Frequency Domain Response Research Articles

Numerical study on the dynamic characteristics of the drive shaft system with diaphragm crack

The diaphragm coupling is widely used in the drive shaft system, which suffer from the crack at the waist of the diaphragm in long-term and high-speed working environments. However, the effect of the diaphragm crack (DC) on the dynamic characteristics of the drive shaft system. To solve the above issues, this paper researched the effect of the DC on the dynamic characteristics of the drive shaft system. The time-varying stiffness of the diaphragm group (DG) with crack was calculated considering friction. The calculation results indicated that the DC causes a decrease in the stiffness of the DG and introduces multiple higher-order harmonic components into the stiffness of the DG. The effect of the DC on the dynamic characteristics of the system was conducted. The accuracy of the system model is verified by comparing the critical speed results of the software and theory. The DC caused 2×, 4× super-harmonic resonance phenomenon. Meanwhile, the frequency-domain response of the system included a significant 2× super-harmonic component and also a significant 4× super-harmonic component at low speed. The super-harmonic components in the system response are introduced by the higher-order harmonic components in the time-varying stiffness of the DG, then leading to the super-harmonic resonance and irregular axis trajectory. The effect of the DC is significantly different from that of the open and breathing cracks in the rotor system. In engineering, it is possible to comprehensively observe the axis trajectory, super-harmonic resonance phenomenon, 2× and 4×super-harmonic components, and the 180° flip of the axis trajectory through the 1/2 first critical speed is used to determine whether the diaphragm has a crack.

GDTE-based crack diagnosis for planetary gear: Mechanism, validation, and advantages compared to vibration-based technology

Effective health monitoring and fault diagnosis technologies are crucial to timely grasping the operation status of the planetary gear train (PGT). In this study, the mechanism for global dynamic transmission error (GDTE)-based crack diagnosis of PGT is revealed from dynamic responses and validated through experiments, and the advantages of this new technique are compared with the commonly used vibration-based technology. Initially, a dynamic model of the PGT considering various crack degrees and transfer path effects is established, and the effectiveness of the model response is verified through experiment. Subsequently, GDTE and vibration signals under different crack conditions are statistically analyzed in time domain and frequency domain to evaluate the differences in the ability to reveal gear failure information. Ultimately, the reasons for the different distribution of fault characterization information in the two signals are explained from a dynamic perspective. The results show that GDTE-based fault diagnosis exhibits greater sensitivity to gear crack degree compared to vibration-based monitoring technology, with both time and frequency domain responses containing richer fault characteristic information, particularly in low-frequency regions. The fault characteristics concentrated in higher-frequency regions in the vibration signal are mainly caused by the modulation between gear crack shock and the gear single and double tooth alternating meshing shock. Conversely, fault frequencies in GDTE signals are mainly found in low-frequency regions, as fault shocks in GDTE signals directly correlate with the rotational frequency of the cracked gear. Modulation effects and attenuation on the transfer path are identified as the main reasons for the weaker representation of gear fault information in vibration signals compared to GDTE signals.

Quantitative evaluation of corrugation severity by using instrumented wheelset

Accurate evaluation of corrugation severity is essential for timely rail maintenance to prevent potential hazards. This paper aims at the excitation characteristics of corrugation and presents a study on the evaluation method using wheel-rail vertical force (WRVF). First, a 3D wheel-rail dynamic model is established by the parameters of service vehicles and track in China’s high-speed railway, corrugated rail was finely modelled with the consideration of out-of-roundness and random track short irregularity. The model was validated with measured data come from instrumented wheelset in time and frequency domain, the stability and dynamic response of the model are studied numerically to explore the excitation characteristics of corrugation. Then, the variation of WRVF with depth and wavelength respectively was discussed, the mapping relationship between the 95th percentile maximum of the WRVF and the corrugation wavelength is revealed, the influences of the natural frequency and contact behavior of the wheel-rail system on the mapping relationship were analyzed. Finally, the corrugation severity index (Csi) is introduced to quantify the degree of rail damage. The applicability of Csi was tested on 65 sets of corrugated sections on high-speed railway, and the results of field measurement showed that the hit rate of Csi in evaluating the severity of corrugation is 93.8%, indicating that the proposed method has a good performance in actual detection. Thus, Csi can provide a scientific reference for the quantitative evaluation of corrugation severity and decision-making for rail grinding in high-speed railway.

