Vibration Transfer Function Research Articles

Theoretical and experimental study of active vibration control of rotating composite laminated beams using Fx-NLMS algorithm

In the study, an adaptive active vibration control model of rotating composite laminated beam is presented by using the filtered-x normalized least mean square (Fx-NLMS) algorithm, and the experimental study is carried out based on the closed-loop control system. The macro fible composite (MFC) patches is employed to contruct the closed-loop control system of rotating composite laminated beam. By considering peizoelectric coupling effect and the influence of rotating angular velocity, the novel analysis model of vibration transfer function of rotating composite laminated beam with MFC patches is established. The calculation accurancy of the theoretical analysis model is validated by the experimental results. The experimental and simulation studies demonstrate that the low-frequnecy vibration of rotating composite beam is effectively controlled by using the lightweight system. The excellent stability and convergence effect of the closed-loop control system are obtained in the experimental testings. Moreover, the filter orders and learning factor on the active vibration control effect of the rotating composite beam are also stuided and discussed. This work provides a novel appoach for the low-frequency vibration control of the rotating cantilever beams by employing lightweight system.

Exploring the Feasibility of Estimating Intraocular Pressure Using Vibrational Response of the Eye: A Methodological Approach.

This study addresses the limitations of current tonometry techniques by exploring vibroacoustic properties for estimating intraocular pressure (IOP), a key diagnostic parameter for monitoring glaucoma-a significant risk factor for vision loss. Utilizing vivo porcine eyeballs, we investigated the relationship between IOP and the nonlinear vibration transfer function ratio (NVTFR). Through applying varying vibration levels and analyzing responses with transfer function analysis and univariate regression, we identified a strong negative correlation between NVTFR and IOP, evidenced by a Pearson correlation coefficient of -0.8111 and significant results from generalized linear model (GLM) regression (p-value < 0.001). These findings indicate the potential of NVTFR as a vital indicator of IOP changes. Our study highlights the feasibility of using vibroacoustic properties, specifically NVTFR, to measure IOP. While further refinement is necessary for in vivo application, this approach opens new possibilities for non-invasive and patient-friendly IOP monitoring, potentially enhancing ophthalmology diagnostic techniques and providing a foundation for future research and development in this critical area.

Investigation of Frequency-Dependent Characteristics of Wire Rope under Tension Based on Transfer Function Method

Wire rope is a complex structure made by twisting wires of various sizes in the longitudinal direction. It is used to support or move engineering structures and is subject to various tensions. Dynamic properties are important parameters to evaluate the resistance to bending deformation and vibration reduction of various structures. They are affected by the magnitude of tension. In this study, an experimental method for measuring the frequency-dependent characteristics of wire rope under tension is proposed. The study analyzed flexural wave propagation employing a vibration transfer function. Experimental results showed that the transfer function of wire rope under tension is affected by tension and bending stiffness. The Newton–Raphson method was employed to numerically measure wavenumbers of the wire rope. The bending stiffness and loss factor were determined from the wavenumbers. Changes in the bending stiffness and loss factor as the tension increased were explained by the dynamic behavior of the structure under tension. As the tension increased, the bending stiffness increased, and the loss factor decreased. Hysteresis analysis indicated that the energy dissipation of wire rope is greater than that of a steel beam due to the friction between the wires. Statistical analysis confirmed a significant correlation between dynamic characteristics and tension in wire rope.

Experimental verification of a translation model of linear transfer function of ultrasonic vibrations with nonlinear wave modulation for detection of contact-type failures

Contact-type failures, such as the crack closure at the tip of a fatigue crack, closed delamination of composite materials, and loosening of bolted joints, are difficult to detect through nondestructive inspections using linear ultrasonic waves or vibrations. When low-frequency vibrations, such as environmental disturbances, operating vibrations, and vibrations excited by actuators, are applied to a structure with contact-type failure, the contact condition of the failure surface fluctuates in synchronization with the low-frequency vibration. The amplitude and phase of ultrasonic waves or vibrations through contact-type failure with fluctuating contact conditions are modulated in synchronization with low-frequency vibrations, that is, realizing nonlinear wave modulation. Previous reports have presented evaluation and localization methods of contact-type failure using amplitude and phase demodulation signals. In this study, amplitude and phase demodulations were affected by the change in the viscous damping of a structure. Therefore, the essence of nonlinear wave modulation was considered to be the fluctuation of the natural frequencies. In this study, a visualization experiment of the fluctuation of natural frequencies caused by nonlinear wave modulation was conducted. The time-varying transfer function was reconstructed by measuring the amplitude and phase demodulation signals with the change in the excitation frequency. Moreover, the translation model of the transfer function of the ultrasonic vibration with nonlinear wave modulation was evaluated.

