Amplitude Of Excitation Force Research Articles

Experimental Study on Identification of Aerodynamic Damping Matrix for the Tower of an Operating Wind Turbine by Artificial Excitation

ABSTRACTQuantitation of damping is of great significance for the design and condition assessment of wind turbines. The authors' previous theoretical and numerical studies showed that compared with damping ratios, a modal aerodynamic damping matrix can better describe the damping coupling in the fore‐aft (FA) and side‐side (SS) tower motions. In the present study, an improved damping identification method was first proposed to identify this damping matrix with artificial exciters and then verified by using OpenFAST simulations under different excitation frequencies, excitation force amplitudes, and turbulent wind fields. Following the numerical study, a scaled wind turbine model with a geometric scale ratio of 1/75 was carefully designed based on the NREL 5‐MW wind turbine prototype, in which the scaled blade design follows the rule in thrust coefficient similarity. An identification study was performed with this scaled model by a series of wind tunnel tests. The modal aerodynamic damping matrix was identified under steady‐state harmonic excitation in the operating state and compared with the identified results by a free decay method and the theoretical values. The results experimentally confirm the correctness of the aerodynamic damping matrix theory under uniform wind and the feasibility of the improved identification method in practice.

Mechanism of Centrifugal Force Amplitude–Frequency Decoupling Exciters for Fruit Tree Vibration Harvest

Centrifugal force is often used as an exciting force for fruit vibration harvest. However, the magnitude of centrifugal force varies quadratically with angular velocity. When the frequency of excitation force remains constant, the amplitude of vibration force cannot be freely adjusted. This study achieves decoupling of the amplitude and frequency of centrifugal force by varying the eccentricity of the eccentric block. Different combinations of eccentric blocks with varying quantities and parameters enable the creation of different types of centrifugal force amplitude–frequency decoupling exciters. Both the amplitude and frequency of excitation force produced by these exciters can be freely adjusted. Furthermore, a physical prototype of a symmetrical dual eccentric block exciter with centrifugal force amplitude–frequency decoupling is developed and tested. It is found that when the exciter frequency or excitation force amplitude remains constant, the vibration acceleration amplitude generated by the exciter changes by adjusting the eccentricity of the eccentric blocks. As the eccentricity of the eccentric blocks decreases, their moment of inertia and kinetic energy decrease. Utilizing mechanisms to adjust the eccentricity of the eccentric block’s center of mass to the rotation axis achieves the dynamic adjustment of the size and frequency of centrifugal force.

Fatigue life prediction of cracked cross beam of mining linear vibrating screen under cyclic load

The cross beam of a mining linear vibrating screen is prone to cracking under long-term cyclic load. In order to accurately predict the fatigue life of the cracked cross beam, a coupled analysis method of vibration and crack propagation is proposed. A 2D dynamic model of the vibrating screen is established based on the finite element method, which is verified by the vibration test platform. The cracked Euler beam element is used to model the cracked cross beam. The effects of crack depth, amplitude of excitation force, frequency of excitation force, and crack location on the crack-tip stress intensity factor of the cracked cross beam are investigated in detail. In addition, an iterative method is proposed on the basis of the Paris model. The residual service life of the beam under different frequencies of excitation force, amplitudes of excitation force, spring stiffness, crack positions, and degrees of stiffness imbalance are discussed. The results demonstrate that the fatigue life of the beam increases as the frequency of excitation force and spring stiffness increase. The increase of the amplitude of excitation force and spring permanent deformation reduces the fatigue life. The conclusion obtained provide some theoretical guidance for the design and routine maintenance of mining linear vibrating screens.

Influence of trailing edge radius of intake struts on excitation force and vibration of rotor blades

Adjusting the trailing edge radius of the intake struts may be advantageous in suppressing the vibration of compressor rotor blades. To explore the impact of the intake struts trailing edge radius on the excitation force and vibration, this study focuses on a compressor with intake struts, and fluid and vibration calculations were conducted. The study revealed that decreasing the trailing edge radius led to a reduction in separation near the strut’s trailing edge, resulting in a narrower wake and weakened mixing near the trailing edge. This caused the total pressure loss region induced by the wake to become more elongated in the low-frequency component, leading to a nonlinear decrease in total pressure amplitude with the reduction of the trailing edge radius. As the trailing edge radius decreased, the excitation force and vibration amplitude of the first-stage compressor rotor blades decreased, while the excitation force distribution showed little variation. The research findings provide insights for the design of intake struts.

