Experimental Modal Analysis Research Articles

Nonparametric approach for structural dynamics of high-voltage cables

High-voltage cables, as applied in the electro-mobility, are highly complex structures regarding their vibration behaviour. The high complexity leads to considerable uncertainty in models for a finite element method (FEM) simulation, which is shown, for example, in the contact modelling between the strands of the cable. To handle this uncertainty and model the structural dynamic, a nonparametric probabilistic approach (NPPA) with random matrices is used for the first time on high-voltage cables. This novel application of NPPA has an advantage over typical FEM analysis by using a more manageable simulation model and eliminating the need for a complex deterministic simulation model. Initially, the NPPA is analysed and enhanced, with an optimization for the dispersion parameter and a frequency shift introduced as methodological improvements. These enhancements result in a comparable scatter band of the frequency response. Following preliminary studies, the cable's dynamic behaviour is examined through experimental modal analysis, after which the dispersion parameters are computed. The NPPA is then applied to the simplified deterministic model with the calculated dispersion parameters, and a Monte Carlo simulation is done. As a result of this simulation, a scatter band is given. The results from the simulation are then compared to the results of an experiment. It is shown that the frequency response from the experiment is almost always in the inner area of the scatter band. Consequently, this innovative method can be used for a risk evaluation according to the path of the frequency response function and an evaluation of the structural behaviour.

Enhanced Design of Sunroof System through Parametric Study Considering Vibration Phenomenon during Vehicle Operation

Recently, performance development related to noise, vibration, and harshness in sunroof systems has attracted significant research attention. However, research thus far has been limited to analytical and experimental studies relating to structural improvement of the individual parts, rather than considering vehicle driving conditions. This study compared the experimental data from actual driving tests with simulation results to examine sunroof vibration characteristics under realistic conditions. Firstly, the characteristics of sunroof vibrations were investigated theoretically in order to derive equations of motion and the natural frequencies of the sunroof. Sunroof vibrations occurring during driving were analyzed through experimental modal analysis and operational deflection shape. A parametric study was conducted adapting design parameters such as the Young’s modulus, glass thickness, and bracket location. The vibration characteristics of the sunroof glass could be improved by changing the support points of the front and rear brackets, which represent the design elements that can achieve the greatest efficiency with minimal design changes.

Identification of natural frequencies of machine tools during milling: comparison of the experimental modal analysis and the operational modal analysis

Modal parameters (natural frequencies, mode shapes and modal damping) help to understand the dynamic behaviour of complex systems like machine tools. There are several approaches for finding the modal parameters. The Experimental Modal Analysis (EMA) has proven to be effective at standstill of a machine tool. The excitation, realized with impulse hammer or shaker, and excited responses at several locations are measured. Alternatively, the Operational Modal Analysis (OMA) can be deployed for finding the modal parameters during operation. Here, responses to excitation resulting from operation are only measured. The modal parameters are mathematically identified from the measured signals in both cases but with different methods. This paper discusses, to what extent both approaches (EMA and OMA) can lead to plausible identification of natural frequencies of a machine tool during milling. Concerning the EMA, attention is paid to capturing the excitation. Process forces can be assumed to be the most significant excitation. However, there are other excitation sources beside the process forces (e.g. drives, hydraulic and pneumatic aggregates), which are considered by this assumption to be a part of disturbances with consequence for the identification of the modal parameters. Regarding the OMA, attention is paid to the fact that the excitation is assumed to be broadband like the white noise. Unfortunately, this assumption does not match the characteristics of a real excitation. This paper contains the identification of natural frequencies of a machine tool during milling within both approaches. The achieved results are compared and discussed.

