Vibration, Volume 4, Issue 1 (March 2021) – 18 articles

Mechanical seals play an important role in the reliability of a process. Currently, the condition monitoring of mechanical seals is restricted due to the limitations of the traditional monitoring methods, including classical vibration analysis. For this reason, the objective of the present work is the detection and analysis of friction mechanisms inside a mechanical seal that are unfavorable and induce fault conditions using the acoustic emission technique, which allows the measurement of high-frequency vibrations that arise due to material fatigue processes on a microscopic scale. For this purpose, several fault condition modes were induced on a test rig of an agitator vessel system with a double-acting mechanical seal and its buffer fluid system. It was possible to detect the presence of inadequate friction mechanisms due to the absence and limited use of lubrication, as well as the presence of abrasive wear, by measuring a change in the properties of the acoustic emissions. Operation under fault condition modes was analyzed using the acoustic emission technique before an increase in the leakage rate was evaluated using traditional monitoring methods. The high friction due to the deficient lubrication was characterized by a pattern in the high-frequency range that consisted of the harmonics of a fundamental frequency of about 33 kHz. These results demonstrate the feasibility of a condition monitoring system for mechanical seals using the acoustic emission technique. Full article

The blades of the horizontal axis wind turbine (HAWT) are generally subjected to significant forces resulting from the flow field around the blade. These forces are the main contributor of the flow-induced vibrations that pose structural integrity challenges to the blade. The study focuses on the application of the gradient boosting regressor (GBR) for predicting the wind turbine response to a combination of wind speed, angle of attack, and turbulence intensity when the air flows over the rotor blade. In the first step, computational fluid dynamics (CFD) simulations were carried out on a horizontal axis wind turbine to estimate the force distribution on the blade at various wind speeds and the blade’s attack angle. After that, data obtained for two different angles of attack (4° and 8°) from CFD acts as an input dataset for the GBR algorithm, which is trained and tested to obtain the force distribution. An estimated variance score of 0.933 and 0.917 is achieved for 4° and 8°, respectively, thus showing a good agreement with the force distribution obtained from CFD. High prediction accuracy and less time consumption make GBR a suitable alternative for CFD to predict force at various wind velocities for which CFD analysis has not been performed. Full article

High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions. Full article

Current models describing the effect of crowd-induced loading require a full-scale validation. To measure the lower-back accelerations during such validation, low-cost accelerometers are used to ensure a sufficient scalability. The goal is to verify to what extent the low-cost sensors can be used for the contact force reconstruction in case the pedestrian walks on a vibrating surface. First, a data set is collected comprising the simultaneous registration of the lower-back accelerations and the contact forces. Three contact force reconstruction methods are presented to accurately reconstruct the contact force in case of walking on a rigid surface. Second, the focus is on the contact force reconstruction in case of walking on a vibrating surface. A numerical study is performed adopting quantities of the Eeklo Benchmark Dataset providing a realistic framework. The additional lower-back accelerations as a result of the vibrating surface are estimated numerically. It is found that directly reconstructing the total contact force leads to inaccurate results. Instead, it is more suited to reconstruct the contact force one would induce on a rigid surface and combine this with an independent model to account for human–structure interaction. The conclusions of this numerical example are case-specific while the presented methodology is generic and can be readily extended to virtually any other structure. Full article

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam). Full article

In this paper, the three-layer model of ballasted railway track with discrete supports is analyzed to access its applicability. The model is referred as the discrete support model and abbreviated by DSM. For calibration, a 3D finite element (FE) model is created and validated by experiments. Formulas available in the literature are analyzed and new formulas for identifying parameters of the DSM are derived and validated over the range of typical track properties. These formulas are determined by fitting the results of the DSM to the 3D FE model using metaheuristic optimization. In addition, the range of applicability of the DSM is established. The new formulas are presented as a simple computational engineering tool, allowing one to calculate all the data needed for the DSM by adopting the geometrical and basic mechanical properties of the track. It is demonstrated that the currently available formulas have to be adapted to include inertial effects of the dynamically activated part of the foundation and that the contribution of the shear stiffness, being determined by ballast and foundation properties, is essential. Based on this conclusion, all similar models that neglect the shear resistance of the model and inertial properties of the foundation are unable to reproduce the deflection shape of the rail in a general way. Full article

