Frequency Domain Response Research Articles

Dynamic Stability Analysis of a Cracked Beam using a Lumped Parameter Model

Vibration based condition monitoring is one of the predictive maintenance strategies applied for structures and rotating machinery. Detection and identification of fatigue crack in structures has been a widely discussed problem in the literature of condition monitoring. This paper discusses the numerical results that have been obtained from the study of bending vibration of a cracked beam. The crack is primarily modelled as an opening/ closing crack resulting in a periodic variation in stiffness. The mathematical model considered for the cracked beam is a lumped single degree of freedom system. The resulting system equation of motion has the canonical form of a Mathieu equation. For obtaining the system response, the equation is written in a state-space form and then solved using fourth order Runge-Kutta numerical integration. The time and frequency domain responses are obtained for a specific harmonic excitation. Further, the stability of the cracked beam is discussed with respect to the variation in stiffness, by numerical analysis, using a Vander Pol and Strutt stability chart diagram.

Estimation of virtual masses for structural damage identification

Adding a virtual mass is an effective method for damage identification. It can be used to obtain a large amount of information about structural response and dynamics, thereby improving the sensitivity to local damage. In the current research approaches, the virtual mass is determined first, and then the modal characteristics of the virtually modified structure are identified. This requires a wide frequency band excitation; otherwise the crucial modes of the modified structure might be out of the band, which would negatively influence the modal analysis and damage identification. This paper proposes a method that first determines the target frequency and then estimates the corresponding value of the additional virtual mass. The target frequency refers to the desired value of the natural frequency after the virtual mass has been added to the structure. The virtual masses are estimated by tuning the frequency response peaks to the target frequencies. First, two virtual mass estimation methods are proposed. One is to directly calculate the virtual mass, using the frequency-domain response at the target frequency point only, whereas the second method estimates the mass using a least-squares fit based on the frequency-domain response around the target frequency. Both proposed methods utilize merely a small part of the frequency domain. Therefore, an impulse, a simple harmonic, or a narrow spectral excitation can be used for damage identification. Finally, a numerical simulation of a simply supported beam and experiments of a frame structure and a truss structure are used to verify the effectiveness of the proposed method.

Rabi oscillation study of strong coupling in a plasmonic nanocavity

Strong interaction between emitters and plasmonic nanocavity has various applications in quantum fields at room temperature. As Rabi oscillation gives the direct proof to the energy exchange in strong coupling, it is more intuitive and necessary to analyze the interaction in time domain. In this paper, we give the Rabi oscillation in a high-dissipation plasmonic nanocavity by using full-quantum method and draw a new strong coupling criterion about mode volume which provides a significant guidance in plasmonic nanocavitys nanofabrication. Moreover, we reveal the relation between Rabi oscillation and Rabi splitting, which is beneficial for exploring emitter–plasmon hybrid systems time-domain property through frequency-domain response. An emitter–hexagon hybrid system with ultrasmall mode volume is designed to verify our theory. The numerical simulation shows good agreements with our theoretical results. Our work has applications in quantum information and quantum computing in the future.

Temperature correction to dielectric modulus and activation energy prediction of oil-immersed cellulose insulation

The dielectric modulus Μ∗(ω) is used for studying the frequency domain response and activation energy (E a ) of transformer immersed cellulose insulation. Existing literatures show that the temperature is a crucial factor affecting the Μ∗(ω) and aging rate of transformer oil-paper insulation, while the E a can be regarded as an indicator to reflect the average aging rate of the transformer immersed cellulose insulation. Therefore, the discussion of the temperature-dependence on both Μ∗(ω) and E a is of great significance. This paper attempts to report an approach for understanding the temperature impact on both Μ∗(ω) and E a . The obtained knowledge can be used to establish two available models for temperature correction on Μ∗(ω) and activation energy prediction of transform immersed cellulose insulation, respectively. These findings are expected to promote the reliability of the condition prediction result of transformer immersed cellulose insulation by using Μ∗(ω) and E a technique.

