Frequency Response Function Method Research Articles

Identification of dynamic coefficients of gas foil bearings by simulated excitation based on coupled fields

The dynamic coefficients (dynamic stiffness coefficient and dynamic damping coefficient) of gas foil bearings (GFBs) are important for transient dynamics calculation and stability analysis of the GFBs-rotor system. Although the perturbation method can be used to calculate the dynamic coefficients, it can only consider a single whirl ratio. Moreover, the whirl ratio is assumed and not practical. Therefore, this paper proposes an identification method of dynamic coefficients of GFBs by simulated excitation. Firstly, based on single journal-single GFB model considering gas-structure interaction by coupled fields, harmonic excitations were applied to the rotor to obtain the shaft orbit. Next, frequency response function method and equivalence coefficient method were used to identify dynamic coefficients. The former method is suitable for the case where response and excitation are same frequency, namely linear problem. The latter method is fit for the situation in which the response has multiple frequency components, namely nonlinear problem. Finally, examples were carried out, and the results from different methods were compared and analyzed. This research work lays a theoretical foundation for the design of the GFBs-rotor system.

Damage Identification of Rotating Blades Based on Fuzzy C-Means and Frequency Response Function Curvature Methods

Rotor blades are one of the key components of helicopter. If the blades are damaged, the safety and reliability of the helicopter will be seriously affected. Therefore, it is necessary to investigate the damage identification of the rotating blades. In this paper, a rotating cantilever beam is used to model the rotor blade. Based on the assumed mode method and Hamilton’s principle, the equation of motion is formulated, and the correctness of the model is verified by numerical and experimental studies. Altogether, two methods are used to identify the damages on the blade. The first one is the cluster analysis method based on the fuzzy C-mean theory. In order to reduce the dimension of the signal features, the singular value decomposition is introduced. The second method is the curvature of frequency response function method that can be used to determine the exact position of damages. Simulation results show that one can use fuzzy C-mean method to determine whether there is damage on the blade firstly and then determine the exact position of the damage through the curvature of frequency response function method.

Evaluation of Pedestrian Comfort for a Footbridge with Hinged Piers

To study the standardized evaluation method of vibration comfort of pedestrian bridges, the effect of the transient response term is ignored based on the generalized single degree of freedom (SDOF) method with reference to the American Institution of Steel Construction inc (AISC 11) specification. The resonance conditions between the crowd and the bridge structure are also considered, and the pedestrian bridge structure is simplified to an SDOF system. Then, the peak acceleration of the structure under crowd excitation is directly calculated using the generalized crowd load, and the comfort evaluation is carried out according to the German EN03 code and the Chinese code. For a new pedestrian bridge with hinged piers, human-induced vibration tests were carried out to obtain the structural acceleration time response data under various crowd load excitation conditions, and the acceleration values calculated with the numerical simulation method, the frequency response function method, the generalized SDOF method, and the proposed method were compared with field measurements. The results show that for the normal excitation condition with a crowd density less than or equal to 0.2 person/m2, the acceleration maximum error for the proposed method is between 4.22% and 13.28%. The error is only 6.35% compared with the finite element simulation results. The method can derive peak acceleration by performing only modal tests, eliminating errors caused by different testers and errors due to deflection measurements. It saves considerable time cost and economic cost, and improves the speed of pedestrian bridge comfort evaluation. Therefore, the method proposed for the first time in this study can accurately assess the human-caused vibration comfort of pedestrian bridges with articulated piers. Although the hinged-pier and column steel pedestrian bridge meets the code requirement of a vertical first-order frequency greater than 3 Hz, it is recommended to add TMD vibration damping measures to the bridge in order to improve pedestrian comfort.

Investigation of Modal Identification of Frame Structures Using Blind Source Separation Technique Based on Vibration Data

This paper investigates system identification algorithms for modal identification of frame structures, such as a suspension bridge and an overhead transmission line-crossing frame, using ambient vibration measurements. The modal identification procedures include two novel blind source separation (BSS) algorithms, complexity pursuit method (CP) and generalized eigen decomposition method (GED), based on modern signal processing technology. Here, the frequency response function (FRF) method is introduced as an important reference to verify the effectiveness of the CP algorithm and GED algorithm. The effectiveness and accuracy of both types of algorithms are verified by numerical simulations and experiments on a suspension bridge. In addition, an engineering application of these two BSS methods is successfully implemented in an overhead transmission line-crossing frame. The results show that the two novel BSS learning rules (CP and GED) are capable of successfully identifying modal parameters of the civil structure under ambient excitation.