Helicopters are known to exhibit higher vibratory levels compared to fixed-wing aircraft. The consequences of vibrations depend on the affected helicopter component or subject. Specifically, pilots are in contact with several parts of the helicopter; vibrations can spoil the pilot-vehicle interaction. To evaluate the effects of vibration exposure on pilots, comfort levels resulting from whole-body vibration are computed. However, specific body parts and organs, e.g., hands, feet, and eyes are also adversely affected, with undesirable effects on piloting quality. Therefore, a detailed assessment is necessary for a more accurate estimation of pilot vibration exposure when comparing different configurations, tracking changes during design, and determining the safety of the flight envelope. A generalized assessment is presented by considering vibrations at the seat surface, hand-grip of controls, eyes, and feet. The suggested vibration measure includes comfort, handling, feet-contact, and vision in a single formulation. It is illustrated by coupling a high-fidelity biodynamic model of the pilot to a helicopter aeroservoelastic model in a comprehensive simulation environment. Using appropriate modeling techniques, vibration exposure of helicopter pilots could be evaluated during all stages of design, to achieve a more comfortable and safer flying environment. Full article

This paper investigates the effect of impeller diameter on the dynamic response of a centrifugal pump using an inverse dynamic method. For this purpose, the equations of motion of the shaft and the impeller are derived based on Timoshenko beam theory considering the impeller as a concentrated mass disk. For practical modeling, the model of Jones and Harris is added to the equation to include the effect of bearings. As a case study, the model is applied to a process pump used in an oil refinery. Computing the eigenvalues of the model and comparing them with the natural frequencies of the structure, the model updating of the problem is performed through an indirect method. Three impellers with different diameters are applied to the updated model. The results show that increasing the diameter of the pump impeller can increase the amplitude of vibration up to 52% at critical speeds of the rotor. It is found that in addition to the hydraulic condition and efficiency, the impeller diameter should be considered as an important factor in the selection of centrifugal pumps. Full article

This paper presents the identification of both location and magnitude of impact forces applied on different positions of a multi-storey tower structure using different types of transducers, i.e., an accelerometer, a laser Doppler vibrometer, and a triangulation displacement sensor. Herein, a model-based inverse method is exploited to reconstruct unknown impact forces based on various recorded dynamic signals. Furthermore, the superposition approach is employed to identify the impact location. Therein, it is assumed that several impact forces are applied simultaneously on potential locations of the multi-storey tower structure, while only one impact has non-zero magnitude. The purpose is then to detect the location of that non-zero impact. The influence of using different hammer tip materials for establishing the transfer function is investigated, where it is concluded that the hammer with a harder tip leads to a more accurate transfer function. An accuracy error function is proposed to evaluate the reconstruction precision. Moreover, the effect of sensor type and location on the accuracy of the reconstruction is studied, where it is shown that the proximity between the impact and sensor locations is a dominant factor in impact force reconstruction. In addition, the efficacy of using different transducers is studied for the impact localization, where it is demonstrated that reducing the degree of under-determinacy by using a combination of system responses of the same type can improve the localization accuracy. Full article

Previous studies of human response to whole-body vibration demonstrated nonlinear softening behaviors with increasing vibration magnitudes. Most of these studies were conducted at relatively low vibration magnitudes of less than 3 m/s² root mean square (RMS), and not much knowledge is available to show if this softening behavior exists when humans are exposed to higher vibration magnitudes. In this work, 26 participants were transported in a supine position inside an army medical vehicle on a road that simulated field scenarios and were exposed to input acceleration magnitudes at 0.60, 0.98, 1.32, 3.25, 5.58, and 5.90 m/s² RMS. Motion response data were collected at the head, torso, and pelvis of the participants using inertial sensors. Transmissibility and coherence graphs were used to investigate the type of nonlinearity induced under these transport conditions. Participant responses showed softening behavior when the vibration magnitude increased from 0.60 to 0.98 to 1.32 m/s² RMS. However, this response behavior changed to stiffening when the vibration magnitude increased to 3.25, 5.58, and 5.90 m/s² RMS. In the stiffening range, the transmissibility of the torso transformed from two dominant peaks to a single peak, which may indicate a tonic muscle behavior. The resulting stiffening behaviors may be considered in the design of transport systems subject to rough terrains. Full article

A frequency-adaptable tuned mass damper (FATMD) using metal cushions as tuneable stiffness components is presented. The dynamic properties of the cushions with respect to stiffness and damping are investigated experimentally in this context. The natural frequency of the experimental FATMD is found to be dependent on the precompression of the metal cushions, which behave like nonlinear springs, yielding an adjustable frequency range from 67 to 826 Hz. As the precompression is increased, the stiffness increases while the damping characteristics decrease, the effect of which was quantified using a viscous mass damper model as a first approximation. Measurements have been carried out under five different excitation amplitudes to investigate the amplitude dependency of the resonance frequency. The FATMD was largely unaffected by changes in input amplitude. It was concluded that metal cushions show great potential for use in FATMDs, surpassing the utility of elastomers, especially with respect to their temperature stability. Full article