Lorentz attractor excitation-based structural damage identification using state space curvature reconstruction- enhanced transformer

Abstract Vibration-based structural damage identification has been widely investigated. Different from previous studies that analyze vibrational responses in time and frequency domains, a new Lorentz attractor excitation-based damage identification is becoming a novel strategy with the advantage of capturing the structure’s nonlinear dynamic effects. In this study, Lorentz attractor-based chaotic signals were employed as excitation signals for the structural damage identification of a frame structure. Nonlinear responses were recorded and damages of bolt looseness at different locations were considered. The structural damages could be revealed in the state-space plot of the responses. A state space curvature reconstruction method was introduced to enhance the key features of the nonlinear responses. A small-sample damage identification is performed using a deep learning algorithm – a Transformer with an accuracy of 92.38%. The advantages of the proposed method over conventional deep learning algorithms were validated. The proposed method can be applied to health conditions identification of buildings, bridges, and trusses.

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Shaking table test of TLD/TLCD vibration control for offshore wind turbine support structure

In this research, a scale-model with a similarity-ratio of 1:15 is specifically designed for shaking table test based on a 6.45MW OWT (Offshore wind turbine). The scale-model is equipped with a TLD (Tuned liquid damper) at the top and a TLCD (Tuned liquid column damper) at 2/3 of its height. Various external excitations with distinct spectral characteristics are applied to analyze the vibration characteristics of the OWT and the damping performance of the TLD/TLCD. The results indicate that the dynamic characteristics satisfy the similarity-ratio between the prototype-model and scale-model. The acceleration response of the OWT is significantly influenced by the external excitation spectrum, whereas the displacement response is primarily governed by the model 1st-order natural-frequency. With the mass eccentricity applied at the tower top and bidirectional excitation input, torsional deformation occurs in the tower, resulting in a ‘beat vibration’ phenomenon. Upon the incorporation of TLD/TLCD, the vibration response attenuation-ratio can reach up to 70 % under harmonic excitation, up to 25 % under seismic excitation and up to 50 % under equivalent base acceleration. After the implementation of vibration attenuation, there is a significant reduction in the time-domain response, and the rate of reduction is accelerated. In the frequency-domain response, the spectral peak at the natural-frequency disappears.

Acoustic emission spectrum characteristics of structural coal destruction in negative pressure environment

Abstract The uniaxial compression experiments under a low-pressure environment were performed by using structural coal samples. The frequency domain response characteristics of coal mass failure under loading in a low-pressure environment were acquired by FFT transformation and wavelet packet decomposition. The results show: As the loading stress of coal increases, the AE spectrum becomes more abundant, and the whole AE spectrum shows a left-shift trend. When the gas pressure increases, the acoustic emission signals change from low-frequency high-energy to high-frequency low-energy, the frequency band gradually narrates, and the spectrum changes from complex multi-peak shape to single-peak shape. As stress increases, the proportion of energy in the band 0-4.38 kHz gradually increases, while that in other bands gradually decreases. The energy response to stress changes in the two frequency bands of 2.92-4.38 kHz and 4.38-5.84 kHz is the most obvious. When the pressure changes, the energy in three frequency bands of 2.92-4.38 kHz, 4.38-5.84 kHz, and 7.3-8.76 kHz present an evident response trend with the pressure change, and the response trend (increase) of the latter two is exactly opposite (decrease) to that of the former. This phenomenon indicates that 2.92-4.38 kHz and 4.38-5.84 kHz are the characteristic frequency bands of the coal fracture process. The findings of this research offer crucial foundational data to support the monitoring and early warning of coal and gas outburst hazards.

On the Love Numbers of an Andrade Planet

AbstractThe Andrade rheological model is often employed to describe the response of solar system or extra‐solar planets to tidal perturbations, especially when their properties are still poorly constrained. While for uniform planets with steady‐state Maxwell rheology the analytical form of the Love numbers was established long ago, for the transient Andrade rheology no closed‐form solutions have been yet determined, and the planetary response is usually studied either semi‐analitically in the frequency domain or numerically in the time domain. Closed‐form expressions are potentially important since they could provide insight into the dependence of Love numbers upon the model parameters and the time‐scales of the isostatic readjustment of the planet. First, we focus on the Andrade rheological law in 1‐D and we obtain a previously unknown explicit form, in the time domain, for the relaxation modulus in terms of the higher Mittag‐Leffler transcendental function Eα,β(z) that generalizes the exponential function. Second, we consider the general response of an incompressible planetary model — often referred to as the “Kelvin sphere” — studying the Laplace domain, the frequency domain and the time domain Love numbers by analytical methods. Through a numerical approach, we assess the effect of compressibility on the Love numbers in the Laplace and frequency domains. Furthermore, exploiting the results obtained in the 1‐D case, we establish closed‐form — although not elementary — expressions of the time domain Love numbers and we discuss the frequency domain response of the Kelvin sphere with Andrade rheology analytically.

