Numerical Frequency Response Functions Research Articles

A 3D finite element model updating of spinal lumber segment applying experimental modal data and particle swarm optimization algorithm

The dynamic loadings can be more harmful than static ones for the human lumbar spine health. Consequently, the prediction of the spine behavior under dynamic and vibration loads is vital and can be achieved by creating a precise finite element model in which the dynamic mechanical properties of the components need to be estimated. For this purpose, noninvasive experimental modal analysis can be applied to evaluate the dynamic mechanical properties of the spine in the numerical simulation by supplying the structural dynamic characteristics (natural frequencies, mode shapes, and damping ratio) of the system. Since the most adequate model for the human lumbar segment is a sheep model, in this paper, a 3D finite element model of a fresh spinal lumber segment of a sheep is generated based on the poroelasticity theory via Abaqus and is updated utilizing particle swarm optimization (PSO) algorithm and experimental modal analysis. In this regard, the frequency response function (FRF) of the specimen is obtained by performing the experimental modal test and the modal parameters are derived by using the rational fraction polynomial method. Afterward, the sensitivity analysis is carried out to determine the appropriate design variables. Finally, the PSO algorithm using experimental data is employed to update the design variables, including the elastic material properties and the structural damping factors of the specimen components, and the stiffness and damping coefficient of the suspension system. According to the results, the error percentage between the numerical FRF and the experimental one decreases remarkably after model updating indicating the high efficiency of the methods used.

Substructuring for Contact Parameters Identification in Bladed-disks

Single stage bladed-disks are fundamental bricks of the rotating parts of a turbomachine. Although made of nominally identical sectors, the presence of imperfections or misalignment produces a large amplification of the forced response. Furthermore, due to their high modal density, friction dampers must be designed to mitigate resonance stresses, since a perfect detuning of the resonances from the excitation forces is impossible. Blade-root joints in these structures can provide the much-desired damping but the contact between the disk slot platform and blade-root lobes is characterized by uncertainty due to the actual locking position and machining tolerances.The cases of two simple beams and a bladed-disk test rig of an array of blades with dovetail root joints are studied to identify contact parameters. A dynamic Lagrange multiplier frequency based sub-structuring (LM-FBS) method is applied in a hybrid manner (experimental and numerical frequency response functions) to identify a parameter associated to each contact by mounting only one blade at a time. A sensitivity analysis is performed that will provide the basis for future work on non-linear frequency response prediction.

Analytical Passive Time Reversal Method Combined With Equivalent Source Method for Sound Source Localization in an Enclosure

The analytical passive time reversal method (APTRM) is a powerful technique for sound source localization. In that technique, it generally requires that the frequency response function relating the measurement point to the focusing point should be known in advance. However, inside an enclosure of arbitrary shape, there is no theoretical formulation of this frequency response function, and using the APTRM with the free-field Green's function might lead to inaccurate localization of sound sources. This paper proposes a method combining the APTRM with the equivalent source method (ESM) to locate sound sources in an enclosure of arbitrary shape. In this method, the frequency response function relating the measurement point to the focusing point inside the enclosure is first calculated numerically using the ESM, and then the APTRM with this numerical frequency response function is used to realize the localization of sound sources. Numerical simulations in a rectangular enclosure and an enclosure of arbitrary shape as well as an experiment in a rectangular wooden cabinet are performed to verify the validity of the proposed method. The results demonstrate that the frequency response function in an enclosure can be accurately calculated using the ESM; based on measurements with a spherical array composed of 48 microphones, the proposed method can effectively locate the sound sources in enclosures of different shapes and work stably under the situation of low signal-to-noise ratio.