System Identification and Fractional-Order Proportional–Integral–Derivative Control of a Distributed Piping System

The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration and reduce pipeline damage. First, a mathematical model of the distributed piping system was established using the finite element analysis method, and the characteristics of the distributed piping system were studied effectively. Further, the time-frequency domain parameter identification method was used to realise the system identification of the cross-point vibration transfer function between the brake and sensor, and the particle swarm optimisation algorithm was utilised to further optimise the transfer function parameters to improve the system identification accuracy. Therefore, a fractional-order PID controller was designed using the D-decomposition method, and the optimal controller parameters were obtained. The experimental and numerical simulation results show that the improved system identification algorithm can significantly improve modelling accuracy. In addition, the designed fractional-order PID controller can effectively reduce the system’s overshoot, oscillation time, and adjustment time, thereby reducing the vibration response of piping systems.

Estimation of Impact Loads Transmitted to Vibro-Ripper Housing Using Transfer Path Analysis

This study aimed to estimate impact loads delivered to vibro-ripper housing through link modules, together with loads transmitted in various directions. Housing vibration resulting from impact loads generated during the operating condition and frequency response functions were assessed by vibration and modal experiments, respectively. Vibration data and transfer functions were applied in a transfer path analysis (TPA) model to analyze the quantified impact loads transmitted through the key components of the vibro-ripper to its housing. Impact loads derived by TPA for different housing parts were compared with those in the tooth derived from load-cell measurements, validating the TPA method. As a result of the verification, the impact load calculated by the TPA method was 193.7 kN, whereas that from the striking force measured by the load cell was 220 kN, a difference of 12.3%. The results of this study may be important input values for numerical analysis in equipment design and can be used as key data for structural safety evaluation and optimization. In summary, this paper introduces the vibration-based TPA method and considers its applicability to construction machinery exposed to impact vibration and loads.

An Approach of Vibration Compensation for Atomic Gravimeter under Complex Vibration Environment.

Atomic gravimeter has been more frequently applied under complex and dynamic environments, but its measurement accuracy is seriously hampered by vibration-induced noise. In this case, vibration compensation provides a way to enhance the accuracy of gravity measurements by correcting the phase noise that resulted from the vibration of a Raman reflector, and improving the fitting of an interference fringe. An accurate estimation of the transfer function of vibration between the Raman reflector and the sensor plays a significant role in optimizing the effect of vibration compensation. For this reason, a vibration compensation approach was explored based on EO (equilibrium optimizer) for estimating the transfer function simplified model of a Raman reflector, and it was used to correct the interference fringe of an atomic gravimeter. The test results revealed that this approach greatly restored the actual vibration of the Raman reflector in a complex vibration environment. With a vibration compensation algorithm, it achieved the correction and fitting of the original interference fringe. In general, it dramatically reduced the RMSE (root mean square error) at the time of fitting and significantly improved the residual error in the gravity measurement. Compared with other conventional algorithms, such as GA (genetic algorithm) and PSO (particle swarm optimization), this approach realized a faster convergence and better optimization, so as to ensure more accurate gravity measurements. The study of this vibration compensation approach could provide a reference for the application of an atomic gravimeter in a wider and more complex environment.

A Vibration Compensation Approach for Atom Gravimeter Based on Improved Sparrow Search Algorithm

Atom gravimeter (AG) is a kind of high-precision absolute gravimeter based on atom interference, which can measure absolute gravitational acceleration. Vibration is one of the important factors which limits measurement accuracy. Vibration compensation is an effective method to reduce the impact of vibration on measurement accuracy and it is especially suitable for complex vibration environments. In this article, an improved vibration compensation method is proposed. Based on the simplified model of the vibration transfer function, the method searches for the optimal parameters through an improved chaotic sparrow search algorithm (CSSA) to effectively restore the real vibration of the Raman mirror and achieve the best compensation effect. The experimental results show that the improved method proposed in this article can achieve better compensation effectiveness in less calculation time than the previous methods. The modified atom interference fringe fitting uncertainty can attenuate by 70.21%, and the search time is reduced by nearly six times, effectively improving the accuracy and stability of the AG measurement. This method can correct the interference fringes in time when the environment changes, which provides a new idea for the design of the vibration compensation method considering dynamic gravimetry with AG.