Dynamic response reconstruction for structural health monitoring using densely connected convolutional networks

This article proposes a novel dynamic response reconstruction approach for structural health monitoring using densely connected convolutional networks. Skip connection and dense block techniques are carefully applied in the designed network architecture, which greatly facilitates the information flow, and increases the training efficiency and accuracy of feature extraction and propagation with fewer parameters in the network. Sub-pixel shuffling and dropout techniques are used in the designed network and applied to reduce the computational demand and improve training efficiency. The network is trained in a supervised manner, where the input and output are the measurements of the available channels at response available locations and desired channels at response unavailable locations. The proposed densely connected convolutional networks automatically extract the high-level features of the input data and construct the complicated nonlinear relationship between the responses of available and desired locations. Experimental studies are conducted using the measured acceleration responses from Guangzhou New Television Tower to investigate the effects of the locations of available responses, the numbers of available and unavailable channels, and measurement noise. The results demonstrate that the proposed approach can accurately reconstruct the responses in both time and frequency domains with strong noise immunity. The reconstructed response is further used for modal identification to demonstrate the usability and accuracy of the reconstructed responses. The applicability of the proposed approach for structural health monitoring is further proved by the highly consistent modal parameters identified from the reconstructed and true responses.

Height Adjustable Sine (HAS) Window Function for Impulse Response Modification of Signal Processing Systems

A widow function, in signal processing and statistics, is a mathematical function that has zero values outside its chosen interval or limit of sequence, normally symmetric around the middle of the interval. Usually the middle of the window is either maximum or near maximum and tappers smoothly as it moves away to the sides. When another function or sequence of data is mathematically multiplied by the window function the product assumes the appearance and characteristics of the window function. That is, the product is also zero-valued outside the interval and tapering from middle to the sides. The impulse response data of some systems used in signal processing truncate suddenly when being designed. Window functions convert the sudden truncation of these impulse response data to gradual truncation. Without this gradual truncation the processing system will degrade the integrity of complex signals when they are applied to them; the degradation appears in form of signal distortions. Windows are used to weight these impulse response data so as to reduce the degradation and distortions. Several windows are in existence and they include Hamming, rectangular, Han, Kaiser, Triangular, Blackman, Sine, Blackman-Harris, Gaussian, Doph-Chebyshev and Lanczos, windows. Others are Parzen, Nuttall, flat top, and Turkey, windows and others. The characteristics of the signal to be processed, types of systems to be implemented and quality of outputs desired determine the best window to weight any particular impulse response data. In this work a new window referred to as Height Adjustable Sine (HAS) window is developed to join the list of the existing windows. The quality of the window is tested by analysing its amplitude, magnitude and phase responses in frequency domain. Result shows that the window is stable and linear.

Height Adjustable Sine (HAS) Window Function for Impulse Response Modification of Signal Processing Systems

A widow function, in signal processing and statistics, is a mathematical function that has zero values outside its chosen interval or limit of sequence, normally symmetric around the middle of the interval. Usually the middle of the window is either maximum or near maximum and tappers smoothly as it moves away to the sides. When another function or sequence of data is mathematically multiplied by the window function the product assumes the appearance and characteristics of the window function. That is, the product is also zero-valued outside the interval and tapering from middle to the sides. The impulse response data of some systems used in signal processing truncate suddenly when being designed. Window functions convert the sudden truncation of these impulse response data to gradual truncation. Without this gradual truncation the processing system will degrade the integrity of complex signals when they are applied to them; the degradation appears in form of signal distortions. Windows are used to weight these impulse response data so as to reduce the degradation and distortions. Several windows are in existence and they include Hamming, rectangular, Han, Kaiser, Triangular, Blackman, Sine, Blackman-Harris, Gaussian, Doph-Chebyshev and Lanczos, windows. Others are Parzen, Nuttall, flat top, and Turkey, windows and others. The characteristics of the signal to be processed, types of systems to be implemented and quality of outputs desired determine the best window to weight any particular impulse response data. In this work a new window referred to as Height Adjustable Sine (HAS) window is developed to join the list of the existing windows. The quality of the window is tested by analysing its amplitude, magnitude and phase responses in frequency domain. Result shows that the window is stable and linear.