Stiffness identification of reinforced concrete beams using rotation rate sensors

Monitoring flexural stiffness variations of cracked reinforced concrete (r/c) structures is one of the most challenging problems of the dynamics of these structures. In this article, the application of rotation rate sensors for structural health monitoring of reinforced concrete beams is proposed as an alternative SHM method to, e.g. those utilising more expensive and laborious fiber optics. This subject was investigated with progressively damaged 6 m long reinforced concrete beams. During each damage state, the cracks were located and described in detail. Experimental modal analyses were carried out. Translational and rotational vibration modes were acquired using translational accelerometers and rotation rate sensors. The stiffness distributions of the damaged reinforced concrete beams were identified from the modal properties using model-updating techniques. It is demonstrated that stiffness distributions calculated using rotational modes are more accurate than those obtained from the familiar translational natural modes of vibrations. Further improvement of stiffness identification of r/c beams from their vibrations was obtained by combining the directly measured rotational modes and their approximations from translational modes by the central difference method.

Free vibration analysis of jute/kenaf/banana hybrid biocomposites: effects of various stacking sequences

This work provides an insight of the free vibration behaviour based on experimental modal analysis of hybrid natural fibre reinforced polymer composites fabricated via compression moulding method. This study aims to study the impact of different polymer matrices (vinyl ester and epoxy) and stacking order of different natural fibres (Jute, Kenaf and Banana) on the composite’s free vibration characteristics. Jute-Kenaf-Banana-Epoxy (JKBE) matrix composites exhibited enhanced free vibration properties compared to single fiber reinforcements, except the banana/epoxy composites. Additionally, Jute-Kenaf-Banana-Vinyl ester (JKBV) composites demonstrated improved free vibration properties in comparison to single fiber reinforcements, with the exception of kenaf/vinyl ester composites. Kenaf-Banana-Jute-Jute-Banana-Kenaf-Epoxy (KBJJBKE) and Kenaf-Banana-Jute-Jute-Banana-Kenaf-Vinyl ester (KBJJBKV) hybrid composites showed the highest natural frequencies of 68.36 Hz and 97.66 Hz, respectively. However, there was no significant improvements in the natural frequencies of Jute-Kenaf-Banana-Kenaf-Banana-Jute-Epoxy (JKBKBJE) and Jute-Kenaf-Banana-Kenaf-Banana-Jute-Vinyl ester (JKBKBJV) hybrid composites. The highest damping factor was observed for JKBKBJE (0.153) and JKBKBJV (0.224) hybrid composites. These hybrid composites with better free vibration properties shall be a potential candidate in the automobile interior applications.

Characterizing Natural Frequencies of the Hybrid III and NOCSAE Headforms

The vibrational characteristics of the Hybrid III and NOCSAE headforms are not well understood. It is hypothesized that they may perform differently in certain loading environments due to their structural differences; their frequency responses may differ depending on the impact characteristics. Short-duration impacts excite a wider range of headform frequencies than longer-duration (padded) impacts. While headforms generally perform similarly during padded head impacts where resonant frequencies are avoided, excitation of resonant frequencies during short-duration impacts can result in differences in kinematic measurements between headforms for the matched impacts. This study aimed to identify the natural frequencies of each headform through experimental modal analysis techniques. An impulse hammer was used to excite various locations on both the Hybrid III and NOCSAE headforms. The resulting frequency response functions were analyzed to determine the first natural frequencies. The average first natural frequency of the NOCSAE headform was 812 Hz. The Hybrid III headform did not exhibit any natural frequencies below 1000 Hz. Comparisons of our results with previous studies of the human head suggest that the NOCSAE headform’s vibrational response aligns more closely with that of the human head, as it exhibits lower natural frequencies. This insight is particularly relevant for assessing head injury risk in short-duration impact scenarios, where resonant frequencies can influence the injury outcome.

Forecasting and characterization of composite pipeline based on experimental modal analysis and YUKI-gradient boosting

The surging demand for fiberglass pipe materials in the Oil and Gas transportation sectors are driven by their exceptional durability and ease of use. This study combined improved experimental and numerical analyses to assess the behavior of composite pipe and focused on characterizing it, especially in terms of identifying the frequency based on different crack lengths. Various tests, such as impact hammer tests and modal analysis, determine the pipe properties and natural frequencies. The study also investigates the impact of varying fiber volume fractions to refine material properties. To understand crack effects behavior, different crack lengths have been introduced into the pipes and analyzing the modal analysis using frequency and mode shapes. The effect of cracks into frequency based on experimental and developed numerical models is investigated. A predective model is developed based on YUKI-Gradient Boosting algorithms and Deep Artificial Neural Networks. To test the robustness of developed algorithm several tests are provided and the results show the effectiveness of YUKI-Gradient Boosting outperforms YUKI-Deep-ANN in accuracy and consistency.