Design and Testing of the Double-Symmetric Eccentric Exciter for Fruit Tree Vibration Harvest

The amplitude of excitation force from exciters used in fruit tree vibration harvesting remains constant at a given frequency, leading to poor fruit detachment ratio and tree damage. A solution has been proposed through the development of a Double-Symmetric Eccentric Exciter (DSEE). This new exciter allows for the adjustment of excitation force amplitude while maintaining a constant frequency by varying the phase angle of the DSEE. To validate the effectiveness of the DSEE, vibration tests were conducted on fruit trees using different parameter exciting forces. Acceleration sensors were employed to measure the vibration accelerations of the tree branches. The experimental results revealed that when a fixed frequency excitation force with a constant phase angle was applied to the trunk, the vibration acceleration of branches exhibited inconsistent variations due to differences in the vibration differential equation parameters of each branch. Furthermore, it was observed that increasing the phase angle of the DSEE at a fixed frequency led to larger vibration accelerations in every branch. This signifies that adjusting the phase angle of the DSEE can effectively increase the amplitude of the exciting force. Consequently, the ability to control both the amplitude and frequency of the excitation force independently can mitigate issues such as low fruit harvest rates and minimize damage to fruit trees.

Novel approach for solving higher-order differential equations with applications to the Van der Pol and Van der Pol–Duffing equations

BackgroundNumerical methods are used to solve differential equations, but few are effective for nonlinear ordinary differential equations (ODEs) of order higher than one. This paper proposes a new method for such ODEs, based on Taylor series expansion. The new method is a second-order method for second-order ODEs, and it is equivalent to the central difference method, a well-known method for solving differential equations. The new method is also simple to implement for higher-order differential equations. The proposed technique was applied to solve the Van der Pol and Van der Pol–Duffing equations. It is stable over a wide range of nonlinearity and produces accurate and reliable results. For the self-excitation Van der Pol equation, the proposed technique was applied with different values of nonlinear damping.ResultsThe results were compared with those obtained using the ODE15s solver in MATLAB. The two sets of results showed excellent agreement. For the forced Van der Pol–Duffing equation, the proposed technique was applied with different values of exciting force amplitude and frequency. It was found that for certain conditions, the solution obtained using the proposed technique differed from that obtained using ODE15s.ConclusionsThe solution obtained using the proposed technique showed good agreement with the solutions obtained using ODE45 and Runge–Kutta fourth order. The results show that the proposed approach is very simple to apply and produces acceptable error. It is a powerful and versatile tool for solving of high-order nonlinear differential equations accurately.

Development of a new damping ratio prediction model for recycled aggregate concrete: Incorporating modified admixtures and carbonation effects

Abstract Recycled aggregate concrete (RAC) has been widely used in practical engineering construction. However, the ability of buildings to resist wind-induced vibration and earthquake effects plays an important role in building safety. It is urgent to ensure that recycled concrete still has good anti-vibration ability within the allowable strength range. By conducting damping tests on recycled concrete specimens, the results show that the damping performance of RAC is better improved compared with natural aggregate concrete. Moreover, the influence of internal factors of recycled aggregates and external environmental conditions on damping performance can be determined, and corresponding damping ratio prediction models can be constructed. However, the current prediction models still have limitations in theory and practice. The existing damping ratio prediction models have a large span of independent variables and do not consider the gradual carbonation effect in the actual environment over time. To overcome these limitations, a new damping ratio prediction model is proposed. Based on the replacement rate of recycled aggregates (RAs) and the amplitude of excitation force, the influence of modified admixtures and carbonation on damping performance is considered, and the corresponding model prediction formula is constructed. In addition, the influence mechanism is further demonstrated and explained from the macroscopic aspect of specimen profile and the microscopic aspect of electron microscopy tests. It is found that, considering both strength and cost factors, recycled concrete still has good damping performance when the replacement rate of recycled aggregates (RAs) is 40%.