Low-stiffness or compliant materials are inherently difficult to characterize in terms of dynamic mechanical properties. Their free-vibration behavior is not frequently analyzed, given that performing classic vibration testing in these type of materials may imply the tampering of the results by external sources, either by changes in the geometry of the sample, by gravity-induced buckling, or the instrumentation itself (e.g., the mass of accelerometers). This study proposes an approach to determine the frequency response of these types of materials, using a noncontact methodology based on acoustic excitation and displacement measurement by Laser Döppler Vibrometry. The detailed method may be optimized by changing the sample design into a half-cane configuration to increase sample stiffness. This approach significantly increases the sample eigenmodes, facilitating their excitation by the acoustic pressure source. Numerical analysis using the values of the dynamic Young’s modulus from the experimental approaches validates the overall procedure. It is shown that the combination of numerical analysis and the proposed experimental method is a possible route for the determination of the dynamic Young’s modulus of these types of materials by inverse engineering. Full article

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem. Full article

For the stability verification of railway wheelsets in Germany, dynamic torsional stresses must be respected as they affect the axle and press fit stability of a wheelset. These dynamic stresses are applied to a wheelset by torsional vibration. However, dynamic stresses cannot be predicted by calculation, and so time-consuming and cost-intensive test runs are performed to measure the maximum dynamic stresses. Therefore, this article deals with the setup of a simulation model that shall enable the simulative prediction of maximum dynamic torsional stresses. This model respects that vibration excitation originates from the wheel-rail contact point and that the vibration energy input comes from a high-frequency drive train control. The first results show successful simulation of vibration excitation and correlations between adhesion change and maximum dynamic stresses. Full article

The effectiveness of vibration-reducing (VR) gloves is conventionally assessed based on the vibration transmissibility of the gloves. This study proposed a method for analyzing and assessing the effectiveness of VR gloves based on how gloves affect the vibration power absorption (VPA) of the hand–arm system and its distribution. A model of the entire tool–handle–glove–hand–arm system was used to predict the VPA distributed in the glove and across the substructures of the hand–arm system. The ratio of the gloved-VPA and ungloved-VPA in each group of system substructures was calculated and used to quantify VR glove effectiveness, which was termed the VPA-based glove vibration transmissibility in this study. The VPA-based transmissibility values were compared with those determined using to-the-hand and on-the-hand methods. Three types of gloves (ordinary work glove, gel VR glove, and air bubble VR glove) were considered in the modeling analyses. This study made the following findings: the total VPA-based transmissibility spectrum exhibits some similarities with those determined using the other two methods; the VPA-based transmissibility for the wrist–forearm–elbow substructures is identical to that for the upper–arm–shoulder substructures in the model used in this study; each of them is equal to the square of the glove vibration transmissibility determined using the on-the-wrist method or on-the-upper-arm method; the other substructure-specific VPA-based transmissibility spectra exhibit some unique features; the effectiveness of a glove for reducing the overall VPA in the hand–arm system depends on the glove effectiveness for absorbing the vibration energy, which seems to be associated primarily with the glove cushioning materials; the glove may also help protect the fingers or hand by redistributing the VPA across the hand substructures; this redistribution seems to be primarily associated with the glove structural properties, especially the tightness of fit for the glove. Full article

This study focuses on the dynamic modelling and analysis of the wind turbine blades made of multiple layers of fibre reinforced composites and core materials. For this purpose, a novel three-dimensional analytical straight beam model for blades is formulated. This model assumes that the beam is made of functionally graded material (FGM) and has a variable and asymmetrical cross section. In this model, the blades are assumed to be thin, slender and long with a relatively straight axis. They have two main parts, namely the core and the shell. The so-called core consists of a lightweight isotropic foam material, which also adds significant damping to the system. The core material is covered by the shell, which is modelled using homogenous and orthotropic material assumptions as the structure is reinforced with continuous fibres. Therefore, the blades are modelled under a straight beam with varying cross-section assumptions, in which the effective elastic properties are acquired by homogenizing the cross section. The beam formulation for modelling the system is performed both analytically and numerically with the finite element method. The results of both methods are in well agreement. The maximum deviation between the results is found below 4%. Full article