Impact wave attenuation using Maxwell-type oscillators in dissipative elastic metamaterials

This work studies the development of a dissipative elastic metamaterial with single and dual-Maxwell type resonator for stress wave mitigation. Mass-spring-damper elements are used to model and analyze the mechanism of wave dissipation effect on the vibration characteristics. It is found that broadband wave attenuation region can be obtained and expanded to a wider range by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. In addition, numerical verifications are conducted for various cases, and excellent agreement between theoretical and numerical frequency response functions are obtained. The design of this dissipative metamaterial system is further applied for blast wave mitigation. By means of the bandgap merging effect that is induced by the Maxwell-type oscillator, the passing blast wave can be almost completely suppressed in the low-frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

Prediction of stability in boring using a multistep tool

This article presents an original study about the dynamic of a machining operation based on the coupling receptance methodology. The Frequency Response Function (FRF) of a machine tool is numerically coupled with the FRF matrix of a multi-stage reaming tool in order to predict its dynamic behavior during the operation. This coupling results in a mix of measured and numerical FRF matrix and is used for solving the stability prediction of the operation with an analytical methodology. Stability lobes are computed in respect with the load factor. It is shown in the paper that this methodology is suitable for adjusting the cutting conditions in the case of a given operation where the tool is identified but also for a numerical model of a tool, for instance at a design stage. As a conclusion, the presented methodology can help to target the best cutting conditions for a given machine-tool and toll but also help the manufacturer in the tool choice or design in order to guaranty the stability of the operation.

On the Pressure Ripple Measurement in Variable Displacement Vane Pumps

Vane pumps exhibit pressure ripple in the pressure evolution trend during a complete shaft rotation. Pressure ripple can determine oscillating forces within the system leading to vibration and noise generation. In this context, this paper is focused on the experimental measurement of the pressure evolution in vane pumps by using two different methodologies. Results of measurements are shown, highlighting advantages and disadvantages of both methodologies. In the first method a pressure transducer is directly facing the volume between two vanes, in the second method the sensor is located inside an external chamber where the oil is transferred via a duct suitably designed in the rotor shaft. Briefly, the first method gives better results in terms of pressure evolution but involves some practical problems in the setup: the measurements exhibit pressure offsets strongly dependent on the tightening torque used for sensor mounting and negative pressure values in the low pressure region. The second method is simpler to set up but the results are influenced by the dynamical behavior of the measurement duct carrying oil. In order to avoid resonances of this duct, a vibro-acoustical finite element (FE) model of the oil cavity has been developed. The numerical frequency response functions obtained by the FE model have been used in order to optimize the geometry of the measurement duct, reducing the effects of the resonances of the oil ducts. It is shown that, using this improved methodology, the dynamical components of the measured pressure are not significantly influenced by the frequency response of the measurement duct when the outlet pressures is higher than 50 bar, while for lower outlet pressure the first resonance of the measurement duct is close to the main vane harmonics.

A new damping modelling approach and its application in thin wall machining

In this paper, a new approach to modelling the damping parameters and its application in thin wall machining is presented. The approach to predicting the damping parameters proposed in this paper eliminates the need for experiments otherwise used to acquire these parameters. The damping model proposed was compared with available damping models and experimental results. A finite element analysis and Fourier transform approach has been used to obtain frequency response function (FRF) needed for stability lobes prediction. Several predicted stable regions using both experimental and numerical FRF’s for various examples gave a good comparison.

On-line fan blade damage detection using neural networks

This paper presents a methodology for monitoring the on-line condition of axial-flow fan blades with the use of neural networks. In developing this methodology, the first stage was to utilise neural networks trained on features extracted from on-line blade vibration signals measured on an experimental test structure. Results from a stationary experimental modal analysis of the structure were used for identifying global blade mode shapes and their corresponding frequencies. These in turn were used to assist in identifying vibration-related features suitable for neural network training. The features were extracted from on-line blade vibration and strain signals which were measured using a number of sensors.The second stage in the development of the methodology entails utilising neural networks trained on numerical Frequency Response Function (FRF) features obtained from a Finite Element Model (FEM) of the test structure. Frequency domain features obtained from on-line experimental measurements were used to normalise the numerical FRF features prior to neural network training. Following training, the networks were tested using experimental frequency domain features. This approach makes it unnecessary to damage the structure in order to train the neural networks.The paper shows that it is possible to classify damage for several fan blades by using neural networks with on-line vibration measurements from sensors not necessarily installed on the damaged blades themselves. The significance of this is that it proves the possibility to perform on-line fan blade damage classification using less than one sensor per blade. Even more significant is the demonstration that an on-line damage detection system for a fan can be developed without having to damage the actual structure.