Vibration, Volume 7, Issue 1 (March 2024) – 15 articles

The goal of this article is to provide a review of the experimental techniques and procedures using vibration methods for the Structural Health Monitoring (SHM) of Polymer-Matrix Composites (PMCs). It aims to be a guide for any researchers to carry out vibration experiments. The linear methods are first introduced. But, as PMC is a complex material, these classic methods show some limits, such as low accuracy for small damages and a high environmental dependency. This is why the nonlinear methods are secondly studied, considering that the complexity of PMCs induces a nonlinear behavior of the structure after damage occurrence. The different damage mechanisms are well-explained in order to evaluate the potential of each vibration method to detect them. Full article

Plates are flat structural elements whose thickness is small in relation to the size of the surface. Their use may include engine foundations, reinforced concrete bridge elements or parts of various floating structures. Consequently, knowledge of their mechanical behavior under static and dynamic loads is of primary importance in engineering applications and of interest from a structural point of view. As a result, numerous works existing in the literature have investigated the mechanical properties of plates using various plate models, such as Reissner’s theory, Levinson’s theory, Kirchhoff’s theory and Mindlin’s theory, and their static and dynamic behavior has been examined. In the present paper the truncated Uflyand–Mindlin plate equation is proposed. According to Uflyand–Mindlin theory, an alternative theoretical formulation is presented for the free-vibration analysis of plates, and the equations of motion and the general corresponding boundary conditions are derived. This paper develops the truncated Uflyand–Mindlin plate equation, i.e., without the fourth-order derivative, by means of the direct method and variational formulation. The first-order shear deformable plate theory developed by Elishakoff, which takes into account rotational inertia and shear deformation and does not include a fourth-order time derivative, is variationally derived here. This derivation complements that performed by Mindlin some 70 years ago. The innovative aspect of the suggested strategy is that variational and direct methods for studying plate dynamics are analogous. Finding the third equation of the reduced Uflyand–Mindlin equations, the accompanying boundary conditions and their mathematical resemblance are the goals of the presented formulations. In order to solve the dynamic equilibrium problem of a truncated Uflyand–Mindlin equation via a variational formulation, it is demonstrated that the differential equations and the corresponding boundary conditions have the same form as those found using the direct technique. This paper successfully completes this task. Finally, in order to validate the effectiveness and correctness of the proposed procedure, a numerical example of the case of a plate simply supported at all four ends is proposed. Full article

In this paper, the main excitation sources of micro vibration of spacecraft flywheel rotor systems (SFRSs) are briefly described, and then the research progress is systematically reviewed from four perspectives, including modeling methods, suppression means, vibration isolation techniques, and ground simulation tests. Finally, the existing problems of current research and the direction of further research are given to better serve the micro-vibration prediction and sensitivity analysis of existing models, and provide reference points for the micro-vibration suppression and isolation of the next generation of high-precision spacecraft. Full article

The safe and cost-effective design of wind turbine towers is a critical and challenging aspect of the future development of the wind energy sector. This process should consider the continuous growth of towers in height and blades in length. Among potential failure modes of tubular steel towers, shell local buckling due to static axial compressive stresses from the rotor, blades, and tower weight, as well as dynamic flexural compressive stresses from wind actions on the rotating blades and the tower itself, are dominant as thickness is optimized to reduce weight. As man door and ventilation openings are necessary for the towers’ operation, the local weakening of the tower shell in those areas leads to increased buckling danger. This is compensated for by tower manufacturers by the provision of stiffening frames around the openings. However, the cold-forming and welding of these frames are among the most time-consuming aspects of tower fabrication. Working towards the optimization of this design aspect, the buckling response of tubular steel towers near such openings is investigated by means of nonlinear finite element analysis, accounting for geometrical and material nonlinearity and imperfections (GMNIA), and also considering several wind directions with respect to the openings. The alternatives of stiffened and unstiffened openings are investigated, revealing that a thicker shell section around the opening may be sufficient to restore lost stiffness and strength, while the stiffener frame may also be eliminated, offering substantial benefits in terms of manufacturing effort, time and cost. Full article