Operating Properties of Deep Hole Boring Tools with Modified Design.

This paper presents the results of research work on the revised design of a deep hole boring tool. The study was divided into three stages: theoretical, experimental and operational. In the theoretical part, a 3D model of the actual boring bar was created, which was subjected to strength tests using the Finite Element Method (FEM), and then prototypes of new deep hole boring tools were made with structural modifications to the shank part of the tool. For the polymer concrete core of a shank, there was a 14.59% lower displacement, and for the rubber-doped polymer concrete (SBR-styrene butadiene rubber) core of a shank there was a 4.84% lower displacement in comparison to the original boring bar. In the experimental part of the study, the original boring bar and the prototypes were subjected to experimental modal analysis and static analysis tests to compare dynamic and static properties. In the operational part of the study, boring tests were carried out for various workpiece materials, during which the basic parameters of the surface geometric structure (SGS), such as roughness Ra and Rz, were studied. Despite the promising preliminary results of the theoretical and experimental studies, using the described modifications to the boring bar is not recommended.

Development of a universal, machine tool independent dynamometer for accurate cutting force estimation in milling

When integrating a dynamometer into a machining system, it is necessary to identify the dynamic relationship between the effective input forces and the measured output signals (i.e., its transmissibility) through dedicated experimental modal analysis. Subsequently, a filter can be derived and applied to reconstruct the effective input forces from the measured signals. Unfortunately this identification phase can be complex, posing challenges to the device’s applicability in both laboratory and industrial conditions. Here this challenge is addressed by introducing a novel dynamometer concept based on both load cells and accelerometers, along with a Universal Inverse Filter. Notably, this filter is independent of the dynamic behavior of the mechanical system where the device is installed. A single calibration suffices, ideally conducted by the device manufacturer or by an expert, allowing the dynamometer’s integration by a non-expert user into any machining system without the need for repeating the identification phase and the filter generation. Furthermore, this new concept offers another significant advantage: it attenuates all inertial disturbances affecting the measured signals, including those arising from the cutting process and those originating from exogenous sources such as spindle rotation, linear axes’ movements, and other vibrations propagating through the machine tool structure. To illustrate, a simplified model is introduced initially, followed by an overview of the novel dynamometer design, innovative identification phase, and filter construction algorithm. The outstanding performance of the novel (non-parametric) Universal Inverse Filter – about 5 kHz of usable frequency bandwidth along direct directions and 4.5 kHz along cross dir. – was experimentally assessed through modal analysis and actual cutting tests, compared against state of the art filters. The efficacy of the new filter, which is even simpler than its predecessors, was successfully demonstrated for both commercial and taylor-made dynamometers, thus showing its great versatility.

A novel approach of fatigue testing and evaluation of electronic systems based on phase tracking

This paper presents an experimental approach to perform fatigue testing of a lightly damped electronic assembly subjected to harmonic excitation. By leveraging the power of the phase locked loop control algorithm, our proposed work aims to accurately track the phase of the system. This innovative approach enables precise measurement of the drop in resonant frequency due to fatigue, enhancing overall damage prediction. The proposed approach exploits the characteristics of the materials that the phase at the resonance is constant and for a lightly damped system, the value is close to pi/2. In the event that the test article experiences fatigue, and the resonant frequency undergoes a change, the controller will promptly adapt to the new frequency while upholding a constant phase, ensuring the uninterrupted continuity of the testing process. The proposed approach is demonstrated by using the Ball Grid Array (BGA) electronic package as an example, where the test setup, data acquisition, and data monitoring for identifying the interconnect failure are presented. Failure analysis of the test article shows that the primary failure mode is the solder joint failure at the Intermetallic (IMC) layer. A finite element model is developed and correlated with experimental modal analysis to accurately estimate maximum stress and deflection in solder joints. By utilizing the obtained results, one can create a more accurate SN curve for the tested material. This will allow for a better understanding of the material's fatigue behavior and enable more precise predictions of its durability in real-world applications.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.

