Calculate Frequency Response Functions Research Articles

An Improved Finite Element Model Updating Method Based on the Singular Values of Frequency Response Functions

Aiming at the problems that Markov chain Monte Carlo algorithm is not easy to converge, has high rejection rate, and is easy to be disturbed by the noise when the parameter dimension is high, an improved model updating method combining the singular values of frequency response functions and the beetle antennae search algorithm is proposed. Firstly, the Latin hypercube sampling is used to extract the training samples. The Hankel matrix is reconstructed using the calculated frequency response functions and is decomposed by singular value decomposition. The effective singular values are retained to represent the frequency response functions. Secondly, according to the training samples and the corresponding singular values, the support vector machine surrogate model is fitted and its accuracy is tested. Then, the posterior probability distribution of parameters is estimated by introducing the beetle antennae search algorithm on the basis of standard Metropolis–Hastings algorithm to improve the performance of Markov chains and the ergodicity of samples. The results of examples show that the Markov chains have better overall performance and the acceptance rate of candidate samples is increased after updating. Even if the Gaussian white noise is introduced into the test frequency response functions under the single and multiple working damage conditions, satisfactory updating results can also be obtained.

Dynamic wheel-rail interaction at high speed based on time-domain moving Green's functions

Many issues of concern in the railway industry are fundamentally caused by dynamic wheel-rail interaction. To deal with these issues, the characteristics of the interaction must be accurately predicted and fully understood; this becomes even more challenging when the train speed is high. Although much research has dealt with wheel-rail interaction, some aspects related to high speed trains still need to be further addressed. In this paper, an approach based on time-domain moving Green's functions developed previously is extended and employed to calculate wheel-rail forces. The extension includes consideration of the flexibility and rotation of the wheelset by incorporating the associated time-domain moving Green's functions in the method. These are derived from the corresponding receptances by applying an experimental modal analysis technique to the calculated frequency response functions. Cases are considered for a single, or multiple, wheelsets rolling over a track represented as an infinitely long periodic structure. Wheel-rail forces are calculated for a set of parameters typical of the Chinese high-speed railway and for a number of typical excitation cases, including purely parametric excitation on a smooth rail, an indentation on the rail, wheel polygonisation and rail corrugation, for the purpose of revealing the frequency content of high-speed wheel-rail interaction. Effects of the wheel rotation on the wheel-rail forces are studied and comparisons are made between a single wheelset and multiple wheelsets.

Inverse identification of mechanical parameters of fiber metal laminates

In this paper, an inverse method to identify the mechanical parameters of fiber metal laminates is proposed on the basis of the measured and calculated frequency response functions. The classical laminates theory, orthogonal polynomial method, and energy method are employed to characterize the theoretical modal of a fiber metal-laminated thin plate under pulse excitation. And, an iterative solution on the basis of frequency response functions and least square method is proposed to identify the mechanical parameters of fiber metal laminates, which conclude the elastic modulus, Poisson's ratios, and loss factors. As an example to demonstrate the feasibility of the developed inverse method, the experimental test of a TA2/TC 300 fiber metal-laminated thin plate is implemented to identify the mechanical parameters. Moreover, the influences of approximation points and calculation step sizes on the identification accuracy and efficiency are discussed.

Experimental and Numerical Investigation into Formation of Metro Wheel Polygonalization

We present a detailed investigation of the mechanism of metro wheel polygonal wear using on‐site experiments and numerical simulation. More than 70% of metro wheels exhibit 6th–8th harmonic‐order polygonal wear; the excitation frequency of the polygonal wear is located in the 50–70 Hz interval at an operating speed of 65–75 km/h. To determine the root cause of the polygonal wear, a dynamic train behavior test is conducted immediately after wheel reprofiling. The results suggest a natural mode resonance in the vehicle/track system, whose frequency coincides with the passing frequency of the 6th–8th order polygonalization. The magnitude of the resonance increases significantly when the vehicle runs on a monolithic concrete bed with DTVI2 fasteners. Thus, a corresponding coupled vehicle/track dynamic model is established and validated by comparing the calculated frequency response functions (FRFs) of tracks and dynamic responses of axlebox acceleration with the measured values. Using multiple timescales, the dynamic model and Archard wear model are integrated in a closed loop for long‐term polygonal wear prediction. The simulated and measured evolution of polygonal wear show good agreement. By combining simulation results and experimental data, we suggest that the P2 resonance is the main contributor to the high amplitude of wheel/rail contact forces in the 50–70 Hz frequency range and the reason for subsequent polygonal wear. Parametric studies show that the dominant order decreases as vehicle speeds increase, representing a “frequency‐constant” mechanism. The wheelset flexibility, especially the bending mode, would aggravate the wheel/rail creepage and further accelerate the formation of polygonal wear. Higher rail pad stiffness will increase P2 resonance frequency and shift the dominant wheel to higher polygonal orders.

