Normal Frequency Response Research Articles

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

Cyber-Physical Testbed Co-Simulation Real-Time: Normal and Abnormal System Frequency Response

Cyber-Physical Testbed Co-Simulation Real-Time: Normal and Abnormal System Frequency Response

Diagnosis of Power Transformer Winding Deformation Based on Centroid Analysis of 3D Frequency Response Curve

Background: As the frequency of transformer winding faults becomes higher and higher, the frequency response analysis used to detect the winding status has attracted more and more attention. At present, there is still a lack of reliable and intelligent technologies for detecting the state of transformer windings in this field. Methods: In this paper, a transformer winding deformation diagnosis method based on centroid analysis of 3D frequency response curve is proposed. A 3D coordinate system is established with frequency, amplitude, and phase as the x, y, and z, respectively. The proposed method calculates the centroid of each 3D frequency response curve through an algorithm, and establishes a 3D coordinate system with the centroid of the normal winding 3D frequency response curve as the origin. The deviation distance and deviation angle between the centroid of mass of the 3D frequency response curve of the faulty winding in different frequency bands and the centroid of the 3D frequency response curve of the normal winding and the correlation coefficient of the traditional Frequency Response Analysis (FRA) curve. are calculated. The deviation distance and angle of the centroid and the correlation coefficient of the calculated frequency band are input as features into the Support Vector Machine (SVM) for intelligent diagnosis to achieve fault classification and optimizing its parameters with three optimization algorithms respectively. Results: The fault classification is realized by analyzing the distribution intervals of the centroids of the 3D frequency response curves of the three simulated faults. The accuracy of fault diagnosis using the 3D frequency response curve feature is significantly higher than the accuracy when using the traditional FRA curve feature and it proves the effectiveness of the proposed method. Conclusion: The proposed model can effectively identify different fault types and the diagnostic rate of the fault type is 100%.

Nicotine withdrawal after chronic exposure in adulthood blunts the ventilatory response to hypoxia in rats

Nicotine is one of the most addictive substances known, and it is estimated that 50.6 million US adults use nicotine in some form. It is well known that smoking, the most common form of nicotine exposure, alters lung structure and function. In contrast, the impact of chronic nicotine exposure during adulthood on neural structures involved in the control of breathing is largely unknown. In preliminary experiments in adult rats, we used plethysmography to study the effects of chronic nicotine exposure on the ventilatory response to hypoxia, which is a critical respiratory chemoreflex that enhances breathing and limits arterial O2 desaturation. Four weeks of chronic nicotine exposure through drinking water had no effect on the ventilatory response to a brief, 5‐ minute episode of hypoxia (10%) (Minute ventilation: One‐way ANOVA, Control vs Nicotine Exposure; P=0.6533). In contrast, nicotine exposed rats show a significantly blunted ventilatory response to hypoxia following 48 hours of nicotine withdrawal (Control vs Nicotine Withdrawal, P=0.0447). The reduced ventilatory response was due to a blunted increase in tidal volume (Amplitude: One‐way ANOVA, Control vs Nicotine Withdrawal; P=0.007), with a normal frequency response (Control vs Nicotine Withdrawal; P=0.2518. This has important clinical ramifications, as hypoxia is a commonly encountered medical complication, and withdrawal symptoms are often observed in hospitalized patients as it is common for them to abstain from smoking during periods of worsening health or in preparation for surgery.

Research on the micro and dynamic characteristics of combination surface based on fractal theory

Abstract. The dynamic characteristics of the mechanical joint surface are important aspects of the dynamic theoretical analysis and optimization design of the machine tool. In this paper, the typical mechanical joint surface is taken as the research object. Through the combination of theoretical analysis and experimental analysis, the dynamic characteristics of typical joint surface parameters with different surface textures and the influence of texture parameters on the dynamic characteristics of the joint surface are studied. Based on the Hertz elastic contact theory and the contact fractal theory, the normal and tangential contact fractal models of the joint surface are derived, and then a mathematical model of the joint surface normal and tangential contact stiffness considering the domain expansion factor is established. The influence of surface texture parameters on the dynamic characteristics of the surface is further studied according to the model. In addition, the design of the experimental device and experimental scheme design are completed by the contact resonance method and the ERA algorithm, and the joint surface parameter identification experiment with texture is conducted. The normal and tangential frequency response functions of the joint surface, the dynamic characteristic parameters of the joint surface and the influence law of the joint surface parameters on the contact characteristics are obtained through the dynamic test analysis technology.