Decoupling design and control of a spaceborne ultra–stable platform for vibration isolation and precise steering

This study concerns the problems of system coupling and large payload mass ratio and designs a spaceborne ultra–stable platform (SUSP) to isolate the payload from the satellite vibration and accomplish high–precision payload steering. First, the dynamic equilibrium of the SUSP and vibration transfer functions are determined. The decoupling condition is then derived to make the coupled vibration transfer functions equal to zero, and the SUSP multi–input multi–output (MIMO) system is decoupled into six single–input single–output (SISO) subsystems. Consequently, the natural frequency matrix can be easily designed to guarantee the vibration isolation performance and obtain identical feedback gain values. Subsequently, a steering controller based on a nominal system simplified by decoupled dynamic equilibrium was designed. The impact of a large payload mass ratio was estimated and eliminated by the improved disturbance observer (IDO) in the steering controller. After rigid–flexible coupling dynamic modeling and analysis, two simulation stages were implemented. The results of the isolation stage exhibit a –40 dB/dec roll–off of the vibration disturbance and a coupled response reduction of approximately –20 dB. The payload tracking error of the isolation–steering integrated stage is reduced to 0.13″ (0.1° circular trace), and the isolation performance is further improved.

Optimization of vibration characteristics and directional propagation of plane waves in branching ligament structures of wind models

To achieve multi-frequency vibration suppression and wave propagation modulation, eight branching ligament structures for wind models are proposed. Using lattice theory, dynamical model and finite element release method, the structures are verified to have multi-frequency bandgaps. By attaching a solid disc at the center of the model, the bandgap coverage of the structure is improved and the bandgap frequency is reduced. The modal analysis shows that the vibration of branch ligaments and border ligaments has a suppression effect on elastic waves. The phase constant surface, phase velocity and wave propagation direction plots at specific frequencies are calculated to verify the directional and regional nature of wave propagation. And the good correspondence of group velocity and wave propagation finite element simulation results at specific frequencies. Finally, the calculated bandgap frequency range is compared with the vibration transfer function, and the two agree well. And the stress cloud diagram also shows that the optimized structure has an excellent vibration suppression capability. The innovatively designed structure has the combined advantages of light weight, ease of fabrication, wide frequency and low frequency vibration control, while the integrated in-plane wave analysis provides the theoretical basis for structural optimization.

Vibration characteristics and elastic wave propagation properties of mirror-symmetric structures of trichiral ligaments

In this paper, two mirror-symmetric structures of three-chiral ligaments are proposed. The lattice theory and Bloch's theorem are combined to construct a theoretical model of the structures, and a finite element method is used to demonstrate that the structure has an ultra-wide bandgap coverage and the lowest bandgap of the new structure with a central entity can be reduced to 316.4 Hz. The rotational resonance and the offset resonance of the central entity of the trichiral ligament are closely related to the opening of the bandgap by vibration analysis. In addition, both the vibration transfer function and the stress cloud demonstrate that the structure is extremely capable of attenuating vibration and noise, with a maximum attenuation peak of − 380. The directional and regional properties of the elastic wave propagation are demonstrated by simulations of the phase constant plane, phase velocity, wave propagation direction diagram, group velocity and wave propagation path. This structure has the combined advantages of light weight, easy fabrication, broadband and low frequency vibration and noise control, while the integrated wave propagation analysis provides theoretical support for structural and bandgap optimization.

Experimental Study on the Vibration Transfer Function of a Small Autonomous Underwater Vehicle

This paper presents the experimental results about vibration characteristics of a small autonomous underwater vehicle (AUV) named OKPO 300. The autonomy of AUVs leads to the increased use of AUVs in scientific, military, and commercial areas because their autonomy makes it possible for AUVs to be utilized instead of humans in hazardous missions such as mine countermeasure missions (MCMs). It is impossible to use devices with electro-magnetic waves for gathering information in an underwater environment. Only sonar systems that use sound waves can be utilized underwater, and the performance of sonar can strongly affect the autonomy of AUVs. Since a thruster system that combines a motor and propeller in a single structure is widely used as the propulsion system of an AUV and is mounted on the outside of the AUV’s stern, the vibration generated by the thruster system can be transferred throughout the shell of the AUV from the stern to the bow. The transferred vibration can affect the performance of various sonar systems that are installed in the AUV such as side-scan sonar or forward-looking sonar. Therefore, it is necessary to identify the effect of the transferred vibration of the AUV on the sonar systems. Even if various numerical methods were used to analyze the vibration problem of surface ships, it would be hard to apply numerical methods of the surface ships to identify the vibration phenomena of an AUV because of the underwater environment. In this work, an experimental study with OKPO 300 and an impact hammer was carried out to analyze vibration features of an actual small AUV in the air. Based on the experimental results, the frequency response function of vibration is presented. Based on the experimental results of this study, the natural frequency of OKPO 300 was confirmed, and the possibility of estimating the vibration characteristics of AUV using the transfer function method was shown.