Modelling transient unloading-triggered dynamic responses in rock mass under a non-hydrostatic geo-stress

Transient excavation unloading of in situ stress affects the stability of surrounding rock in the deep tunnel engineering. This paper focuses on the dynamic responses triggered by the transient unloading of a non-hydrostatic geo-stress field in deep-buried engineering. With resort to the integral transformation, the frequency-domain responses of stress, displacement and velocity components induced by the transient unloading are obtained under a non-hydrostatic in situ stress. Based on the numerical inversion of the Laplace transformation, the corresponding time-domain theoretical results are determined. Agreement of the current solutions with the existing results and the numerical simulations verifies the proposed scheme in this paper. The elastic analytical results indicate that the influence of unloading path on the stress redistribution is characterized by the unloading rate. The higher the unloading rate is, the larger the stress magnitude is. The smaller the unloading time is, the more remarkable vibration is. The elasto-plastic dynamic numerical responses are investigated on the basis of a self-developed code, elasto-plastic cellular automaton (EPCA), which is a module of CASRock. The numerical results demonstrate that the transient excavation unloading results in the stress redistribution and concentration of surrounding rock mass, inducing damage for the case of exceeding the capacity of rock mass. For the small lateral pressure coefficient (less than 0.25), the tensile-shear failure is the major damage mechanism of surrounding rock, while the shear failure is the major damage mechanism for the large lateral pressure coefficient. The analytical and numerical results can provide theoretical basis for the support and reinforcement of underground tunnel.

Rheological properties of porcine organs: measurements and fractional viscoelastic model.

The rheological properties of porcine heart, kidney, liver and brain were measured using dynamic oscillatory shear tests over a range of frequencies and shear strains. Frequency sweep tests were performed from 0.1Hz to a maximum of 9.5Hz at a shear strain of 0.1%, and strain sweep tests were carried out from 0.01% to 10% at 1Hz. The effect of pre-compression of samples up to 10% axial strain was considered. The experimental measurements were fit to a Semi-Fractional Kelvin Voight (S-FKV) model. The model was then used to predict the stress relaxation in response to a step strain of 0.1%. The prediction was compared to experimental relaxation data for the porcine organ samples, and the results agreed to within 30%. In conclusion, this study measured the rheological properties of porcine organs and used a fractional viscoelastic model to describe the response in frequency and time domain.

Accelerating optimization of terahertz metasurface design using principal component analysis in conjunction with deep learning networks

Metamaterials are a class of artificial materials that have exceptional physical properties that do not exist in nature. They are widely used in various fields, such as electromagnetics, optics, and acoustics. However, designing metamaterials can be a challenging and time-consuming task. Traditional methods rely on simulations and trial-and-error, which are inefficient and often require significant computational resources. Recently, deep learning has emerged as a promising tool to design metamaterials. Deep learning involves training neural networks to learn complex patterns and relationships in data, which can be used to predict the behavior of metamaterials under different conditions. This paper proposes a neural network that maps geometric parameters to frequency domain responses for optimized design. The network utilizes PCA (Principal Component Analysis) to reduce the training time by approximately 5%, and this combination method is far superior to similar algorithms in terms of prediction accuracy and generalization ability. Experimental results demonstrate that the designed network model can be used for optimized design, achieving a remarkably low RMSE (Root Mean Square Error) of 0.0408 and a prediction accuracy of 97.64% in the reverse network, outperforming similar articles. The proposed network model improves the design efficiency of metamaterials, providing a more efficient and effective approach for designing these metamaterials.

DAC phase and amplitude noise experimental studies in RZ, NRZ and RF modes

Amplitude and duration of pulses generated by current cells of multimode DAC may differ in real DACs. In this case the problem arises of current pulse parameters defining, their relationship with frequency domain response and noise parameters of DAC, which can be experimentally determined. The article describes the measurements of frequency domain response, phase noise and amplitude noise of multimode DAC output signal in RZ, NRZ and RF (mixed) mode. Phase noise and amplitude noise of multimode DAC in RZ and RF modes calculation uses experimental data obtained in RZ mode. Measurement and consequent calculation of AD9739 DAC phase and amplitude noise confirmed the theoretical analysis.