Damping Matrix Identification by Finite Element Model Updating Using Frequency Response Data

Accurate modeling of damping is essential for prediction of vibration response of a structure. This paper presents a study of damping matrix identification method using experimental data. The identification is done by performing finite element (FE) model updating using normal frequency response functions (FRFs). The paper addresses some key issues like data incompleteness and computation of the normal FRFs for carrying out the model updating using experimental data. The effect of various levels of damping in structures on the performance of the identification techniques is also investigated. Experimental studies on three beam structures made up of mild steel, cast iron and acrylic are presented to demonstrate the effectiveness of the identification techniques for different levels of damping.

주파수 응답 데이터를 이용한 비비례 점성감쇠행렬 추정

Accurate identification of damping matrix in structures is very important for predicting vibration responses and estimating parameters or other characteristics affected by energy dissipation. In this paper, damping matrix identification method that use normal frequency response functions, which were estimated from complex frequency response functions, is proposed. The complex frequency response functions were obtained from the experimental data of the structure. The nonproportional damping matrix was identified through the proposed method. Two numerical examples (lumped-mass model and cantilever beam model) were considered to verify the performance of the proposed method. As a result, the damping matrix of the nonproportional system was accurately identified.

Vibration Response Prediction of the Printed Circuit Boards Using Experimentally Validated Finite Element Model

A spacecraft consists of a number of mechanical and electronic sub-assemblies. An electronic package is consists of printed circuit boards placed in mechanical housings which are stacked together. Electronic components are mounted on the printed circuit board (PCB). A spacecraft experiences various types of mechanical loads during its launch such as vibration, acoustic and shock loads. The understanding of dynamic behaviour provides valuable insight to a design engineer, to improve the mechanical design and product reliability when used in harsh vibration condition. Generally electronic package design for vibration loads is verified by conducting tests on actual hardware.This paper addresses on using basic FEA tool to accurately investigate the dynamic characteristics of the PCB and avoid costly testing methods which require hardware. Here the normal modes & frequency response functions (FRF) of PCB are determined and validated using vibration test on PCB. The validated model is used to predict vibration response for random vibration input. It is shown here how the responses are accurately predicted for random vibration input for a design parameter variation of PCB. The results are also validated using vibration test on PCB.

Structural damping identification method using normal FRFs

All structures exhibit some form of damping, but despite a large literature on the damping, it still remains one of the least well-understood aspects of general vibration analysis. The synthesis of damping in structural systems and machines is extremely important if a model is to be used in predicting vibration levels, transient responses, transmissibility, decay times or other characteristics in design and analysis that are dominated by energy dissipation. In this paper, new structural damping identification method using normal frequency response functions (NFRFs) which are obtained experimentally is proposed and tested with the objective that the damped finite element model is able to predict the measured FRFs accurately. The proposed structural damping identification is a direct method. In the proposed method, normal FRFs are estimated from the complex FRFs, which are obtained experimentally of the structure. The estimated normal FRFs are subsequently used for identification of general structural damping. The effectiveness of the proposed structural damping identification method is demonstrated by two numerical simulated examples and one real experimental data. Firstly, a study is performed using a lumped mass system. The lumped mass system study is followed by case involving numerical simulation of fixed–fixed beam. The effect of coordinate incompleteness and robustness of method under presence of noise is investigated. The performance of the proposed structural damping identification method is investigated for cases of light, medium, heavily and non-proportional damped structures. The numerical studies are followed by a case involving actual measured data for the case of a cantilever beam structure. The results have shown that the proposed damping identification method can be used to derive an accurate general structural damping model of the system. This is illustrated by matching the damped identified FRFs with the experimentally obtained FRFs.