Design of a simplified cranial substitute with a modal behavior close to that of a human skull.

Individuals exposed to the propagation of shock waves generated by the detonation of explosive charges may suffer Traumatic Brain Injury. The mechanism of cranial deflection is one of many hypotheses that could explain the observed brain damage. To investigate this physical phenomenon in a reproducible manner, a new simplified cranial substitute was designed with a mechanical response close to that of a human skull when subjected to this type of loading. As a first step, a Finite Element Model was employed to dimension the new substitute. The objective was indeed to obtain a vibratory behavior close to that of a dry human skull over a wide range of frequencies up to 10kHz. As a second step, the Finite Element Model was used together with Experimental Modal Analyses to identify the vibration modes of the substitute. A shaker excited the structure via a metal rod, while a laser vibrometer recorded the induced vibrations at defined measurement points. The results showed that despite differences in material properties and geometry, the newly developed substitute has 10/13 natural frequencies in common with those of dry human skulls. When filled with a simulant of cerebral matter, it could therefore be used in future studies as an approximation to assess the mechanical response of a simplified skull substitute to a blast threat.

Mode-shape magnification in high-speed camera measurements

If motion, identified using image-based methods, is too small to be seen with the naked eye, motion magnification can be used to help with the visualization. Established motion-magnification methods magnify (typically up to 1000 times) the band-passed content of the image data. Especially at higher frequencies, the amplitudes of measured displacements are often below the noise floor. In this research, a novel method for amplifying vibrations, based on experimental modal analysis (EMA), is introduced. The response of the examined structure to dynamic excitation is measured with a simplified, gradient-based, optical flow method and used to perform a hybrid modal analysis in conjunction with a reference accelerometer response measurement. Such a hybrid approach can: (a) identify structural dynamics significantly in the sub-pixel range, and (b) significantly below the image noise floor. The image of the vibrating structure is subdivided using a planar triangle mesh, which is then warped in accordance with the identified mode shape. A mesh-element-wise affine transformation is performed to obtain an image of the magnified mode shape. In the experimental part, the proposed method achieved magnification factors of approximately 40 thousand times, which is an order of magnitude deeper into noise than available before; additionally, the proposed approach is numerically significantly less demanding.The introduced mode-shape magnification presents an alternative to existing motion-magnification methods for applications where the harmonic displacement information is hidden by image noise.

Chatter Identification in Milling of Titanium Alloy Using Machine Learning Approaches with Non-Linear Features of Cutting Force and Vibration Signatures

The generation of chatter during machining operations is extremely detrimental to the cutting tool life and the surface quality of the workpiece. The present study aims to identify chatter conditions during the end milling of Ti6Al4V alloy. Experimental modal analysis is carried out, and stability lobe diagrams (SLDs) are developed to identify machining parameters under stable and chatter conditions. Experiments are conducted to acquire cutting force and vibration signatures corresponding to machining conditions selected from the SLD. Non-linear chatter features, such as Approximate Entropy, Holder Exponent, and Lyapunov Exponent extracted from the sensor signatures, are used to build Machine Learning (ML) models to identify chatter using Decision Trees (DTs), Support Vector Machines (SVMs) and DT-based Ensembles. A feature-level fusion approach is adopted to improve the classification performance of the ML models. The DT-based Adaboost model trained using dominant non-linear features classifies chatter with an accuracy of 96.8%. The non-linear features extracted from the sensor signatures offer a direct indication of the chatter and are found to be effective in identifying the machining chatter with good accuracy.