Experimental study on vibration response of wooden house façade to low-frequency outdoor sound

Generally wooden house has low sound insulation performance for low-frequency outdoor noise due to the lightweight façade wall system. Moreover, the sound insulation performance is caused by the vibration responses of window and wall systems, that are strongly coupled with normal modes in a room. In order to clarify the complicated phenomena, field measurements of vibration characteristics are conducted for a test house with Japanese traditional wooden structure, under the cases with single/double window systems. As outdoor sound source, low-frequency band noise from 25 Hz to 160 Hz is emitted from a subwoofer, and vibration acceleration is measured on each element, such as window glazing, interior walls, floor and ceiling. From the analysis of measured vibration transfer functions and indoor sound pressure distribution, the vibration characteristics of the whole coupled system are discussed, especially on the effect of different window systems.

Flexural vibration bandgaps in one-dimensional periodic rods with tri-wing rhombus ligament resonators

Structural stiffness of phononic crystals (PnCs) can affect their bandgap properties. It thus needs to consider stiffness in the design of the unit cell of a PnC. In this paper, a local resonant (LR) rod composed of tri-wing rhombus ligament (TRL) resonators arranged periodically within a common hollow rod is proposed to create a low-frequency flexural vibration bandgap. The dispersion relations, mode of resonances and vibration transfer function are studied using a finite element method. Low-frequency forbidden bands can be effectively shifted by changing the resonator geometries. In addition, both numerical simulations and sample test are conducted to verify the low-frequency bandgap. The results show that the hollow rod with TRL resonators can create a low-frequency flexural vibration bandgap as well as have high support structure stiffness.

Research on acoustic reconstruction methods of the hull vibration based on the limited vibration monitor data

The prediction of hull vibration response is the basis for the quantitative control of cabin noise and underwater radiated noise, which has an important engineering value to obtain vibration characteristics accurately. In this paper, a new method is proposed to reconstruct hull vibration by some monitoring data in low frequencies. The hull vibration response is reconstructed by the monitoring data and the transfer function, and the ill-posed problem of inversion for the transfer function matrix is solved by the total least-squares regularization. A P-GRU (Peak-based Gated Recurrent Unit) neural network correction model is proposed to improve the prediction accuracy of vibration response. Taking a certain cabin structure as an example, some research such as the hull vibration data monitoring, the vibration transfer function calculation, vibration response reconstruction, and correction based on experimental data were carried out, and the simulation calculations and verification of experiment models were obtained. The multi-parameter comprehensive method is adopted to quantitatively evaluate the results between the simulation and the experiment. The results show that the acoustic reconstruction results are in good agreement with the experimental data. The overall level error is within 3 dB, the main peak value correlation coefficient is above 0.9, and the main peak difference is within 4 dB. The mechanism of the rapid and accurate prediction of the low-frequency vibration for the hull based on limited monitoring data is discussed by using a semi-physical simulation method combining the simulation calculation, vibration monitoring, and machine learning. The problem of phase asynchrony was solved, and strong support was provided for the construction of the ship's acoustic digital twin.

A Hybrid Calculation Method of Electromagnetic Vibration for Electrical Machines Considering High-Frequency Current Harmonics

This article proposes a hybrid evaluation method of electromagnetic force and vibration for electrical machines considering high-frequency current harmonics caused by the inverter. First, the permeance and armature magnetomotive force (MMF) is calculated based on the virtual MMF and the slot matrix. Then, the air-gap flux density and electromagnetic force construction process under arbitrary current is thoroughly studied. The vibration transfer function is obtained by utilizing the modal analysis and the modal test. Finally, the vibration can be calculated according to the modal superposition method. By applying this method to an interior permanent magnet machine, it can significantly reduce the computation efforts compared with the multiphysics procedure due to the extensive use of the finite-element method. In addition, the accuracy of this method is validated by conducting an experimental study.

Gearbox fault diagnosis under nonstationary condition using nonlinear chirp components extracted from bearing force

The main challenges in gearbox condition monitoring and fault diagnosis are the heavy noises caused by harsh operating environments and the complicatednonstationary condition during the runtime. It is extremely difficult and even impossible to obtain sensitive faultcharacteristics through direct measurements. Thus, it is ofgreat significance of faultcharacteristic inversion based on the structure vibration transfer paths for complicated mechanical systems fault diagnosis. This paper proposes a gearbox fault diagnosis method under nonstationary condition through using nonlinear chirp components extracted from bearing force (BFNCC). In the proposed method, the bearing dynamic forces are first identified based on the vibration transfer function matrix, and the intrinsic signal components are then decomposed through a nonlinear chirp mode decomposition method. The proposed method improved the quality of vibration signals by removing the effect of the structure vibration transfer paths. In comparison with order tracking, the BFNCC is capable of clearly reflecting the magnitude increase phenomenon under gear fault condition. Numerical simulation and experimental studies show that the proposed method is effective for gear fault diagnosis under nonstationary condition. The proposed method is demonstrated to be superior to the existing approaches and robust to the location of measuring points, and thus shows potential in machinery fault diagnosis under the interference of complicated structure transfer paths.