Bridge modal identification using acceleration measurements within moving vehicles

Vehicles commuting over bridge structures respond dynamically to the bridge’s vibrations. An acceleration signal collected within a moving vehicle contains a trace of the bridge’s structural response, but also includes other sources such as the vehicle suspension system and surface roughness-induced vibrations. This paper introduces two general methods for the bridge system identification using data exclusively collected by a network of moving vehicles. The contributions of the vehicle suspension system are removed by deconvolving the vehicle response in frequency domain. The first approach utilizes the vehicle transfer function, and the second uses ensemble empirical modal decomposition (EEMD). Next, roughness-induced vibrations are extracted through a novel application of second-order blind identification (SOBI) method. After these two processes, the resulting signal is equivalent to the readings of mobile sensors that scan the bridge’s dynamic response. Structural modal identification using mobile sensor data has been recently made possible with the extended structural modal identification using expectation maximization (STRIDEX) algorithm. The processed mobile sensor data is analyzed using STRIDEX to identify the modal properties of the bridge. The performance of the methods are validated on numerical case studies of a long single-span bridge with a network of moving vehicles collecting data while in motion. The analyses consider three road surface roughness patterns. Results show that for long-span bridges with medium- to high-ongoing traffic volume, the proposed algorithms are successful in extracting pure bridge vibrations, and produce accurate and comprehensive modal properties of the bridge. The study shows that the proposed transfer function method can efficiently deconvolve the linear dynamics of a moving vehicle. EEMD method is able to extract vehicle dynamic response without a priori information about the vehicle. In addition, proposed identification methods provide secondary information about the roughness pattern and the vehicle. This study is the first proposed methodology for complete bridge modal identification, including operational natural frequencies, mode shapes and damping ratios using moving vehicles sensor data.

Research and Field Application of Oil-paper Insulation Material Aging State Based on FDS

The effects of three factors, such as aging degree, water content and temperature, on the dielectric response characteristics of oil-paper insulating materials were studied by setting up a frequency-domain dielectric response experimental platform. In this paper, the frequency domain dielectric spectrum (FDS) test is carried out for the on-site transformer paper insulated casing, and it is found that the method is more abundant than the traditional power frequency dielectric loss method, which is less affected by the work frequency electromagnetic field, and can realize the nondestructive measurement of the aging state of the oil-grease insulation.

Numerical Study of the Flow-Induced Vibration During Tunnel Surging at the Intake Section of Chenderoh Dam

Chenderoh Dam that located in Malaysia is one of renewable energy power plant that beneficial to mankind. However, in some cases, the dam suffers from the vibration effect during the water spilling from upstream to downstream. This study focused on major part of the dam which is the intake section during the tunnel surging condition. A detail 3D model of the intake section was constructed and used in the prediction of flow-induced vibration response. The results of frequency domain response and operational defection shapes (ODS) from the effect of flow-induced vibration are compared with the natural frequencies and mode shapes of the dam. From the results, the transient vibration responses due to the flow of water occurred at the frequency of 8.63 Hz with the maximum deformation of 8.24 x 10−1 m, meanwhile, the modal analysis obtained at 2.76 Hz of natural frequency with deformation of 9.1 x 10−4 m. The deformation of ODS is high because of the water flow and tunnel surging condition. However, there is no resonance phenomenon occurred, yet a safety precaution must still be considered by the operator based on this result.

Assessment of Structural Performance and Integrity for Vibration-based Energy Harvester in Frequency Domain

A vibration-based energy harvester (VEH) utilizes vibrations originated from various structures and specifically maximizes the displacement of its moving parts, using the resonance between the frequency of external vibration loads from the structure and the natural frequency of VEH to improve power production efficiency. This study presents the procedure to evaluate the structural performance and structural integrity of VEH utilized in a railway vehicle under frequency domain. First of all, a structural performance test was performed to identify the natural frequency and assess the structural response in frequency domain. Then, the static structural analysis was carried out using FE analysis to investigate the failure critical locations (FCLs) and effect of resonance. Finally, we conducted a frequency response analysis to identify the structural response and investigate the structural integrity in frequency domain. Based on these results, the authors assessed the structural performance and integrity of VEHs in two versions.

