to strengthen the ITC. Our results also show that the out-of-plane deformation weakens the in-plane vibration of atoms, leading to a reduction of the interfacial thermal energy transport.

Vibration suppression of floating offshore wind turbines using electromagnetic shunt tuned mass damper

This paper investigates the suppression of in-plane vibrations of a floating offshore wind turbine (FOWT) using the electromagnetic shunt tuned mass damper (EMSTMD), where the dashpot is replaced by a shunted electromagnetic (EM) transducer for improving performance and durability of the damper. A series resistive–capacitative–inductive (RCL) network is designed as the supplemental shunt for the EM transducer, which results in an additional resonance for performance improvement. A 17-degree-of-freedom (17-DOF) aero-hydro-servo-elastic model is established for the FOWT, which is used for performance evaluation of the EMSTMD in the time domain. A reduced-order 6-DOF model is then developed for the FOWT in-plane vibrations with EMSTMD mounted, accounting for rotor mass moment of inertia, stiffness from buoyancy and mooring lines, as well as hydrodynamic added mass. This model facilitates an efficient frequency-domain optimization procedure for the EMSTMD, taking into account uncertainties in the environmental conditions. The performance of the optimized EMSTMD is compared with that of the classic TMD in both frequency and time domains. It is shown that both EMSTMD and TMD effectively reduce tower side–side vibrations of FOWT, and also have lightly positive effect on the spar roll and blade edgewise vibrations. EMSTMD consistently outperforms TMD for all environmental conditions, at the cost of slightly increased absorber stroke.

Combined Feature Extraction and Random Forest for Laser Self-Mixing Vibration Measurement without Determining Feedback Intensity.

To measure the vibration of a target by laser self-mixing interference (SMI), we propose a method that combines feature extraction and random forest (RF) without determining the feedback strength (C). First, the temporal, spectral, and statistical features of the SMI signal are extracted to characterize the original SMI signal. Secondly, these interpretable features are fed into the pretrained RF model to directly predict the amplitude and frequency (A and f) of the vibrating target, recovering the periodic vibration of the target. The results show that the combination of RF and feature extraction yields a fit of more than 0.94 for simple and quick measurement of A and f of unsmooth planar vibrations, regardless of the feedback intensity and the misalignment of the retromirror. Without a complex optical stage, this method can quickly recover arbitrary periodic vibrations from SMI signals without C, which provides a novel method for quickly implementing vibration measurements.