Numerical analysis for temporal and spectral responses of electromagnetic waves in spatially homogeneous time varying medium

This paper presents simple numerical solutions for electromagnetic plane waves in spatially homogenous time varying medium. The solution is based on converting the resulting second order differential equation into two combined ordinary differential equations which are solved numerically by using the built-in ode113 function in Matlab. By using this method, the time domain responses of the electric and magnetic fields at fixed point in space are obtained. The proposed method is applied on two cases: linearly time varying medium and sinusoidally time varying medium. The corresponding frequency domain response is obtained by using inverse Fourier transformation of the obtained time domain response. The proposed method is compared with FDTD solution. It is found that the proposed method has the same accuracy of FDTD with much less computational time.

Crowdsensing-based automatic bridge health condition assessment using drive-by measurements and deep learning

In recent decades, assessing the structural health conditions of aging bridges has emerged as a significant concern. A recent drive-by measurement method has attracted substantial attention, in which only several sensors are installed on crowdsensing vehicles rather than bridges, providing a more economical and convenient solution. This paper proposes an automatic bridge condition assessment framework incorporating drive-by measurements and deep learning techniques. The methodology involves collecting and segmenting accelerations from a vehicle passing a healthy bridge into short-time overlapped frames. Over multiple vehicular passes, all frames are then transformed into frequency-domain responses, forming the input for training an unsupervised deep learning model. The model is then trained to reconstruct the input using these frequency-domain responses. In assessing the bridge with an unknown health state, the trained model is employed to reconstruct the passing vehicle’s new short-time frames, and the response construction error automatically determines the bridge’s health condition. Experimental validation utilizing a laboratory bridge and scaled truck demonstrated that the trained model could consistently identify a healthy bridge during passages, with larger reconstruction errors indicating that the bridge was damaged. The innovative framework showcased promise for efficient and reliable bridge health condition assessment.

Vibration Analysis using Finite Element Analysis (FEA): An Evaluation of Pico-Tubular Bulb Type Turbine Blades Fabricated in Composite Materials

Tubular turbines have been widely employed and evolved fast when its introduction in the 1930s due to their strong technical and economic qualities and application. Because its performance and structure differ from those of ordinary vertical shaft units, local and international academics worked extensively on research techniques and technological means using numerical simulation and model testing. The transmissions of a high quantity of power, which may cause unwanted vibrations that reduce efficiency, increase wear, and, in the worst-case scenario, cause serious damage. In this paper, the material propose in order to substantiate that the random excitations and excess vibration of the pico-turbine can be prevented is the use of CFRP (carbon fiber reinforced polymer) and PLA (polylactic acid). In this paper, ANSYS® Mechanical modal simulation is used to evaluate the structures’ robustness behavior of the composite materials that were used as the main material in the fabrication of turbine blades for bulb-type turbine application. The use CFD simulation in SOLIDWORKS® is needed to examine the pressure fluctuation caused by unsteady flow that can contribute in the unwanted pulsation and to conform the modal simulation results. To validate the results, pressure pulsation experimentation is conducted to evaluate the fluctuation of the pressure affecting the blades or in the rotating region and it is analyzed through frequency response domain. Hence, in this paper, it is proven that the vibration behavior of the material is acceptable since the resulting natural frequency provides resulting stress, strain, and deformation that is allowable and below its ultimate tensile strength.

Output-only response migration method of single-layer reticulated shells based on generative adversarial network

As an important form of important public building roofs, single-layer latticed shells (SLRSs) are equipped with health monitoring systems (SHMs) to collect extensive data to study their complex response characteristics. For SLRSs without structural SHMs, limited response data can only be obtained through on-site measurements, which limits the further application of data-driven machine learning methods on SLRSs. Based on the measured actual response, a traditional generative network can generate fake responses similar to the actual responses to expand the existing response dataset. However, this method is not subject to enough constraints, leading to a small portion of the generated fake responses do not match the actual situation. This paper proposes a response migration method to expand the response dataset of SLRS. Firstly, the output-only response migration method for SLRS is proposed, utilizing frequency domain responses from two different response domains to expand the responses of the actual SLRS through response migration. Then, more constraints are applied to the response migration process to reduce the occurrence of abnormal fake responses through cycle consistency generation adversarial network (GAN). The adaptive response migration generation adversarial network (ARMGAN) is proposed based on cycle consistency GAN, which can automatically select networks with better migration performance. Finally, two numerical spherical SLRS examples and an engineering example are used to verify the proposed method. The responses migrated through ARMGAN have characteristics similar to the actual responses, and ARMGAN can significantly reduce abnormal fake responses.