An equivalent NVH model of vehicle door seal strip and its application in door vibration problem

The vehicle door seal strip has complex dynamic characteristics and is a critical component in the vibration and sound transmission of the vehicle system. However, in noise, vibration, and harshness (NVH) analysis, the seal strip is commonly simulated as a linear spring model, which results in inaccurate vibration and sound prediction. Thus, it is necessary to propose an alternative model, which allows characterising the complex dynamic behaviour of the seal strip accurately. In the present study, an overlay material model of rubber was encoded and embedded in ABAQUS with the UMAT subroutine. The overlay model was used in a seal strip finite element model validated by the quasi-static and dynamic measurements. By analysing the effects of frequency, amplitude, and pre-compression on the dynamic stiffness of a seal strip, an equivalent NVH model consisting of spring and damping elements was proposed. The proposed model was validated by comparing the simulated mode and vibration transfer function results with experimental ones. Using the spring model, the deviations of vibration transfer function with the experimental results are 37% and 8.3% at the first and second peaks, respectively. The corresponding deviations are only 4.6% and 2.6% employing the proposed model, demonstrating that the proposed model provides higher accuracy than the spring model. With the assist of the proposed model for vibration transmission analysis, a typical door vibration problem was successfully addressed, which proved the effectiveness of the equivalent model in engineering practice.

Dynamic characteristics of single door electrical cabinet under rocking: Source reconciliation of experimental and numerical findings

Seismic qualifications of electrical equipment, such as cabinet systems, have been emerging as the key area of nuclear power plants in Korea since the 2016 Gyeongju earthquake, including the high-frequency domain. In addition, electrical equipment was sensitive to the high-frequency ground motions during the past earthquake. Therefore, this paper presents the rocking behavior of the electrical cabinet system subjected to Reg. 1.60 and UHS. The high fidelity finite element (FE) model of the cabinet related to the shaking table test data was developed. In particular, the first two global modes of the cabinet from the experimental test were 16 Hz and 24 Hz, respectively. In addition, 30.05 Hz and 37.5 Hz were determined to be the first two local modes in the cabinet. The high fidelity FE model of the cabinet using the ABAQUS platform was extremely reconciled with shaking table tests. As a result, the dynamic properties of the cabinet were sensitive to electrical instruments, such as relays and switchboards, during the shaking table test. In addition, the amplification with respect to the vibration transfer function of the cabinet was observed on the third floor in the cabinet due to localized impact corresponding to the rocking phenomenon of the cabinet under Reg.1.60 and UHS. Overall, the rocking of the cabinet system can be caused by the low-frequency oscillations and higher peak horizontal acceleration.

Effects of Strongbacks and Strappings on Vibrations of Timber Truss Joist Floors

It is well known that the vertical vibrations of lightweight timber floors would cause discomfort to the occupants. As a new kind of flooring system, the metal‐plate‐connected timber truss joist floors were developed due to their larger spans and easier crossing of pipes and cables after sawn timber and I‐joist floors. In this paper, the vibration modes and transfer functions of sixteen metal‐plate‐connected timber truss joist floors over a nominal span of 6 m were determined experimentally to measure the changes in vibration frequencies and transmissions obtained after the installation of strongbacks and strappings. The results showed that the fundamental natural frequencies of the metal‐plate‐connected timber truss joist floors at a 400 mm joist spacing were about 15 Hz, while the frequencies of the floors at a 600 mm joist spacing were about 12.5 Hz. The bracing elements of the strongbacks and strappings mainly enhanced the system stiffness in the across‐joist direction of the flooring system, but they did not govern the fundamental natural frequencies of the floors and just changed the spacing of adjacent natural frequencies. The bracing elements as secondary elements of the floors also altered the vibration transmission paths in the across‐joist direction. The frequencies where the stronger vibration transfers happened in the direction perpendicular to floor joists were generally above 15 Hz. Proper installation measurements of bracing elements in practical control need to be taken to alleviate the vibration response intensity at the targeted locations and frequencies.