The measurement of the meshing stiffness in gear pairs is a technological problem. Many studies have been conducted, but a few results are available. A tailored test bench was designed and realized to measure the Static Transmission Error in two mating gears to address this issue. The bench is capable of testing several kinds of gears, e.g., spur, helical, conical, and internal, and it measures the transmission error concerning the applied torque. The Static Transmission Error is due to the variable stiffness of the gear teeth during a mesh cycle. In this paper, a dynamical method for measuring gear mesh stiffness is presented. The tooth stiffness is estimated from the torsional modal behavior of the rotating parts of the test bench. The dynamics of the system are acquired using accelerometers and very precise encoders to measure the angular accelerations and displacements of rotating parts. The torsional mode shapes are identified; those that show a vibrational behavior of the gears that do not follow the transmission ratio’s sign of the mating kinematic condition are selected because they depend on the flexibility of the teeth. In such a way, the engagement stiffness is estimated from the natural frequencies of the selected mode-shapes and the known inertia of gears and shafts. The experimentally identified results are also compared with numerical values computed with a commercial software for mutual validation. Full article

In studies of structural mechanics, modal analysis, presented in this paper, is an important tool for analyzing the vibration of an object and its frequencies. In modal analysis, different modes of vibration and the frequencies that generate them are considered. The study covers the nondestructive identification of the elastic characteristics of materials, which involves stochastic algorithms and the application of reverse engineering (i.e., the comparison of reference eigenfrequencies with the results of mathematical models). Identification is achieved by minimizing the objective function—the smaller the value of the objective function, the higher the identification accuracy obtained. By changing the parameters of a material’s mathematical model during identification, certain (usually higher order) modes can change places in a natural frequency spectrum. This leads to the comparison of different order eigenfrequencies, slow convergence and poor accuracy of the identification process. The technique involved in this work is the mode-shape recognition of a specimen of material with an “incorrect” set of elastic properties. The results prove that the identification accuracy of a material’s elastic properties can be increased if an “incorrect” set of elastic properties is removed from the identification process. The research covers only numerical research, with a physical experiment simulation. Full article

In this work, an advanced 2D nonparametric correlogram method is presented to cope with output-only measurements of linear (slow) time-varying systems. The proposed method is a novel generalization of the kernel function-based regularization techniques that have been developed for estimating linear time-invariant impulse response functions. In the proposed system identification technique, an estimation method is provided that can estimate the time-varying auto- and cross-correlation function and indirectly, the time-varying auto- and cross-correlation power spectrum estimates based on real-life measurements without measuring the perturbation signals. The (slow) time-varying behavior means that the dynamic of the system changes as a function of time. In this work, a tailored regularization cost function is considered to impose assumptions such as smoothness and stability on the 2D auto- and cross-correlation function resulting in robust and uniquely determined estimates. The proposed method is validated on two examples: a simulation to check the numerical correctness of the method, and a flutter test measurement of a scaled airplane model to illustrate the power of the method on a real-life challenging problem. Full article

The present study encompasses a thorough analysis of the vibrations in a splash musical cymbal. The analysis is performed using a hybrid methodology that combines experimental measurements with parametric computer-aided design and finite element method simulations. Experimental measurements, including electronic speckle pattern interferometry, and impulse response measurements are conducted. The interferometric measurements are used as a reference for the evaluation of finite element method modal analysis results. The modal damping ratio is calculated via the impulse response measurements and is adopted by the corresponding simulations. Two different approximations are employed for the computer-aided design and finite element method models: one using three-point arcs and the other using lines to describe the non-smooth curvature introduced during manufacturing finishing procedures. The numerical models employing the latter approximation exhibit better agreement with experimental results. The numerical results demonstrate that the cymbal geometrical characteristics, such as the non-smooth curvature and thickness, greatly affect the vibrational behavior of the percussion instrument. These results are of valuable importance for the development of vibroacoustic numerical models that will accurately simulate the sound synthesis of cymbals. Full article

Radio frequency (RF) cavities hold a crucial role in Electron Linear Accelerators, serving to provide precisely controlled accelerating fields. However, the susceptibility of these cavities to microphonic interference necessitates the development of effective controllers to mitigate vibration due to interference and disturbances. This paper undertakes an investigation into the modeling of RF cavities, treating them as cylindrical beams. To this end, a pseudo-rigid body model is employed to represent the translational vibration of the beam under various boundary conditions. The model is systematically analyzed using ANSYS software (from Ansys, Inc., Canonsburg, PA, USA, 2022). The study further delves into the controllability and observability of the proposed model, laying the foundation for the subsequent design of an observer-based controller geared towards suppressing longitudinal vibrations. The paper presents the design considerations and methodology for the controller. The performance of the proposed controller is evaluated via comprehensive simulations, providing valuable insights into its effectiveness in mitigating microphonic interference and enhancing the stability of RF cavities in Electron Linear Accelerators. Full article