Research on Digital Modeling Method of Triaxial Vibration System

To meet the demand of providing basis for improving triaxial vibration system, it is necessary to extract the overall Frequency Response Function (FRF) matrix of triaxial vibration system from its digital model. The mechanical parts of triaxial vibration system is connected tightly which satisfy rigid connection assumption. The Jetmudsen FRF method is used to construct the overall frequency response function matrix of triaxial vibration system. The electrodynamic shaker (referred to as the shaker) is an important component of the three-axis vibration system, and its function is to provide the test bench with an excitation force in a certain direction. Therefore, it is necessary to define a large number of internal nodes on the shaker. The FRF matrix of shaker (including origin FRF matrix of internal nodes and joints, cross-point FRF matrix of internal nodes and joints) should be obtain to carry out the construction of overall FRF matrix of triaxial vibration system. It is difficult because the size of FRF matrix of shaker is too large. So a way to simplify the distributed loads exerting on the structure into multi-point concentrated loads is proposed, it can be used to obtain the simplified digital model of the electrodynamic shaker. Based study above, the overall frequency response function matrix of the triaxial vibration system is obtained, and the digital modeling of the triaxial vibration system is completed.

Modal Test and Model Modification of the Rotating Parts of a Self-propelled Antiaircraft Gun

The rotating parts of a self-propelled antiaircraft gun is taken as the research object, the single point excitation and multi-point response frequency response function method were used to test the experimental mode. At the same time, the finite element simulation model is established, and the frequency and mode of vibration are obtained. Combined with the modal test and analysis of the rotating parts, the stiffness of the connection between the rotating parts and the turret is selected as the optimization parameter. The numerical simulation model was optimized and modified by comparing the experimental and simulation modes and combining with the sensitivity analysis of the connection parameters, the correction variable with the higher sensitivity of the parameters to the results was selected. After optimization, the error between the first order calculation frequency and the test frequency is reduced from 8.61% to 1.13%, it is shown that the simulation model optimized by parameters can better reflect the physical characteristics of the real structure.

Model and experimental analysis of a rotor rig dynamics with time-varying characteristics

This work is motivated by the rapid developments of a broad range of electrically powered vertical take-off and landing vehicles which frequently feature two-bladed thrust generating rotor propulsion units. The interaction between a two-bladed rotor and the surrounding structure causes an emergence of the complex dynamics specific to the systems with the time-varying characteristics. This paper introduces a new rotor-structure test rig aimed to support the focused analyses of such systems. The test rig is realized as an idealised configuration consisting of a flexible slender cantilevered beam-like support structure which accommodates a single brushless electrical motor and a two-bladed propeller at its free end. Whilst retaining relative simplicity and scalability, this system allows analysis of complex flexible structure-propeller coupled phenomena, some of which are evidenced in this study. To form a compact and fully defined low-order model suitable for the computationally efficient in-vacuo analysis presented here, a Lagrange-based energy formulation is used to derive the equations of motion. The frequency and time domain techniques, including the complex modal analysis of the linear time-periodic systems, frequency response function and Udwadia-Kalaba method, are used to describe and explain the observed dynamics. The predicted dynamic changes, their impact on the modal interactions and the validity of the finite-sized time-invariant approximating system are successfully demonstrated through correlation with the experiment in the frequency range which encompasses the first four modal families and the rotor speed range spanning up to the first observed experimental instability. Specifically, the study confirms the occurrence of the modal veering and lock-in phenomena, modal splits as well as the strong dominance of the 0th order frequency modulation clusters in the structural response. The results presented in this work show that the proposed experimental platform represents a useful minimal dynamic system with the behavioral characteristics of high significance for the design of novel electrically powered and propeller-driven aircrafts.

Frequency response function method for dynamic gas flow modeling and its application in pipeline system leakage diagnosis

Timely diagnosing leakages is significant for the safety and reliability of gas pipeline systems, where an efficient and accurate modeling and solution method is critical to identify the leakage rate and location. Here, a frequency response function-based modeling method for dynamic gas flow in pipelines is proposed. Based on the frequency-domain flow resistance of pipelines and Fourier Transform, original dynamic flow model is transformed into the frequency response function model consisting of linear lumped transmission constraints, nonlinear frequency response function, and nonlinear pipeline resistance characteristics, which are efficiently solved according to their different mathematical properties. Dynamic simulation cases show the proposed modeling and solution method greatly improves the computational efficiency keeping the accuracy. Besides, taking the difference between measurements and simulation results under leakage condition as objective, an iterative bilayer optimization algorithm is proposed based on the mathematical categorization of system constraints to efficiently diagnose leakages. Four leakage diagnosis cases in single pipeline and pipeline network with measurement noise and transient boundary conditions are studied to validate the leakage diagnosis method. Absolute location errors in the results are all within 1%, demonstrating the accuracy and robustness of the proposed method for single leakages and multiple leakages occurring successively or simultaneously.