Real-Time Ground Aeroservoelastic Test for Slender Vehicles Based on Condensed Aerodynamic Force Loading

Slender vehicles often encounter significant aeroservoelastic challenges due to their low elastic mode frequencies and wide servo control system bandwidths. Traditional analysis methods have limitations, including low modeling accuracy for real vehicles in numerical methods, scale errors in wind tunnel tests, and significant risks in flight tests. The ground aeroelastic stability test is an innovative experimental method designed to address these challenges. This novel method employs shakers to apply condensed unsteady aerodynamic forces in real-time to actual vehicles, serving for both the ground flutter test (GFT) and the ground aeroservoelastic test (GAT). While extensive research exists on the GFT, there is limited exploration of the GAT. For the GAT of a slender vehicle in this paper, the condensed aerodynamic forces are calculated using the quasi-steady aerodynamic derivative method. An improved, partially decoupled inverse model controller is designed for force control, guided by an assessment of coupling strength among different shakers. Ground experiments under various flight control laws and flight dynamic pressures produce accurate results. Numerical simulations and experimental results demonstrate high precision, with excitation force amplitude deviations within ±10% and phase deviations within ±5° within the frequency range relevant to aeroservoelastic stability.

Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon

This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator(SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.

Size-dependent nonlinear forced vibration of microbeam using two-phase local/nonlocal viscoelastic integral model with thermal effects

Combination strain-driven (εD) and stress-driven (σD) two-phase local/nonlocal integral models (TPNIM) with classic Kelvin-Voigt viscoelastic model, εD- and σD-two-phase local/nonlocal viscoelastic integral models (TPNVIM) are proposed to study the viscoelastic nonlinear forced vibration behaviors of microbeams in thermal environment. Based on von-Karman large deformation theory and the Hamilton’s principle, the differential governing equations of motion and boundary conditions are derived for nonlinear forced vibration of microbeam. Several non-dimensional variables are introduced to simplify the mathematical formulation. Nonlocal viscoelastic equations in integral form are transferred unitedly into equivalent differential form with constitutive constraints. The axial force of nonlocal microbeam with immovable ends is derived explicitly. Vibration frequency and corresponding linear vibration mode shape are derived through Laplace transformation for linear thermo-elastic vibration of microbeam using εD- and σD-TPNIMs. The Ritz-Galerkin approach is utilized to derive the reduced differential governing equation for nonlinear vibration of microbeam, which has exact same form as single-degree-of-freedom oscillator with cubic nonlinearity when material viscosity is neglected. The method of multiple scales (MMS) based on trigonometric functions is utilized to solve the reduced nonlinear differential equation approximately. The frequency-amplitude responses are addressed for primary and super-harmonic resonances of microbeam. The effects of viscous coefficient, amplitude of excitation force and environmental temperature variation as well as nonlocal length parameter on the nonlinear vibration behavior of microbeam are investigated numerically for different boundary conditions.

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

Self-shrouded torsional blade model equivalence and blade vibration response analysis

In steam turbines, the operation of turbine blades can lead to vibrations, which may result in turbine accidents. Traditional calculation methods are difficult to use due to the complex structure of the torsional blade, and simulation analysis can be time-consuming. Therefore, it is necessary to use the equivalent model instead. Most of the previous studies have simplified the straight blade to a cantilever beam model without considering the shear effect, and used harmonic response analysis to study the vibration of the blade for simulation. The blade body of the torsional blade can be regarded as a torsional variable section beam, and the Timoshenko beam model is the same as the variable section beam. Therefore, the Timoshenko beam model can be regarded as the equivalent of the sheathed torsional blade. Considering the complexity of the calculation of the self-shrouded torsional blade model. According to the theory of Timoshenko beam, the model of the shrouded blade of Timoshenko beam with different torsion angles was established. The first sixth-order modes of the blade model and the vibration response of the adjacent blades under forced vibration are compared, respectively. The results show that the results obtained from the Timoshenko beam blade model considering the torsion angle are closer to the torsional blade model. In addition, the blade vibration response of the same model under different excitation force amplitudes was further compared, and the results showed that the vibration amplitude, acceleration and velocity of the shrouded blade increased with the increase of the excitation force amplitude. However, the magnitude of the inter-shroud collision force and the number of collisions between adjacent blade shrouds are non-linearly related to the amplitude of the excitation force.