The dynamic behavior of non-polarized erbium-doped fiber ring laser under experimental pump modulation

An Erbium-doped fiber ring laser subjected to sinusoidal pump modulation has been studied experimentally and its bifurcation diagram analyzed. Data from oscilloscope is used to analyze the interesting spectral features observed via the time domain response and frequency domain response which shows the different dynamical regimes occurring when the modulation frequency and amplitude are being varied respectively. Linear and non-linear (chaos) dynamical behaviors are observed, as well as optical bi-stability. The dynamical response of an Erbium-doped fiber ring laser can easily be studied through pump modulation.

Identification of the stick and slip motion between contact surfaces using artificial neural networks

The paper presents work related to nonlinear system parameters identification. The research is focused on systems with hysteretic stiffness characteristics. The identification procedure is developed with use of artificial neural networks. The presented method assumes two separate clusters of neural networks, which are supported by additional signal processing block. Such approach gives an advantage over the conventional identification methods due to its small restrictions. The validation process considers structural responses in time and frequency domains as well as the restoring force plane of the dynamic structure. First, verification of the identification method is performed on the numerical simulation of the system with hysteretic stiffness. Next, the identification of the real dynamic system with contact-related nonlinearity is carried out. The steel samples with contacting surfaces were used in the experiment. Electromagnetic shaker was used to excite the structure and enforce a relative shear motion between surfaces in contact. The system response was recorded using the Polytec laser vibrometer.

Experimental investigation on coupled vibration characteristics of wind-excited tall buildings

Contemporary tall buildings constructed with high-strength and light-weight materials become relatively flexible and lightly damped, and the fluctuating wind forces acting on the buildings may cause excessive vibrations, especially at the vicinity of vortex lock-in wind speed, where the natural frequency of the buildings is synchronized with the vortex shedding frequency. Given that tall buildings tend to be designed with unconventional shape involving innovative structural systems and complex geometry, the correlations among three force components may accentuate building motions significantly. In this study, the coupling characteristics between the alongwind and crosswind vibrations of tall buildings with symmetric shape and distinct natural frequencies in two directions are investigated through a serious of aeroelastic model tests. The response standard deviations and power spectral densities are calculated, respectively, based on the displacement data measured at multiple levels of wind speed and structural damping ratio. Then the coupled response is extracted from the alongwind response in frequency domain through Fourier transform and inverse Fourier transform, and the standard deviations of the coupled response are calculated based on time history analysis, which are compared with that of the crosswind response to investigate the relationship between the alongwind and crosswind motions. Moreover, the amplitude ratio, phase difference, and coherence of the response components are also calculated for further discussing the coupling effects and examining the coupled vibration characteristics.

Modeling and state-space identification of deformable mirrors.

To develop high-performance controllers for adaptive optics (AO) systems, it is essential to first derive sufficiently accurate state-space models of deformable mirrors (DMs). However, it is often challenging to develop realistic large-scale finite element (FE) state-space models that take into account the system damping, actuator dynamics, boundary conditions, and multi-physics phenomena affecting the system dynamics. Furthermore, it is challenging to establish a modeling framework capable of the automated and quick derivation of state-space models for different actuator configurations and system geometries. On the other hand, for accurate model-based control and system monitoring, it is often necessary to estimate state-space models from the experimental data. However, this is a challenging problem since the DM dynamics is inherently infinite-dimensional and it is characterized by a large number of eigenmodes and eigenfrequencies. In this paper, we provide modeling and estimation frameworks that address these challenges. We develop an FE state-space model of a faceplate DM that incorporates damping and actuator dynamics. We investigate the frequency and time domain responses for different model parameters. The state-space modeling process is completely automated using the LiveLink for MATLAB toolbox that is incorporated into the COMSOL Multiphysics software package. The developed state-space model is used to generate the estimation data. This data, together with a subspace identification algorithm, is used to estimate reduced-order DM models. We address the model-order selection and model validation problems. The results of this paper provide essential modeling and estimation tools to broad AO and mechatronics scientific communities. The developed Python, MATLAB, and COMSOL Multiphysics codes are available online.

Vehicle model response in frequency domain

The offered article deals with one of the possibilities of numerical analysis of the vehicle response in frequency domain. It works with quarter model of vehicle. For the selected computational model of vehicle it quantifies the Frequency Response Functions (FRF) of both force and kinematic quantities. It considers the stochastic road profile. The Power Spectral Density (PSD) of the road profile is used as input value for the calculation of Power Spectral Density of the response. Al calculations are carried out numerically in the environment of program system MATLAB. When we know the modules of FRF or the Power Response Factors (PRF) of vehicle model the calculation of vehicle response in frequency domain is fast and efficient.