A parallel power system linear model reduction method based on extended Krylov subspace

With the ever-increasing scale of power systems, stability analysis and control usually bear heavy storage and massive calculation burdens. In view of this, the model order reduction technique proves valuable by constructing a low-dimensional approximate model of the original system, which is crucial for efficiently handling large-scale systems. Balanced truncation (BT), a famous model reduction method, confronts practical limitations as it requires the systems to be stable and cannot deal with unstable models. Therefore, a parallel linear balanced truncation method for power systems based on extended Krylov subspace (EKS) is proposed in this work. Besides extending the BT method to unstable systems by α-shift, the key contribution also lies in strategies to enhance the convergence of the EKS method, whereupon the algorithm improvements include effective and efficient techniques for solving dual Lyapunov equations, and parallel acceleration of the singular value decomposition. The results of the simulation case verify that the proposed method can effectively improve the convergence of the EKS method by increasing α-shift, and the improvement work in this paper reduces the total time consumption of the BT method by about 26 %–33 % of the original, exhibiting better calculation efficiency. In addition, the case studies show that the simplified model still retains the time-domain and frequency-domain response characteristics of the original high-dimensional model.

Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.

Numerical Analysis of Hydrodynamic Characteristics of Two-Dimensional Submerged Structure in Irregular Waves

A comprehensive two-dimensional (2D) time-domain numerical model is established to investigate the interaction of irregular waves and submerged structures with different sections. The model specifically focuses on the dual-lane submerged floating tunnel (SFT) designs, encompassing elliptical, twin-circular, and round rectangular sections. For the hydrodynamic analysis, we adopt the second-order potential flow theory, while for the mooring line simulations, we employ the slender rod theory, taking into account the entire hydrodynamic load acting on it. In the coupled dynamic analysis, the fourth-order Adams–Bashforth–Moulton method, Newmark-β method, and Newton–Raphson iteration scheme are utilized for the coupled motion equation of the floating body and the dynamic equation of the mooring riser system. Experimental free decay tests are conducted to determine the damping coefficients of various section shapes in different directions. Our analysis delves into the detailed motion responses and mooring tensions of the SFTs with different section forms under irregular waves. We compare and contrast these responses in both time and frequency domains, particularly focusing on movement trends. The elliptical section structure emerges as the most stable design based on our comparisons. These findings provide valuable insights for the selection of optimal section shapes for dual-lane SFTs.

Frequency-domain analysis of two controllable attenuators for control processes and perturbations in a constant temperature chilled-water system

Constant temperature and humidity rooms (CTHRs) that require ultra-high precision (≤±0.1 °C) are widely used in semiconductors and other high-end manufacturing. To achieve this, the air handling unit’s chilled water system should be able to handle temperature fluctuations in all frequencies. However, traditional methods use attenuators for internal perturbations (usually at high frequency) and electric heating with PID control for external ones (usually at low frequency) separately and can’t differentiate frequencies and their sources, which can lead to ineffective control and energy waste. Therefore, this study proposed two chilled water systems based on two controllable attenuators, i.e., a plate heat exchanger (PHE) and a water mixing pump (WMP), that can simultaneously achieve full frequency range control at an ultra-high precision without reheating. An experimental setup was used to validate and obtain the attenuation performance of the two schemes. The fast Fourier transform was conducted to decouple the system’s internal and external perturbations in the frequency domain. The frequency-domain response features of the thermal control and attenuation processes for low-frequency and high-frequency fluctuations under the two schemes were analyzed. The results showed that, first, both schemes can achieve ultra-high precisions. Second, the PHE scheme had a more robust attenuation performance, while the WMP scheme exhibited a broader effective control frequency range. Third, the pumps in both schemes were the primary source of perturbations that constitute the temperature fluctuation, and the flow rate stability was closely related to the degree of pump perturbation. Finally, 10-3 Hz can be considered the delineation frequency between the low- and high-frequency of the system’s fluctuations, which can be simultaneously attenuated by the proposed controllable attenuators.