Pyroshock Response Prediction of Spacecraft Structure in Wide Frequency Domain Based on Acceleration FRF

The initiating explosive shock environment of an aerospace mission has the characteristics of instantaneity, high amplitude and a wide frequency domain. An improved method based on the acceleration frequency response function (FRF) and virtual mode synthesis method (VMSS) is proposed to predict the pyroshock response of a spacecraft structure in a wide frequency domain. Firstly, the statistical energy analysis (SEA) model of the spacecraft structure was established, and the FRF and modal density of the model were obtained. Then, the paper explains how, due to the small number of modes in the low-frequency band, the calculation results of the SEA method in the low-frequency band were not accurate enough. The FRF of the SEA model in the low-frequency band was modified by an FRF test of the structure. Finally, the shock response spectrum (SRS) was obtained based on the VMSS and the modified FRF. A shock experiment on the spacecraft structure was conducted by using the shock experiment system, which is based on a light-gas gun. The accurate shock force function and acceleration response results were obtained. The numerical results based on the improved method are in line with those in the experiment. This verifies that the novel method can better grasp the response characteristics of the structure in the broadband domain. The novel method effectively improves the response prediction accuracy of the SEA model in the relatively low-frequency band. While ensuring the computational efficiency, more accurate shock response results in a wide frequency domain were obtained. The novel method presented in this paper provides support of numerical analysis for pyroshock response prediction of spacecraft structure in a wide frequency domain.

Estimation of Lamb wave propagation by means of Fourier spectral frequency response function

ABSTRACT Considering the frequency dispersion and the scale sensitivity in wave propagation, the central frequency and bandwidth should be carefully selected in Lamb wave-based structural health monitoring. These crucial parameters are hardly determined without the prior knowledge. Therefore, massive trials should be conducted before the formal test. A Fourier spectral Frequency Response Function (FRF) method is proposed to address this problem. As the FRF contains wide-band information on the relationship between excitation and output, the Lamb wave responses in a wide frequency range can be estimated by using an arbitrary virtual input within the frame of single FRF test, being free from the massive experimental works. The theoretical FRF can be obtained from the unit impulse response of a linear system, but this path is impracticable due to the difficulty of exciting the ideal impulse. Considering the integral relationship and Fourier differential properties between step excitation and the ideal impulse, a robust approximation of wave signal by FRF is developed. Synthetic data tests and experiments both verified that the present method can accurately extract the response in isotropic and anisotropic materials for the specifically designed excitation signal in a wide parameter range.

Dynamic testing and numerical simulation of human-induced vibration of cantilevered floor with tuned mass dampers

The vibration control of a cantilevered floor with tuned mass dampers (TMDs) was investigated using dynamic testing and numerical simulation methods to better satisfy the structural serviceability requirement. The human-induced vibration response under walking and running conditions were firstly presented based on a series of dynamic testing with a single pedestrian and groups of pedestrians. A fast-evaluated frequency response function (FRF) method suggested by AISC Design Guide 11 was also used to evaluate the vibration response and further verified by the dynamic testing. A passive TMDs system was applied to reduce the vibration response; the vibration control of the cantilevered floor with TMDs was also evaluated by the dynamic testing with a single pedestrian and groups of pedestrians. The results showed that the maximum acceleration response of the cantilevered floor under the running load exceeded the limit, which was on average nine times that of the values under the walking condition. The FRF method could provide a fast and conservative vibration evaluation, in which the maximum acceleration response was 26% higher than that from dynamic testing. The acceleration response was significantly reduced with a maximum reduction effect of 64% after the installation of TMDs, resulting in satisfactory vibration serviceability of the cantilevered floor; the numerical simulation of that agreed well with the dynamic testing results. The vibration control of the cantilevered floor as a case study can serve as reference for the application of TMDs.

Identifikasi Kerusakan Altenator Daihatsu Luxio dengan Metoda Fungsi Respon Frekuensi

Gasoline engines should sound soft, even tend to be minimal. But when the symptom of a rough sound emerged from the engine room, it was even more like a diesel sound that was quite loud. So that many customers have complained about the rough sound of their vehicle's engine when the engine is started, from the results of the initial inspection that was carried out as a result of the rough noise coming from the bearings on the alternator which experienced wear due to reduced lubrication in the bearings. This requires that preventive maintenance checks on the alternator are a must in the automotive world. On the basis of the above, in this paper, we will discuss the damage to the Daihatsu Luxio alternator with the frequency response function (FRF) method. Damage to the alternator can be seen at point A and point D, seen with a frequency at 1500 Hz in a damaged condition, while in good condition there is no frequency at 1500 Hz. At points B, C, E, and F have the same vibration pattern between the damaged and undamaged conditions. Visually checking results show that the bearing component at point A, it is known that the ball bearing is peeling. This results in a rough spinning of the bearing and makes the alternator make a rough noise while working.

