Acceleration Frequency Response Functions Research Articles

Longitudinal Vibration Transmission Control of Marine Propulsion Shafting with Friction Damper Integrated into the Thrust Bearing

Propeller-induced longitudinal vibration resonance in marine propulsion shafting systems causes great harm to the hull structure and is the primary source of shipboard noise. Integrating a friction damper with designed parameters into thrust bearings can prevent these issues. To investigate the performance of the damper-integrated thrust bearing in longitudinal vibration transmission control, an experimental and theoretical study is carried out in a laboratory-assembled test rig, which consists of components similar to the existing marine propulsion system. We developed a prototype of a thrust bearing designed with a friction-damping generation that allows switching from two supporting states, i.e., damper-connected and damper-disconnected states. Furthermore, a nonlinear analysis method for friction dampers is proposed. By this method, the way in which the friction damper changes the dynamic characteristics of the shafting system is analyzed. Based on the test rig, the acceleration frequency response function (AFRF) of the thrust bearing with and without a friction damper is measured. By comparison, the effectiveness of the friction damper is proved. The experimental results show that the friction damper suppresses the shafting longitudinal vibration response in a broadband frequency range and also confirms the stability of the damping effect, which does not change with the shafting rotational speed or static thrust from the propeller.

Pyroshock Response Prediction of Spacecraft Structure in Wide Frequency Domain Based on Acceleration FRF

The initiating explosive shock environment of an aerospace mission has the characteristics of instantaneity, high amplitude and a wide frequency domain. An improved method based on the acceleration frequency response function (FRF) and virtual mode synthesis method (VMSS) is proposed to predict the pyroshock response of a spacecraft structure in a wide frequency domain. Firstly, the statistical energy analysis (SEA) model of the spacecraft structure was established, and the FRF and modal density of the model were obtained. Then, the paper explains how, due to the small number of modes in the low-frequency band, the calculation results of the SEA method in the low-frequency band were not accurate enough. The FRF of the SEA model in the low-frequency band was modified by an FRF test of the structure. Finally, the shock response spectrum (SRS) was obtained based on the VMSS and the modified FRF. A shock experiment on the spacecraft structure was conducted by using the shock experiment system, which is based on a light-gas gun. The accurate shock force function and acceleration response results were obtained. The numerical results based on the improved method are in line with those in the experiment. This verifies that the novel method can better grasp the response characteristics of the structure in the broadband domain. The novel method effectively improves the response prediction accuracy of the SEA model in the relatively low-frequency band. While ensuring the computational efficiency, more accurate shock response results in a wide frequency domain were obtained. The novel method presented in this paper provides support of numerical analysis for pyroshock response prediction of spacecraft structure in a wide frequency domain.

Stochastic Model Updating Based on Kriging Model and Lifting Wavelet Transform

In order to improve the efficiency of stochastic model updating and reduce the amount of calculation, a stochastic model updating method based on Kriging model and lifting wavelet transform is proposed. Firstly, perform lifting wavelet transform on the acceleration frequency response function, and extract the fifth-level approximate coefficients to replace the original frequency response function; secondly, use the Latin hypercube sampling to sample the parameters to be updated and the corresponding approximate coefficients as the outputs to build the Kriging model. A butterfly optimization algorithm with the Lévy flight(LBOA) is proposed and use to improve the accuracy of the Kriging model; finally, with the goal of minimizing the Wasserstein distance, the mean value of the parameters to be updated is solved by the whale optimization algorithm. The results of the test function show that LBOA has greatly improved in terms of optimization, convergence accuracy and stability. The updating errors of the numerical examples are all less than 0.4%, verifying that the proposed model updating method has high accuracy and efficiency.

Comparison of damping parameters based on the half-power bandwidth methods of viscous and hysteretic damping models

The half-power bandwidth method is usually used to calculate structural damping parameters by frequency response function (FRF). In this note, the half-power bandwidth methods for the displacement FRF, the velocity FRF, and the acceleration FRF are proposed based on viscous and hysteretic damping models, respectively. Comparison results show that the application conditions of half-power bandwidth methods for the displacement and acceleration FRFs are limited. They can only be used to calculate the small damping ratio/loss factor. The application condition of half-power bandwidth method for the velocity FRF is not limited. It can be used to calculate the large or small damping ratio/loss factor, which should be the first choice for calculating damping parameters. Besides, when the damping ratio is less than 0.2546 or the loss factor is less than 0.5658, the relative difference between the loss factor and twice the damping ratio is less than 10%. With the increase of the damping ratio or loss factor, the relative difference will increase rapidly, and the approximate relationship is no longer applicable.