Tracking Error Fitness Function V/F Control of Micro-Grid Based on Genetic Algorithm

This paper presents a method of V/f control parameters tuning for micro-grid based on genetic algorithm. Firstly, the fitness function which representing the tracking error of V/f control system in micro-grid is established. The solving path of genetic algorithm is optimized by using the offset threshold condition between the output voltage and the instruction voltage of the load side, leading to that the individuals with high priority will tend to the optimal solution in the target solution, obtaining the global optimal V/f control parameters. Secondly, the frequency domain response characteristics of equivalent output impedance of V/f control system are analyzed, and the influence of PI parameters on the whole control system is compared. The results shows that the V/f control parameters tuning based on genetic algorithm with the tracking error fitness function can effectively guarantee a constant output of micro-grid’s voltage and frequency. The effectiveness and the advantages of the method is verified by simulation result, which indicated that the proposed method is easy to implement and has a wide range of applications.

Customized Inverse Design of Metamaterial Absorber Based on Target-Driven Deep Learning Method

Metamaterials (MMs) have already achieved wide applications in academia and industry. The traditional design approach for MMs highly relies on full-wave numerical simulations and trial-and-error methods. It is time-consuming and laborious to obtain the optimal design parameters. Recently, extensive researches have shown advantages and superiority of the deep learning method in solving non-intuitive problem. Several attempts have been made to demonstrate Artificial Intelligence (AI) usage in the electromagnetic field. In this article, a target-driven method empowered by deep learning to realize customized metamaterial absorber (MMA) design has been proposed and demonstrated numerically. Unlike previous deep-learning-based design methods for MMs which directly use the spectrum response to generate the MM’s design parameters, this method takes the frequency domain response of the absorber as the intermediary bridge to establish the mapping between MMAs geometry/material parameters and customized figure-of-merits. The proposed design framework greatly simplified the design process of MMAs, and it can also be generalized to realize automatic inverse design for other kinds of metasurfaces.

高山-峡谷复合地形对入射平面P-SV波的散射

As a common composite site, the hill-canyon topography has complex coherence effects on seismic wave scattering. However, the publications of related research are still very limited. Therefore, a multi-domain indirect boundary element method was proposed to solve the scattering of in-plane elastic waves, and the scattering and diffraction of plane P-SV waves by hill-canyon topography were studied. The method takes advantages of both full-space Green’s function and half-space Green’s function to construct the scattered field in the independent closed region and the half-space open region, respectively. Combined with the auxiliary function method, dynamic wavefield solutions for the hill-canyon site were given, with the calculation accuracy ensured and the solution efficiency improved. The proposed method was verified through comparison of the results with published ones, and numerical calculations were performed in the frequency domain and time domain in the case of a Gaussian hill-canyon site. Results show that, the distribution of the surface displacement amplitude is very complex. There is significant dynamic interaction between the hill and the canyon, and the frequency-domain response depends on the frequency and angle of the incident wave. The presence of hills has an inhibition effect on the canyon for vertically incident waves, which significantly changes the peak acceleration and spectrum characteristics inside the canyon. Different height-to-width ratios of hills will cause changes in the seismic effect, and the presence of bedrock will also obviously amplify the seismic effect of the overall terrain.

Dynamic stress state around shallow-buried cavity under transient P wave loads in different conditions

The failure of underground structure is always caused by local stress redistribution resulted from transient impact loads. An analytical model is established and solved by using the complex variable function method to illustrate the dynamic stress concentration around a shallow-buried cavity under transient P wave loads. The transient wave response is attained as an integration of steady-state wave response in circular frequency domain. By adopting a Butterworth filter, the jump points in the dynamic stress concentration factor (DSCF) curve which is not in line with the overall trend is filtered out to obtain more reasonable results. The convergence and accuracy of the solutions are verified and discussed in detail. DSCF distributions of high wavenumber incidences differ from that of low wavenumber incidences significantly in amplitudes and distribution patterns. The effects of the cavity depth, incidence angle and position of wave peak on DSCF distributions are illustrated.