Model Updating of Dynamic Systems Using Structural Reanalysis Method

Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are unavoidably corrupted with uncorrelated noise content. In this paper, reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. A numerical example is employed to illustrate the applicability of the proposed method. The result indicates that the present method is effective.

Analysis of Structural System Dynamic Model Updating Method

Model updating methods are successful in use of simulated data without noise, but inevitably lead to damaged uncorrelated noise levels and real experimental data, and it is often unpredictable. In this paper, the use of the frequency response function associated with re-analysis and updating of dynamic systems are proposed. Transformation matrix complexity and the normal frequency response function relationship between the structures are obtained. The transformation matrix is used to calculate the modified damping matrix of the system. The modified mass and stiffness matrices by using the least squares method is used to determine the frequency response function from the normal. A numerical example is tested to illustrate the applicability of the proposed method. The results show that this method is effective.

Mixed Mode Precession Display Based on Normal Directional Frequency Response Functions of Rotor Dynamic Systems

Mixed Mode Precession Display Based on Normal Directional Frequency Response Functions of Rotor Dynamic Systems

A method for damping matrix identification using frequency response data

Accurate modeling of damping in structures is of great importance for vibration response analysis and control. This paper addresses the issue of identification of damping matrix of a structure by posing it as a finite element damping matrix updating problem. Many of the current updating approaches, dealing with updating of damping matrix, perform simultaneous updating of mass, stiffness and damping matrices. However, such a strategy is faced with numerical problems in practical implementation, since the magnitude of stiffness and mass matrix elements is generally much more than that of the damping matrix elements causing difficulties in accurate identification of the damping matrix. Some other approaches divide the process of updating of the mass and stiffness matrix and the damping matrix into two stages, but their application is restricted to structures with low levels of damping. This paper addresses these issues by developing an updating formulation that seeks to separate updating of the damping matrix from that of updating of the stiffness and the mass matrix. The proposed damping matrix updating method utilizes the concept of normal frequency response functions (FRFs) available in the literature. The method is formulated so as to reduce the difference between the complex FRFs, which can be measured in practice, and the normal FRFs, whose estimates can be obtained from the measured complex FRFs. The effectiveness of the proposed method is demonstrated through a numerical study on a simple but representative beam structure. The issue of coordinate incompleteness and robustness of the method under presence of noise is investigated. It is found that the proposed method is effective in the accurate identification of the damping matrix in cases of complete, incomplete and noisy data and is not limited by the level of damping in the structure.

Evaluation of Effects of Wave-induced Vibrations on Fatigue Damage of Large Ships

Low frequency response to normal wave loads and high frequency response due to wave-induced vibrations coexist in the ship's structural loads. This paper addresses the effect of the wave-induced vibrations on long-term fatigue damage in various types of ships. A bulk carrier, a VLCC, and a container carrier are employed as subject ships. A weakly nonlinear method proposed by one of the authors is employed for evaluating the load effects. Slamming loads are separately implemented by using momentum theory.The whole ship is represented by using shell FE model. The calculations are performed for various short-term sea states. Stress cycles are counted by using Rainflow counting method. Then, long-term fatigue damage is evaluated by using the Palmgren-Miner rule. A series of sensitivity analysis is also performed to clarify the characteristics of the fatigue damage by the wave-induced vibrations in oblique seas as well as in head seas. It is shown that the amount of the increase in fatigue damage depends on the wave load characteristics of the ships in waves as well as the structural properties such as natural frequencies of flexible mode.

Structural Reanalysis of Dynamic Systems Using Model Updating Method

Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are unavoidably corrupted with uncorrelated noise content. In this paper, reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. A numerical example is employed to illustrate the applicability of the proposed method. The result indicates that the present method is effective.