Welding distortion generated uncertainties in the vibrational behavior of a ladder-like structure

Recent developments in acoustic simulation methods allowed engineers to assess the vibroacoustic behavior of various type of structures within a virtual environment, thus allowing the replacement of prototype-based development with simulations. However, there are some factors, that cannot be considered in simulations in advance. In the present study, the effect of the distortions generated due to welding on a ladder-like structure equipped with flat plates was investigated. The measured acceleration frequency response functions were compared to finite element simulation results. The measured responses differed significantly from the simulation, even in the low frequency range, where the global modes were not expected to be altered or vanished. Investigation of the simulated results revealed that the additional modes were related to the vibration of the plates, which were assumed to be flat, instead of considering the warping caused by the welding process. After measuring the approximate deformation of the plates, an updated simulation model was made, introducing an approximate curvature in them. The results obtained with the updated simulation model performed much better in the low frequency range as well as in the third octave-averaged frequency bands up 1200 Hz. The sensitivity of the warping was also systematically evaluated.

Finite Element Analysis of Origin Dynamic Stiffness and Vibration Sensitivity of BIW

In this paper, Hyperworks software is used for geometric cleaning, meshing and grid quality checking of the BIW model. The BIW model is assembled with solder joint units, and then the dynamic stiffness of the joints is analyzed. The acceleration frequency response function (IPI) curve is obtained by simulating the body with the method of origin admittance. The dynamic stiffness deficiency is found by comparing with the dynamic stiffness curve of the target value. Vibration transfer function of the body is obtained by vibration sensitivity analysis, and the sensitive parts of the body under excitation are located more accurately. Some corresponding suggestions and optimization are put forward to improve the NVH performance of the body.

Finite element model updating of jointed structure based on modal and strain frequency response function

To acquire a reasonable model for structural dynamic strength analysis, a bottom-up finite element modeling and updating methodology based on multi responses is proposed. The fundamental principles of structural dynamics analysis and model updating were introduced, and the proposed strategy was applied to the case study of an L-shaped jointed structure. Components of the jointed structure were modeled sequentially, and inaccurate model parameters were updated based on the corresponding experimental modal results in the first stage. In the second stage, components were connected together by bolts. The joint interfaces were represented by thin-layer elements, and local joint parameters were updated based on strain frequency response function (FRF). Finally, the precision of finite element model (FEM) was validated by acceleration frequency response function. The results indicated that the proposed methodology is able to reduce model simulation errors in both components and the overall jointed structure. Not only can the updated model of a jointed structure reproduce the experimental results used in updating, but also predict responses that are not used in the process of model updating.

Model Updating Method Based on Kriging Model for Structural Dynamics

Model updating in structural dynamics has attracted much attention in recent decades. And high computational cost is frequently encountered during model updating. Surrogate model has attracted considerable attention for saving computational cost in finite element model updating (FEMU). In this study, a model updating method using frequency response function (FRF) based on Kriging model is proposed. The optimal excitation point is selected by using modal participation criterion. Initial sample points are chosen via design of experiment (DOE), and Kriging model is built using the corresponding acceleration frequency response functions. Then, Kriging model is improved via new sample points using mean square error (MSE) criterion and is used to replace the finite element model to participate in optimization. Cuckoo algorithm is used to obtain the updating parameters, where the objective function with the minimum frequency response deviation is constructed. And the proposed method is applied to a plane truss model FEMU, and the results are compared with those by the second-order response surface model (RSM) and the radial basis function model (RBF). The analysis results showed that the proposed method has good accuracy and high computational efficiency; errors of updating parameters are less than 0.2%; damage identification is with high precision. After updating, the curves of real and imaginary parts of acceleration FRF are in good agreement with the real ones.

A damping estimation method based on power ratio

A bandwidth method based on power ratio is proposed to evaluate the system damping by using frequency response functions. For single-degree freedom systems, exact formula for calculating damping ratio from displacement frequency response function is established. Additionally, an approximate formula to estimate the damping ratio from acceleration frequency response function is also derived. Both are represented in terms of the power ratio and the bandwidths relative to the corresponding peak frequencies. In contrast to the well-known half-power method, the proposed method can be used for relatively large damping ratios by selecting a corresponding high power ratio. The accuracy of the proposed formulas in damping estimation is investigated for a four-degree of freedom system by numerical experiments. The results show that by increasing the power ratio, the estimation errors in damping ratios for the four-degree of freedom system can be significantly reduced.

Mid-frequency dynamic characteristics prediction of thin plate based on B-spline wavelet on interval finite element method

Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1 type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1 type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1 type WFEMs. On the other hand, the method combining c1 type B-spline wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.