The Application of Neural Networks to Modular Arrangements of Predetermined Time Standards

To study the method of reducing the low-frequency vibration noise of tires, a passenger car tire (205/55R16) is taken as the research object. The dynamic grounding characteristics and vibration reduction mechanism of the cat’s paw pad are analysed. The research showed that the swing deformation characteristics of paw pads during the walking process of cats are one of the main ways to reduce the impact from the ground and achieve vibration reduction and silencing. To analyse the influence of tire grounding on noise, tire grounding is divided into five areas, and the characteristics of ten tire grounding areas are analysed through tests. Pearson correlation analysis is used to obtain the characteristics of the eight most relevant grounding parameters with tire noise, and multiple linear regression is conducted between the characteristics of the eight grounding areas. The product of the correlation coefficient and the average value of the characteristics of the ground contact area shows that the central area of the tire tread contributes the most to the tire noise. The swing deformation characteristics of the bionic cat paw pad are realized by setting the staggered side branch pipe groove in the centre of the tire, and the vibration reduction characteristics of the bionic tire are analysed using the finite element method. The results showed that when the tire rolls, the amplitude and fluctuation range of the ground radial excitation force acting on the bionic tire are reduced compared with the original tire, and the vibration and noise characteristics of the tire are improved.

Influence of the Side Branch Structure Pattern of the Imitation Cat's Claw Function on the Vibration and Noise of Tires

To study the method of reducing the low-frequency vibration noise of the tire, a passenger car tire(205/55R16) is taken as the research object. The dynamic grounding characteristics and vibration reduction mechanism of the cat's paw pad are analyzed. The research showed that the swing deformation characteristics of paw pads during the walking process of cats is one of the main ways to reduce the impact from the ground and achieve vibration reduction and silencing. To analyze the influence of tire grounding on noise, the tire grounding is divided into five areas, and the characteristics of ten tire grounding areas are analyzed through tests. Pearson correlation analysis is used to obtain the characteristics of the eight most relevant grounding areas with tire noise, and multiple linear regression is conducted between the characteristics of the eight grounding areas. The product of the correlation coefficient and the average value of the characteristics of the ground contact area shows that the central area of the tire tread contributes the most to the tire noise. The swing deformation characteristics of the bionic cat paw pad are realized by setting the staggered side branch pipe groove in the center of the tire, and the vibration reduction characteristics of the bionic tire are analyzed by using the finite element method. The results showed that when the tire rolls, the amplitude and fluctuation range of the ground radial excitation force acting on the bionic tire are reduced compared with the original tire, and the vibration and noise characteristics of the tire are improved.

Stabilization effect of dynamic stabilizer with different operation parameters

Dynamic stabilization operation can effectively improve the mechanical performance of ballast bed by using stabilizer. To improve the stabilization effect, a rigid-flexible coupling dynamics simulation model of the stabilizer-ballast bed system was established according to the actual structure of the stabilizer, and the effect of different operation parameters of stabilizer on the stabilization operation was analyzed. The simulation results showed that: the maximum value of lateral displacement response of the sleeper decreased with the increase in clamping wheel force normal angle, excitation force frequency and downforce; and increased with the increase in excitation force amplitude. The optimized operation parameters were obtained as follows: clamping wheel force normal angle 0°, excitation force frequency 18 Hz, excitation force amplitude 180 kN, downforce 60 kN. A vibration test bench simulating the stabilization operation process was built according to the working principle of the stabilizer, and the reliability of the simulation was verified by testing.