Automated modal parameter estimation for coupled rotor–foundation systems using seal forces as excitation source

Modal analysis techniques are widely used to characterize vibrations in structures, vehicles, machinery, etc. Modal parameters obtained through modal analysis are useful for structural health monitoring and condition monitoring. The common goal is to ensure the integrity of a mechanical system through monitoring of different operational conditions. Operational conditions described by spatial measurements can for instance be used to observe the vibration characteristics of the system and its parts. Therefore, the main originality of this work is to experimentally investigate if the presence of a turbulent gas flow in seal geometries can facilitate operational modal analysis for a coupled rotor–foundation system. A consistent and automatic way of obtaining the vibration characteristics is necessary to be included in the monitoring schemes. Therefore, this work also proposes a method to automatically obtain modal parameters for a bed plate of a rotor–foundation system when the rotor is affected by active magnetic bearings and gas seals. The automatic modal parameter algorithm is built on the stabilization diagram of modal parameters obtained from the stochastic subspace identification. Intermediate results from the automatic modal parameter algorithm show that some of the distance measures i.e., dωn,d, dζ, dMACX, dλ, dMACXωn,d, dMACXζ, and dMACXλ, for modal parameters in a stabilization diagram are better suited than others when distinguishing between possible physical modes and certainly spurious poles. The frequency band of interest for the system is found to influence the number of possible physical modes identified by the automatic algorithm. Measurements from 13 roving accelerometers are combined with the automatic modal parameter algorithm to obtain the vibration characteristics of the rotor and bed plate. For different operational conditions in the seal geometry, seven modes are consistently identified as physical modes by the automatic modal parameter algorithm. The algorithm uses (i) a combination of a white noise disturbance pattern intentionally introduced into the system through the active magnetic bearings and (ii) the operational disturbance coming from the seals, non-intentionally introduced by the turbulent gas flow. The seven physical modes are also identified when (iii) the rotor–foundation system is only disturbed from the turbulent gas flow in the seals. The seven physical modes identified by the algorithm under conditions (i), (ii), and (iii) compare well to the vibration characteristics found in experiments via experimental modal analysis and impact hammer testing as well as via a mathematical model of the rotor–foundation system.

Efficacious constrained layer damping of carbon black‐reinforced nitrile butadiene rubber‐polyvinyl chloride blend vulcanizates: A comprehensive study

AbstractWe report efficacious vibration damping of carbon black reinforced nitrile butadiene rubber‐polyvinyl chloride blend (NVC) vulcanizates in a constrained layer damping (CLD) configuration. The objective is to compare numerical simulations using finite element method (FEM) and the widely used Ross‐Kerwin‐Ungar (RKU) model with the experimental results. NVC blend (50:50 by weight), was compounded with carbon black as reinforcing filler and vulcanized using a sulfur‐based curative system. Significant reinforcement and toughening were observed for the carbon black reinforced vulcanizates compared to the pristine blend. The viscoelastic properties of the vulcanizates were assessed using dynamic mechanical analysis (DMA), exploring their behavior concerning temperature variations and different frequencies to generate the Prony series coefficients for input in FEM analysis. Vibration damping experiments were conducted using the Oberst beam method in a single cantilever mode, with steel as the vibrating substrate, aluminum as the constraining layer, and the NVC vulcanizates as viscoelastic materials (VEM). Numerical simulations were performed using FEM to analyze mode shapes and frequency response function (FRF), and the RKU model was employed to quantify CLD system loss factors (SLF). The salient finding of this study was the observed SLF values in the range of 0.08–0.20 in the frequency regime of 200–2000 Hz. These values qualify the studied material as effective VEMs for CLD treatment of structural vibrations. This study supports design optimization efforts in a wide range of engineering applications where effective vibration damping is critical.Highlights Enhancement of NVC blend properties through carbon black reinforcement. Detailed analysis of viscoelastic behavior using DMA. Validation of findings through experimental modal analysis. Promising results in terms of system loss factors for CLD applications.