Structural parameters identification using improved normal frequency response function method

An improved method that is based on a normal frequency response function (FRF) is proposed in this study in order to identify structural parameters such as mass, stiffness and damping matrices directly from the FRFs of a linear mechanical system. This paper demonstrates that the characteristic matrices may be extracted more accurately by using a weighted equation and by eliminating the matrix inverse operation. The method is verified for a four degrees-of-freedom lumped parameter system and an eight degrees-of-freedom finite element beam. Experimental verification is also performed for a free–free steel beam whose size and physical properties are the same as those of the finite element beam. The results show that the structural parameters, especially the damping matrix, can be estimated more accurately by the proposed method.

System Matrices Identification of Structure: An Insensitive Procedure for Data Point Configurations.

A frequency-domain method for estimating the mass, stiffness and damping matrices of a structure is presented. The method is developed based on the normal frequency response functions extracted from the complex ones. In this method, a transformation matrix is obtained first from the complex frequency response functions of a structure. The damping matrix is calculated independently from this transformation matrix, while the mass and stiffness matrices are identified from the extracted normal frequency response functions by using the least squares method. Furthermore, in this paper, it is emphasized that the accuracy of identified system matrices for different data point configurations are addressed. The simulated and experimental results indicate that a more accurate damping matrix can be identified and the present method is insensitive to the data point configurations used in the identification procedure even for cases with only few data points.

D1 agonist CY208–243 attenuates the pattern electroretinogram to low spatial frequency stimuli in the monkey

We investigated whether or not the D1 agonist, CY 208–243, affects the spatial tuning function of pattern electroretinogram (PERG). Two lightly anaesthetised monkeys were studied before and after CY 208–243 or placebo administration. The results show that the PERG response to 0.5 cycles/degree (c/d; coarse), but not to 2.3 c/d (medium) spatial frequency stimuli disappears following systemic administration of this drug. Since previous results show that D2 blockers attenuate the PERG only above 2.3 c/d, foremost the peak of the normal spatial frequency response function, the current results suggest that dopamine itself, via D1 receptors, may be responsible for the low spatial frequency decline of normal spatial PERG tuning function. We infer that the synergistic activation of D1 and D2 receptors is needed to shape the spatially tuned primate ERG.

Estimation of Mass, Stiffness and Damping Matrices from Frequency Response Functions

A frequency-domain method for estimating the mass, stiffness and damping matrices of the model of a structure is presented. The developed method is based on our previous work on the extraction of normal modes from the complex modes of a structure. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the damping matrix of the system. The mass and the stiffness matrices are identified from the normal frequency response functions by using the least squares method. Two simulated systems are employed to illustrate the applicability of the proposed method. The results indicate that the damping matrix can be identified accurately by the proposed method. The reason for the good results is that the damping matrix is identified independently from the mass and the stiffness matrices. In addition, the robustness of the new approach to uniformly distributed measurement noise is also addressed.

Estimation of system matrices by dynamic condensation and application to structural modification

A method for estimating mass, stiffness, and damping matrices of a dynamic system was presented in our previous paper. That technique is based on extracting the normal frequency response functions from the experimental complex ones. Independent from the mass and stiffness matrices, the damping matrix is calculated alone, whereas the mass and the stiffness matrices are identified from the normal frequency response functions by using the least squares method. In this paper, we extend that method to deal with an incomplete system and to indicate that the condensed physical system matrices can also be obtained by that method. These condensed system matrices represent a dynamic condensation of the original full system. Furthermore, the condensed system matrices are applied to the problem of determining the structural modifications necessary to shift the damped natural frequency to a desired value. Both simulation and experimental examples are carried out to illustrate the applicability of the present method. The results indicate that the method is effective and accurate. Nomenclature C = viscous damping matrix of original system Cr viscous damping matrix of reduced system f(t) = force vector of original system in time domain f(to) = force vector of original system in frequency domain fr (to) = force vector of reduced system in frequency domain Hc(to) = complex frequency response function matrix for the original system Hf (to) = complex frequency response function matrix for the reduced system HN(co) = normal frequency response function matrix for the original system H? (to) = normal frequency response function matrix for the reduced system //(A) = transfer function matrix in Laplace domain / = identity matrix K = stiffness matrix of original system Kr = stiffness matrix of reduced system