A Comparison of the Improved and Classic Half-Power Bandwidth Methods in Estimating Damping for Multi-DOF Systems

It is significant to estimate the damping ratios for stability of some engineering structures and micro-structures. This note will evaluate Multi-DOF (MDOF) linear system damping ratios. This note is concerned with presenting improved approximate formulas of half-power bandwidth method (HPBM) for evaluating MDOF linear system damping ratios based on their DFRF and AFRF curve. A two-DOF (TDOF) linear vibration system is specially given to establish numeric experiments. The classic, third-order corrections and improved formulas of HPBM are listed. More specifically, using its displacement frequency response function (DFRF) and acceleration frequency response function (AFRF), the damping ratios of a linear system with TDOF are evaluated for a large range of significant factors. It is observed that the present improved formulas of evaluating damping ratios with HPBM are explicit and precise for a certain range.

Milling force identification from acceleration signals using regularization method based on TSVD in peripheral milling

Milling forces are important signals that can be used to monitor the condition of machine operating and milling process. In general, milling forces can be measured by special equipment, for example, Kistler dynameters. However, dynameters are very expensive and require particular geometry of workpiece, which causes that dynameters are limited in research laboratories rather than actual production. In this paper, a force identification method in frequency domain, the regularization method based on the truncated singular value decomposition (TSVD), is employed for milling force reconstruction using acceleration signals in peripheral milling process. The two acceleration sensors are mounted on the spindle box in the feed and cross-feed directions for reconstructing the milling forces. The regularization method based on TSVD is adopted for inverse problem in force identification because of its high identification accuracy, which can possess ill-conditioned matrixes well. Finally, the method is validated by numerical simulation and cutting experiments. In the experiment, the milling forces and acceleration signals from spindle box are acquired synchronously. Then, the frequency response functions between milling tool nose and acceleration sensors in the feed and cross-feed directions are obtained by impact tests. With the acceleration signals and frequency response functions, the milling forces can be reconstructed. Identified results show that the calculated forces and the measured forces are in good agreement on the whole, which verify the effectiveness of the employed method on milling force identification.

Experimental investigation of fan-folded piezoelectric energy harvesters for powering pacemakers

This paper studies the fabrication and testing of a magnet free piezoelectric energy harvester (EH) for powering biomedical devices and sensors inside the body. The design for the EH is a fan-folded structure consisting of bimorph piezoelectric beams folding on top of each other. An actual size experimental prototype is fabricated to verify the developed analytical models. The model is verified by matching the analytical results of the tip acceleration frequency response functions (FRF) and voltage FRF with the experimental results. The generated electricity is measured when the EH is excited by the heartbeat. A closed loop shaker system is utilized to reproduce the heartbeat vibrations. Achieving low fundamental natural frequency is a key factor to generate sufficient energy for pacemakers using heartbeat vibrations. It is shown that the natural frequency of the small-scale device is less than due to its unique fan-folded design. The experimental results show that the small-scale EH generates sufficient power for state of the art pacemakers. The 1 cm3 EH with tip mass generates more than of power from a normal heartbeat waveform. The robustness of the device to the heart rate is also studied by measuring the relation between the power output and the heart rate.

Frequency response function-based model updating using Kriging model

An acceleration frequency response function (FRF) based model updating method is presented in this paper, which introduces Kriging model as metamodel into the optimization process instead of iterating the finite element analysis directly. The Kriging model is taken as a fast running model that can reduce solving time and facilitate the application of intelligent algorithms in model updating. The training samples for Kriging model are generated by the design of experiment (DOE), whose response corresponds to the difference between experimental acceleration FRFs and its counterpart of finite element model (FEM) at selected frequency points. The boundary condition is taken into account, and a two-step DOE method is proposed for reducing the number of training samples. The first step is to select the design variables from the boundary condition, and the selected variables will be passed to the second step for generating the training samples. The optimization results of the design variables are taken as the updated values of the design variables to calibrate the FEM, and then the analytical FRFs tend to coincide with the experimental FRFs. The proposed method is performed successfully on a composite structure of honeycomb sandwich beam, after model updating, the analytical acceleration FRFs have a significant improvement to match the experimental data especially when the damping ratios are adjusted.