The analysis and design of nonlinear vibration isolators under both displacement and force excitations

In this study, a novel criterion known as the comprehensive transmissibility is proposed to estimate the isolation performance of nonlinear isolation systems under complex loading excitations. A combined quasi-zero-stiffness (QZS) isolator is enumerated, and the comprehensive performance of other common isolator systems and the existing QZS system is analyzed. Based on the normalized differential equations of the isolation system, the isolation performances of different isolation systems are studied by using the comprehensive transmissibility criterion, showing that the combined QZS isolator has better isolation performance than others. In addition, the output frequency response function (OFRF) representation of the comprehensive transmissibility is derived, and the optimal design of the QZS isolation system is developed by using the OFRF. The simulation results demonstrate that the design can meet the requirements of the vibration isolator with both the force and displacement excitations and is promised to be applied to the design of nonlinear isolation systems in engineering practice. To solve the issue of the analysis and design of nonlinear vibration isolation systems under multi-excitation, a new criterion known as comprehensive transmissibility is proposed. Based on the comprehensive transmissibility, the isolation performance of the combined vibration isolation system is analyzed, and the output frequency response function (OFRF) method is applied to conduct the design of the isolation system.

Nonlinear Magnetic Field Vector Control With Dynamic-Variant Parameters for High-Power Electrically Excited Synchronous Motor

Identifying the air-gap flux is a prerequisite for realizing the decoupling control between the air-gap flux and torque in an electrically excited synchronous motor (EESM) vector control system. For the nonlinear problem of EESM, the frequency response function method is introduced to analyze the air-gap flux voltage and current models’ sensitivity to the motor parameters in this article. A dynamic air-gap current model for EESM based on the equivalent reaction inductance is proposed to solve the parameter dynamic-variant problem caused by the nonlinear magnetic distribution of the EESM. Meanwhile, the comparative analysis of effectiveness caused by linear and nonlinear flux identification errors in the hybrid air-gap flux model of vector control system is carried out. The effectiveness of the nonlinear dynamic model has been verified by simulation and experimental results, which shows its excellent control performance.

Improved Modal Damping Characterization for Small-Scale Heliogyro Blades

The heliogyro solar sail maneuvers by actuating high-aspect-ratio blades at their root with sinusoidal pitch profiles, producing spin-averaged forces and moments. The lightweight blade material has little inherent damping, requiring active control to attenuate blade vibration caused by maneuvering. Paradoxically, some amount of inherent damping at the blade’s higher-frequency modes is needed to add damping to the larger-magnitude low-frequency modes, and so the control design’s robustness depends on the accuracy of the blade damping model. Therefore, characterization of blade damping is critical for increasing the Technology Readiness Level for the heliogyro. This paper describes damping characterization tests performed on small-scale heliogyro blades hanging in a high-vacuum chamber, the closest analog possible for centrifugally loaded blades in space. Improvements to the measurements and a new modal damping algorithm, which the authors call the incremental and reduced frequency response function method, allowed separate flap and twist damping ratios to be calculated for the first three modes of these lightly damped blades to within ±2% error. This unprecedented precision enables definitive conclusions that the residual air damping is insignificant and that an assumption of a linear viscous torsional blade damping model is insufficient for the design of a robust proximal blade twist feedback controller.

Processing method and governing parameters for horizontal wave impact loads on a semi-submersible

Semi-submersible platform has been widely used in offshore oil exploitation due to its excellent performance, but can be attacked by wave impact loads in extreme ocean environments. Determining wave impact loads accurately is of great significance to the design and operation of offshore structures. An experimental study was carried out to investigate the critical governing parameters for the horizontal wave impact loads on a semi-submersible. The wavelet denoising technique and the frequency response function method are employed successfully to remove the effect of noise and dynamic contamination from the experimental data. The strongly nonlinear characteristics of the wave impact load are demonstrated. The results show that wave impact events are governed by the upwell height and upwell velocity. Most major wave impact events occur where both the two parameters are large, and the upwell velocity is more dominant in the wave impact process. In general, larger parameters tend to result in larger peak pressures and higher probabilities of wave impacts. The motion behaviors of the platform are benefit to reduce the occurrence probabilities of wave impact events and maximum impact pressures, owing to the escape velocities following the wave direction and the rotations leading to the above-water structure away from the waves. The insights given in this study provide a motivation and foundation for developing a sophisticated prediction model of the wave impact load on floating platforms.