Implementation of a Central Sensorimotor Integration Test for Characterization of Human Balance Control During Stance.

Balance during stance is regulated by active control mechanisms that continuously estimate body motion, via a “sensory integration” mechanism, and generate corrective actions, via a “sensory-to-motor transformation” mechanism. The balance control system can be modeled as a closed-loop feedback control system for which appropriate system identification methods are available to separately quantify the sensory integration and sensory-to-motor components of the system. A detailed, functionally meaningful characterization of balance control mechanisms has potential to improve clinical assessment and to provide useful tools for answering clinical research questions. However, many researchers and clinicians do not have the background to develop systems and methods appropriate for performing identification of balance control mechanisms. The purpose of this report is to provide detailed information on how to perform what we refer to as “central sensorimotor integration” (CSMI) tests on a commercially available balance test device (SMART EquiTest CRS, Natus Medical Inc, Seattle WA) and then to appropriately analyze and interpret results obtained from these tests. We describe methods to (1) generate pseudorandom stimuli that apply cyclically-repeated rotations of the stance surface and/or visual surround (2) measure and calibrate center-of-mass (CoM) body sway, (3) calculate frequency response functions (FRFs) that quantify the dynamic characteristics of stimulus-evoked CoM sway, (4) estimate balance control parameters that quantify sensory integration by measuring the relative contribution of different sensory systems to balance control (i.e., sensory weights), and (5) estimate balance control parameters that quantify sensory-to-motor transformation properties (i.e., feedback time delay and neural controller stiffness and damping parameters). Additionally, we present CSMI test results from 40 subjects (age range 21–59 years) with normal sensory function, 2 subjects with results illustrating deviations from normal balance function, and we summarize results from previous studies in subjects with vestibular deficits. A bootstrap analysis was used to characterize confidence limits on parameters from CSMI tests and to determine how test duration affected the confidence with which parameters can be measured. Finally, example results are presented that illustrate how various sensory and central balance deficits are revealed by CSMI testing.

Efficient aerodynamic derivative calculation in three-dimensional transonic flow

ABSTRACTOne key task in computational aeroelasticity is to calculate frequency response functions of aerodynamic coefficients due to structural excitation or external disturbance. Computational fluid dynamics methods are applied for this task at edge-of-envelope flow conditions. Assuming a dynamically linear response around a non-linear steady state, two computationally efficient approaches in time and frequency domain are discussed. A non-periodic, time-domain function can be used, on the one hand, to excite a broad frequency range simultaneously giving the frequency response function in a single non-linear, time-marching simulation. The frequency-domain approach, on the other hand, solves a large but sparse linear system of equations, resulting from the linearisation about the non-linear steady state for each frequency of interest successively. Results are presented for a NACA 0010 aerofoil and a generic civil aircraft configuration in very challenging transonic flow conditions with strong shock-wave/boundary-layer interaction in the pre-buffet regime. Computational cost savings of up to 1 order of magnitude are observed in the time domain for the all-frequencies-at-once approach compared with single-frequency simulations, while an additional order of magnitude is obtained for the frequency-domain method. The paper demonstrates the readiness of computational aeroelasticity tools at edge-of-envelope flow conditions.