Understanding pickleball noise at the source: The vibroacoustics of the pickleball paddle and ball

Pickleball continues to be America's fastest-growing sport, growing by roughly 150% every year with 48.3 million US adults (19% of the adult population) having played at least one game in 2023. This immense popularity and growth is accompanied by a similar increase in the number and voracity of complaints from the residential communities surrounding pickleball courts. This paper aims to explain the source of the pickleball noise—a short duration impulse with a strong tonal component near 1250 Hz—due to the impact of the pickleball ball and paddle, with a specific focus on the vibrational modes of the paddle that contribute most strongly to the tonal nature of the sound. Experimental modal analysis was performed on several paddles (wood, aluminum, composite, and carbon fiber) as well as the first paddle to meet the new USA Pickleball Quiet Category requirements. Spectral analysis of the impact identifies the offending tonal component near 1250 Hz to be a strongly radiating “membrane-type” mode of the paddle surface. Paddles for which this mode shape has a significantly higher or lower in frequency and amplitude result in a much less annoying impact sound. The role of vibrational modes in the ball will also be considered.

Mitigating footfall-induced vibrations in cross-laminated timber floor-panels by using beech or birch

Long-span floors are particularly sensitive to footfall-induced vibrations, making their analysis and design critical for ensuring occupant comfort. Cross-laminated timber (CLT) panels have high stiffness relative to their self-weight and are commonly made of spruce. Hardwoods such as birch and beech possess higher stiffness and mass density, which can potentially improve the vibrational performance of CLT panels. In this study, the vibrational performance of CLT panels made of beech and birch with different mechanical properties was investigated using finite element (FE) models calibrated via experimental modal analysis (EMA) tests, yielding calibration with less than 1% error in natural frequencies. The study demonstrated that birch or beech laminations, compared with spruce ones, can provide a significant mitigation of vibrational responses, both for broadband (to approximately 40% of the spruce reference level) and footfall-induced vibrations (to approximately 20%–30% of the spruce reference level). It is noteworthy that low quality beech can result in a marked amplification that may nearly double the level of footfall-induced vibrations.

Analytical and Experimental Modal Analysis of a Bladed Disk

The conference paper discusses a study on the modal behavior of a bladed disk in rotating machinery system using analytical and experimental modal analysis techniques. The process involves measuring natural frequencies under different operating conditions. The modal properties from both approaches are compared, and the effects of rotational speed on the modal behavior of the bladed disk are presented and discussed. The analytical and experimental findings provide a comprehensive understanding of the bladed disk’s modal characteristics under varying rotational speeds. The integration of these different modal analysis techniques enhances the accuracy of the results and enables a more thorough investigation of the bladed disk’s behavior in rotating machinery systems.

Modal Analysis of Combustion Chamber Acoustic Resonance to Reduce High-Frequency Combustion Noise in Pre-Chamber Jet Ignition Combustion Engines

<div>The notable increase in combustion noise in the 7–10 kHz band has become an issue in the development of pre-chamber jet ignition combustion gasoline engines that aim for enhanced thermal efficiency. Combustion noise in such a high-frequency band is often an issue in diesel engine development and is known to be due to resonance in the combustion chamber. However, there are few cases of it becoming a serious issue in gasoline engines, and effective countermeasures have not been established. The authors therefore decided to elucidate the mechanism of high-frequency combustion noise generation specific to this engine, and to investigate effective countermeasures. As the first step, in order to analyze the combustion chamber resonance modes of this engine in detail, calculation analysis using a finite element model and experimental modal analysis using an acoustic excitation speaker were conducted. As a result, it was found that there are two combustion chamber resonance modes in the 7–10 kHz band, both of which affect the high-frequency oscillation of the in-cylinder pressure. Both resonant modes have mode shapes that form a single nodal plane in the diametrical direction including the central axis of the cylinder, but the orientations of those nodal planes differ by 90 degrees. In addition, the two resonance frequencies are influenced by not only the bore diameter, temperature, and heat capacity ratio, but also the spatial shape of the combustion chamber. Therefore, when the piston descends and the spatial shape of the combustion chamber changes, the resonance frequencies change as well.</div>