Analysis and optimal design of a vibration isolation system combined with electromagnetic energy harvester

This work investigates a vibration isolation energy harvesting system and studies its design to achieve an optimal performance. The system uses a combination of elastic and magnetic components to facilitate its dual functionality. A prototype of the vibration isolation energy harvesting device is fabricated and examined experimentally. A mathematical model is developed using first principle and analyzed using the output frequency response function method. Results from model analysis show an excellent agreement with experiment. Since any vibration isolation energy harvesting system is required to perform two functions simultaneously, optimization of the system is carried out to maximize energy conversion efficiency without jeopardizing the system’s vibration isolation performance. To the knowledge of the authors, this work is the first effort to tackle the issue of simultaneous vibration isolation energy harvesting using an analytical approach. Explicit analytical relationships describing the vibration isolation energy harvesting system transmissibility and energy conversion efficiency are developed. Results exhibit a maximum attainable energy conversion efficiency in the order of 1%. Results suggest that for low acceleration levels, lower damping values are favorable and yield higher conversion efficiencies and improved vibration isolation characteristics. At higher acceleration, there is a trade-off where lower damping values worsen vibration isolation but yield higher conversion efficiencies.

IMPLEMENTATION OF FREQUENCY RESPONSE FUNCTION ON TAPPER BEARING MAINTENANCE

Bearing acts as a pad that supports a shaft to rotate without excessive friction, hold the radial load and maintain the motion towards the left and right shafts (Thrust Load) when turning together. Due to frequent taper bearing damage to the wheels, predictive maintenance is therefore necessary. One of the predictive maintenance methods widely used today is vibration analysis. The principles of vibration-based bearing damage detection using the Frequency Response Function (FRF) method will be shown in this paper. Harmonics signal is given to the bearing surface in a vertical or perpendicular direction to the taper bearing surface. The vibration response measurement was carried out on three axes (x, y, and z). The results of this study indicated the ability of FRFs to predict any damage on the bearing taper.

Analytical and experimental investigation on the free vibration of a floating composite sandwich plate having viscoelastic core

This paper focuses on the free vibration analytical solution of a composite sandwich plate consisting of woven carbon laminated faces and a viscoelastic foam core. In addition to the dry condition, a case of floating on bounded water is considered for the sandwich plate not only in analytical work but also in verification experiments. The equations of motion for the first-order shear-deformation plate in contact with the fluid are derived by using Hamilton's principle, and analytically solved using Navier's procedure. Bounded water boundary conditions and velocity potential function are used to describe the fluid motion. The viscoelastic properties of a marine PVC foam core are extracted from dynamic mechanical analysis. Frequency response function (FRF) method is applied in modal testing for measuring the natural frequencies of the dry and wet sandwich plates. Experimental results demonstrate the validity of the analytical results. The effects of the foam core behavior, core thickness, plate dimension ratio, and the fluid density on the natural frequencies are examined and discussed. The decrease of the fundamental mode natural frequency with the presence of the viscoelastic foam core is more prominent for the dry sandwich plate with respect to the wet one already damped by water.

Detailed Study on Breaking Wave Interactions With a Jacket Structure Based on Experimental Investigations

Wave breaking is one of the major concerns for offshore structures installed in shallow waters. Impulsive breaking wave forces sometimes govern the design of such structures, particularly in areas with a sloping sea bottom. Most of the existing offshore wind turbines were installed in shallow water regions. Among fixed-type support structures for offshore wind turbines, jacket structures have become popular in recent times as the water depth for fixed offshore wind structures increases. However, there are many uncertainties in estimating breaking wave forces on a jacket structure, as only a limited number of past studies have estimated these forces. Present study is based on the WaveSlam experiment carried out in 2013, in which a jacket structure of 1:8 scale was tested for several breaking wave conditions. The total and local wave slamming forces are obtained from the experimental measured forces, using two different filtering methods. The total wave slamming forces are filtered from the measured forces using the empirical mode decomposition (EMD) method, and local slamming forces are obtained by the frequency response function (FRF) method. From these results, the peak slamming forces and slamming coefficients on the jacket members are estimated. The breaking wave forces are found to be dependent on various breaking wave parameters such as breaking wave height, wave period, wave front asymmetry, and wave-breaking positions. These wave parameters are estimated from the wave gauge measurements taken during the experiment. The dependency of the wave slamming forces on these estimated wave parameters is also investigated.