Acoustic radiation modes and normal modes in exterior acoustic problems

Acoustic radiation modes are eigenvectors of the real and symmetric acoustic impedance matrix Z, which is usually computed by the boundary element method (BEM) matrices G and H at the surfaces of inner obstacles in an unbounded fluid-filled domain. Application of the finite element method (FEM) and the infinite element method (IFEM) allows the computation of the acoustic radiation modes as well, but also normal modes can be computed as right eigenvectors of a state-space eigenvalue problem. Modal superposition of both radiation modes and normal modes leads to accurate results of the radiated sound power. However, normal modes additionally provide modal sound pressure distributions in the whole computational domain and can therefore be used to calculate frequency response functions. In this work, modal superposition and reduction in exterior acoustics are presented and discussed.

Activation of GABAA receptors modulates all stages of mechanoreception in spider mechanosensory neurons

GABA(A) receptors mediate mainly inhibitory effects, but there are also many examples of excitatory effects in both mammalian and invertebrate preparations. Here, we aimed to create a complete, quantitative picture of GABA(A)-mediated excitation in a mechanosensory neuron where this phenomenon has been well established. We used muscimol to activate GABA(A) receptors in spider VS-3 neurons and measured the dynamic behavior independently and separately at each of three stages of mechanoreception (receptor current, receptor potential, and action potentials) before and during modulation. We calculated frequency response functions between each stage, estimated information as signal entropy, and estimated information capacity from coherence. Since coherence is sensitive to both noise and nonlinearity, we measured signal-to-noise separately at each stage by averaging responses to repeated mechanical inputs. Muscimol depolarized VS-3 neurons and, after brief inhibition, increased their firing rates. During this excitation, we found significant changes at each stage. Receptor current was attenuated but became more selective to high frequencies. Membrane impedance and time constant fell, favoring higher frequency transmission from receptor current to receptor potential. Action potential firing increased and had higher total entropy. Information capacity from signal-to-noise was always much higher than from coherence, confirming that intracellular noise does not limit signal transmission in these neurons. We conclude that GABA(A) receptor activation shifts each stage of mechanotransduction to higher frequency sensitivity, while the elevated firing rate increases the amount of information that can be encoded. These results show that a single neurotransmitter can finely modulate a sensory neuron's sensitivity and ability to transmit information.

Comparison of FRF measurements and mode shapes determined using optically image based, laser, and accelerometer measurements

Today, accelerometers and laser Doppler vibrometers are widely accepted as valid measurement tools for structural dynamic measurements. However, limitations of these transducers prevent the accurate measurement of some phenomena. For example, accelerometers typically measure motion at a limited number of discrete points and can mass load a structure. Scanning laser vibrometers have a very wide frequency range and can measure many points without mass-loading, but are sensitive to large displacements and can have lengthy acquisition times due to sequential measurements. Image-based stereo-photogrammetry techniques provide additional measurement capabilities that compliment the current array of measurement systems by providing an alternative that favors high-displacement and low-frequency vibrations typically difficult to measure with accelerometers and laser vibrometers. Within this paper, digital image correlation, three-dimensional (3D) point-tracking, 3D laser vibrometry, and accelerometer measurements are all used to measure the dynamics of a structure to compare each of the techniques. Each approach has its benefits and drawbacks, so comparative measurements are made using these approaches to show some of the strengths and weaknesses of each technique. Additionally, the displacements determined using 3D point-tracking are used to calculate frequency response functions, from which mode shapes are extracted. The image-based frequency response functions (FRFs) are compared to those obtained by collocated accelerometers. Extracted mode shapes are then compared to those of a previously validated finite element model (FEM) of the test structure and are shown to have excellent agreement between the FEM and the conventional measurement approaches when compared using the Modal Assurance Criterion (MAC) and Pseudo-Orthogonality Check (POC).