Effects of Asymmetric Vane Pitch on Reducing Low-Engine-Order Forced Response of a Turbine Stage

Asymmetric vane pitch is a key technique to suppress the forced response of downstream rotor blades. To address the problem of low-engine-order (LEO) excitation with high amplitude under an asymmetric configuration (half-and-half layout) widely recognized in the previous literature, we first apply the in-house computational fluid dynamics code Hybrid Grid Aeroelasticity Environment to perform full-annulus unsteady aeroelasticity simulations of the turbine stage, comparing the resonance response of rotor blades on different asymmetric configurations and analyzing the flow field at the vane exit, as well as the excitation force, modal force, and maximum vibrational amplitude on the rotor blades. Second, we reveal that the potential field of the vane row is the main source of the LEO excitation caused by asymmetric configuration on rotor blades, the vane wake and potential field jointly determine the LEO excitation strength of rotor blades, and the vane pitch difference ΔS can be used to regulate the strength of the LEO excitation. Finally, based on an in-depth understanding of flow physics under an asymmetric configuration, a more preferable and effective asymmetric configuration (non-half two-segment layout) is proposed. Our findings demonstrate that, with the proposed asymmetric configuration, the amplitude of the vane passing frequency was reduced by 48.32% compared to the uniform configuration; furthermore, the maximum vibrational amplitude of the three-nodal-diameter response of the rotor blade at the three-engine-order crossing decreased by 45.49% compared to the half-and-half layout. The non-half two-segment layout also significantly improves upon the half-and-half layout in terms of aerodynamic performance. The results presented in this paper provide a good theoretical basis for reducing blade vibration by applying asymmetric vane pitch in engineering practice.

Field testing of gravel-rubber mixtures as geotechnical seismic isolation

We present the results of the forced-vibration experiments performed at the large-scale prototype structure of EuroProteas founded on gravel-rubber mixture (GRM) layers acting as a means of Geotechnical Seismic Isolation (GSI). Three GRM with different rubber content per mixture weight (0%, 10%, and 30%) but the same mean grain size ratio were used as foundation soil. Each GRM-structure system was subjected to harmonic forces in a wide range of excitation frequencies and force amplitude. It was found that a 0.5 m thick GRM foundation soil layer with 30% rubber content can effectively isolate the structure. The strong effect of the rubber fraction was expressed in the detected period elongation and the dominating rocking component which leads to a more “rigid-body” response of the structure. Moreover, the developed base shear and base moment are significantly reduced regardless of the excitation frequency, while the increased damping of the system and the important energy dissipation demonstrate the effectiveness of the GRM foundation soil layer. Overall, the experimental results demonstrated that the use of GRM as a GSI system can be considered as a low-cost alternative seismic isolation technique.

Dynamic modeling and load transfer prediction of drill-string axial vibration in horizontal well drilling

A three-dimensional finite element dynamics model of drill-string is established considering dynamic friction model and buckling effect. The modified dynamics model is proved to have higher computational accuracy by laboratory experiment. A parameters study is conducted based on the dynamics model. Results show that the exciting force amplitude, drilling fluid density, axial force, friction coefficient, and drill-string dimension have significant effects on the friction reduction performance and effective propagation distance of axial vibration. A prediction model for vibration propagation distance is established, which facilitates efficient optimization of the axial vibration parameters in horizontal well drilling. This study can provide theoretical guidance for axial vibration to safely and efficiently reduce the sliding friction in exploitation of unconventional oil-gas reservoirs.

Nonlinear super-harmonic and sub-harmonic resonance analysis of the horizontal-axis wind turbine blades using multiple scale method including the pre-twist effects

The focus of this paper is on the nonlinear secondary resonance of HAWT blades under the super-harmonic and sub-harmonic excitations. To pursue this goal, a 3-DOF dynamic model of the blade is presented including the pre-twist effects and then the method of multiple scale (MS) method is employed to investigate the nonlinear secondary resonance. Nine different cases of secondary resonances including 3 (2) super-harmonic resonance cases of order 2 (3) as well as 2 (2) sub-harmonic resonance cases of order 1/2 (1/3) are detected. For each case, the amplitude-frequency and phase-frequency responses are derived analytically. The stability of each branch of the solution is evaluated through the Hartman-Grobman theorem and several saddle-node bifurcation points are revealed, considering the NREL 5 MW HAWT blade as the case study. Moreover, a parametric study is carried out to study the effects of damping, pre-twist, angular velocity, and excitation force amplitude. It is found that these parameters have a great influence on amplitude-frequency response (AFR) curves. Eventually, some comparisons are made to demonstrate the validity of the formulation and simulation results.