Structural dynamic model updating based on Kriging model using frequency response data

Metamodel technique is attracting more and more attention in structural dynamic model updating. In this paper, an attempt is made to explore the effectiveness of Kriging method for acceleration frequency response function based model updating. A Kriging model is constructed based on the input variables selected by F-test method specially, which is applied to the results of design of experiment. The response of design of experiment is obtained based on the errors between acceleration response curves of analytical model and experimental model. Two examples of representative structure are discussed, the comparison of updated results of different metamodel shows that a less error of updated results can be obtained based on Kriging model, and the updated analytical model has a good prediction capability. It can be concluded that the Kriging model is suitable for the frequency response function based model updating.

Piezoelectric energy harvesting from heartbeat vibrations for leadless pacemakers

This paper studies energy harvesting from heartbeat vibrations using fan-folded piezoelectric beams. The generated energy from the heartbeat can be used to power a leadless pacemaker. In order to utilize the available 3 dimensional space to the energy harvester, we chose the fan-folded design. The proposed device consists of several piezoelectric beams stacked on top of each other. The size for this energy harvester is 2 cm by 0.5 cm by 1 cm, which makes the natural frequency very high. High natural frequency is one major concern about the micro-scaled energy harvesters. By utilizing the fan-folded geometry and adding tip mass and link mass to the configuration, this natural frequency is reduced to the desired range. This fan-folded design makes it possible to generate more than 10 μW of power. The proposed device does not incorporate magnets and is thus Magnetic resonance imaging (MRI) compatible. Although our device is a linear energy harvester, it is shown that the device is relatively insensitive to the heartrate. The natural frequencies and the mode shapes of the device are calculated. An analytical solution is presented and the method is verified by experimental investigation. We use a closed loop shaker controller and a shaker to simulate the heartbeat vibrations. The developed analytical model is verified through comparison of theoretical and experimental tip displacement and acceleration frequency response functions.

Importance of Selecting a Suitable Analysis Frequency Range in Impact Force Identification for Automobile Test Rig

In this study, the effectiveness of selecting a suitable analysis frequency range in impact force identification is highlighted. A methodology that utilizesOperating Deflection Shape (ODS) analysis, Modal Analysis (MA) and Modal Transformation Method (MTM) to evaluate the dynamic force in three cases of analysis frequency ranges was presented. These three cases are the over-estimated, even-estimated, and under-estimated cases, which consist of higher, similar andlower analysis frequency range respectively, compared to the actual excitation frequency range. The performance of this approach was demonstrated via experiment. A Perspex plate with four ground supports was used as the automobile test rig. By measuring the acceleration response and Frequency Response Function (FRF) of the test rig, the time history of unknown force was recovered by the proposed method where the impact location was known in advance. It showed that the force identification result for even-estimated case falls within acceptable range while the force identification result for over-estimated and under-estimated cases isnot acceptable

A correction of the half-power bandwidth method for estimating damping

The half-power bandwidth method is commonly used to evaluate the system damping by using frequency response curves and assuming a small damping ratio. Preceding derivations obtain the third-order corrections to the classical formula but still show large errors when the damping ratio is high, especially for the acceleration case. In this note, new approximate formulas for damping ratio in terms of the half-power bandwidth are established using displacement and acceleration frequency response functions, respectively. The proposed formulas, third-order correction and classical approximations are compared by using relative errors of calculated damping ratios for both displacement and acceleration cases. The new formulas for damping ratio are brief and show excellent accuracy for small as well as high damping ratios.

Structural Integrated State Evaluation Base on Acceleration Frequency Response Function

Structural Integrated State Evaluation Base on Acceleration Frequency Response Function

Study of open crack in rotor shaft using changes in frequency response function phase

In recent years, significant efforts have been devoted to developing non-destructive techniques for damage identification in structures. This study investigated the effects of cracks and damages on the integrity of structures, with a view to detect, quantify, and determine their extents and locations. Previous works have used parameters, such as, changes in natural frequencies and mode shapes, as detectors. However, such parameters are not sensitive enough to detect early defects. In this paper, phase measurements are sought. Measurements of the acceleration frequency responses at different points on each rotor shaft were taken using a multi-channel frequency analyzer. The damage detection schemes used in this study depended on the changes in the phase of the measured acceleration frequency response functions. To study the changes of phases, it was interpreted in phase spectrum and Nyquist plot. Nyquist plot was used as it includes both real and imaginary parts of the amplitude and this was used to study phase shifts due to the presence of crack. The changes in phase depended on crack depth and how close the crack is to that mode shape node. Meanwhile, the changes in phase of lower eigenvectors were observed clearly. Thus, first mode shape was helpful in identifying the location of the crack. The vibration behavior of the rotor shaft was shown to be very sensitive to the crack depth, crack location and mode number. It is concluded that changes in phase as a function of crack depths and locations can be effective in crack detection methodology.