A Test Rig for Noncontact Traveling Wave Excitation of a Bladed Disk With Underplatform Dampers

This paper presents a static test rig called “Octopus” designed for the validation of numerical models aimed at calculating the nonlinear dynamic response of a bladed disk with underplatform dampers (UPDs). The test rig supports a bladed disk on a fixture and each UPD is pressed against the blade platforms by wires pulled by dead weights. Both excitation system and response measurement system are noncontacting. This paper features the design and the setup of the noncontacting excitation generated by electromagnets placed under each blade. A traveling wave excitation is generated according to a desired engine order by shifting the phase of the harmonic force of one electromagnet with respect to the contiguous exciters. Since the friction phenomenon generated by UPDs introduces nonlinearities on the forced response, the amplitude of the exciting force must be kept constant at a known value on every blade during step-sine test to calculate frequency response functions. The issue of the force control is therefore addressed since the performance of the electromagnet changes with frequency. The system calibration procedure and the estimated errors on the generated force are also presented. Examples of experimental tests that can be performed on a dummy integral bladed disk (blisk) mounted on the rig are described in the end.

The significance of continuity in a multi-panel composite floor

The paper identifies the significance of continuity between panels in a multi-panel composite floor. It examines dynamic behaviour through a comparison of the results from a forced vibration test, an eigenvalue analysis and a simulated sweeping test using an FE model. It also considers static behaviour comparing the results from a load test with an equivalent value from the FE model. Although the natural frequencies from the three different dynamic evaluations are close, there are significant differences between the measured and calculated frequency response functions; there are also significant differences in the static evaluations. It is suggested that this is because the continuity between adjacent panels is not perfect. The imperfect continuity is simulated using rotation springs along the edges between panels. The effect of the stiffness of the rotation springs is investigated using simulated sweep tests based on a five-span beam and a five-span plate. This provides an explanation for the differences observed between the tests and the FE model. Then the rotation spring model is applied to model the composite floor. By selecting appropriate stiffnesses the calculations align reasonably well with the measurements. The importance of selecting an appropriate model considering continuity is then discussed.

Analysis of the Forced Vibration of Two Bolted Half‐Pipes with Extended Friction Contacts

AbstractThe present paper deals with the forced vibration analysis of a test structure. The test structure consists of two parts, an upper and a lower half pipe, joint in two bolted flanges which represent the extended friction contacts. Depending on the clamping loads different normal pressure distributions can be established in the contact interfaces. Since the test structure is loaded with a harmonic external force relative displacements occur in the contact interface. This leads to microslip effects affecting the dynamic behaviour. The experimental validation of the calculation method accounting for these effects is shown by comparing measured and calculated frequency response functions (FRF). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 2—Numerical case studies

This work introduces a numerical algorithm to calculate frequency response functions of damped finite element models with fuzzy uncertain parameters. Part 1 of this paper focusses on the numerical procedure for the solution of the underlying interval finite element problem, based on the undamped procedure and the principle of Rayleigh damping. Part 2 of this paper illustrates the applicability of the methodology through four case studies. The concepts of the interval and the fuzzy finite element frequency response function analysis are illustrated for different types of uncertainties. The obtained results are compared with the results of Monte Carlo simulations.

Thickness Deformation of Constrained Layer Damping: An Experimental and Theoretical Evaluation

This paper presents a study of thickness deformation of the viscoelastic material in constrained layer damping (CLD) treatments. The first goal of the study is to demonstrate the feasibility of using direct measurement to investigate thickness deformation in CLD treatments. The experimental setup consisted of a constrained layer beam cantilevered to a shaker, an accelerometer mounted at the cantilevered end, and two laser vibrometers that simultaneously measured the responses of the base beam and the constraining layer, respectively, at the free end. A spectrum analyzer calculated frequency response functions (FRFs) between the accelerometer inputs and the vibrometer outputs. Measured FRFs of the base beam and the constraining layer were compared to detect thickness deformation. Experimental results showed that direct measurements can detect thickness deformation as low as 0.5 percent. The second goal is to evaluate the accuracy of a mathematical model developed by Miles and Reinhall [7] that accounts for thickness deformation. FRFs were calculated by using the method of distributed transfer functions by Yang and Tan [13]. Comparison of the numerical results with the experimental measurements indicated that consideration of thickness deformation can improve the accuracy of existing constrained layer damping models when the viscoelastic layer is thick.

DAMPING FUNCTION ESTIMATION BASED ON MEASURED VIBRATION FREQUENCY RESPONSES AND FINITE-ELEMENT DISPLACEMENT MODES

An estimation strategy for extraction of isotropic material damping is presented. The method is based on a modal receptance model, material damping functions and experimentally measured frequency response functions (FRF). Least-squares estimation of modal parameters is done by projections of the measured vibration responses onto a set of finite-element calculated elastic displacement modes. From identified modal parameters, based on the modal receptance model, a fast straightforward incremental least-squares material damping parameter estimation method is proposed. The methodology is demonstrated on two Plexiglas (PMMA) plates. Estimated material damping parameters are then validated on a third Plexiglas plate, with considerably different geometry, in the frequency interval 40–500 Hz. Results from comparisons between measured and calculated frequency response functions, using direct finite element method calculations, show extremely good agreement with respect to resonance frequency ‘location’ and response amplitude values. Finally, sources of uncertainty between model simulation and measurements are briefly discussed.

Experimental Verification Of A Non-HertzianContact Model

In the model presented the non-Hertzian contact planes are discretised. For each contact element the developed three-dimensional Point-Contact-Model is used to calculate the corresponding tangential and normal forces. The PointContact-Model includes the roughness, the normal pressure distribution, the stiffness in normal and tangential direction and dry friction. Due to roughness of the contact planes the contact stiffnesses are nonlinear dependent on the relative normal displacements. Effects of microslip due to roughness are investigated. An experiment with two non-Hertzian contacts is used to verify the developed model. The comparison between measured and calculated frequency response functions for three-dimensional vibrations of the elastic structures show a good agreement.

Dynamic Train/Track/Ballast Interaction - Computer Models and Full-Scale Experiments

A numerical method has been developed by which the vertical dynamic behaviour of a railway track subjected to the loading of a moving train may be investigated. The interacting train and track are both modelled as dynamic systems and the compound train/track system is treated as a whole. In the track model, the rail is treated as a Rayleigh-Timoshenko beam discretely supported, via railpads, by rigid sleepers. Below each sleeper, a rigid mass accounts for the mass of the ballast and those parts of the subgrade that participate in the vibration. The rigid mass is connected to the adjacent masses, to the foundation and to the sleeper by linear springs and viscous dampers. The mass, stiffness and damping of these track components and also the sleeper spacings can be arbitrarily varied. The contact between the wheelsets and the rail is modelled by non-linear Hertzian spring elements. The model permits calculation of deflections, accelerations and forces in various track components, and also enables engineers to investigate how parameters such as train speed, axle load, bogie wheelbase, rail corrugations, wheel flats and so on influence the track and vehicle components. To verify the computational method, two full-scale measurement programmes were carried out on the Swedish West Coast Line in 1993 and 1995. Track parameters are determined by use of measured frequency response functions. Measured and calculated frequency response functions show acceptable agreement. Variations in measured parameter values are discussed.

Practical method of dynamic analysis of symmetrically laminated composite plates.

This paper presents eigenvalue, eigenvector and frequency response analysis techniques based on FEM for symmetrically laminated composite plates by using stand-alone desktop microcomputers. In order to realize these dynamic analyses on a microcomputer, a technique has been proposed to substitute a symmetrically laminated orthotropic plate in a single anisotropic plate model. By using this technique, 12 d.o.f. rectangular and 9 d.o.f. triangular finite elements have been formulated. A subspace iteration algorithm is used for the eigenvalue and eigenvector analyses. A modal analysis effective for this particular problem has been developed to calculate frequency response functions using the results of the eigenvalue analysis. Furthermore, pre- and postprocessor for eigenvalue analyses have been conducted. A vibration test using CFRP (carbon fiber-reinforced plastics) symmetrically laminated composite plates as test pieces is performed to prove the effectiveness of the method. Study shows that this dynamic analysis technique could be of practical use and the proposed eigenvalue analysis technique could be effective for the plates whereby not only a wide range of fiber angles but aldo a dynamic coupling effect between bending and torsion forces are taken into consideration.

Imaging properties of a photoheliograph with a Lyot plane shutter

In a photoheliograph the shutter (a slit moving with constant velocity) may be placed in the Lyot plane, where the image of the objective is formed by the enlarging lens. This degrades the frequency response function of the objective, depending on the width of the slit. Calculated frequency response functions for a ideal objective and various slit widths are presented.