In the paper, we first develop a novel automatically energy-preserving scheme (AEPS) for the undamped and unforced single and multi-coupled Duffing equations by recasting them to the Lie-type systems of ordinary differential equations. The AEPS can automatically preserve the energy to be a constant value in a long-term free vibration behavior. The analytical solution of a special Duffing–van der Pol equation is compared with that computed by the novel group-preserving scheme (GPS) which has fourth-order accuracy. The main novelty is that we constructed the quadratic forms of the energy equations, the Lie-algebras and Lie-groups for the multi-coupled Duffing oscillator system. Then, we extend the GPS to the damped and forced Duffing equations. The corresponding algorithms are developed, which are effective to depict the long term nonlinear vibration behaviors of the multi-coupled Duffing oscillators with an accuracy of $\mathcal{O}\left(h^4\right)$ for a small time stepsize h. Full article

The AMB-rotor system is complex and has strong coupling characteristics, which allows multi-harmonic disturbances to enter the system through different ways to produce vibrations with rich spectrum components, which has a great influence on the improvement of micro-vibration accuracy of the rotor system. To further achieve active control of the micro-vibration in the AMB-rotor system, firstly, the mechanism of multi-source disturbance is analyzed according to the working principle of the AMB-rotor system, and the mathematical and physical relationship between the mechanism of disturbance generation and the inducement is deeply studied. Then, the structure of a novel adaptive notch filter, the method of adaptive frequency estimation and analysis of harmonic current suppression in the AMB system are presented. Finally, simulation and experimental research using an MSCMG system demonstrate the feasibility of the proposed method regarding the elimination of harmonic control current. Full article

Low-income regions do not have the economic strength to use conventional isolators; therefore, low-cost alternatives are needed. The recent series of earthquakes in Turkey has once again demonstrated the destructive power of this natural disaster and highlighted the need for high-quality earthquake-resistant structures. In this context, a comprehensive experimental parametric study on the use of natural stone pebbles (ASL-1) and stone pebbles in combination with a geogrid layer (ASL-2) as suitable materials for a GSI system is conducted and the main results are presented. The seismic behavior of five different models was tested using four different acceleration diagrams with different peak ground accelerations (PGAs). Characteristic displacements, accelerations, and strains were measured. The results and conclusions presented are based on the integration and synthesis of several previously conducted studies. Full article

A reliable prediction model can greatly contribute to the research of car seating system vibration control. The novelty of this paper lies in the development of a hybrid method of an artificial neural network (ANN) and response surface methodology (RSM) to predict the peak seat-to-head transmissibility ratio of a seating suspension system and to evaluate its ride comfort for different seat design parameters. Additionally, this method can remove the experimental design of the RSM model. In this paper, four seat design parameters are selected as input parameters and arranged using the central composite design method. The peak transmissibility ratio from seat to head at 4 Hz is chosen as the response target output value. To illustrate this hybrid method, the response target output value of the peak transmissibility ratio is calculated from the frequency response of a five-degrees-of-freedom (5-DOF) lumped-parameter biodynamic seating suspension model. The input design parameters and the response target output values are used to train an ANN to establish the relationship between the seat design parameters and the peak transmissibility ratio. At the same time, the input design parameters and the response target output values predicted by the ANN are used to develop the relationship between the seat design parameters and the peak transmissibility ratio using the response surface method and linear regression models. The hybrid of the ANN and response surface methods makes the planning or design of experiments not essential. The hybrid model of the ANN and response surface method is more accurate and convenient than a linear regression model for the study of seating system vibration isolation. Full article

The contact-less sensing and fault diagnosis characteristics induced by fixing short Metglas^® 2826MB ribbons onto the surface of thin cantilever polymer beams are examined and statistically evaluated in this study. Excitation of the beam’s free end generates magnetic flux from the vibrating ribbon (fixed near the clamp side), which, via a coil suspended above the ribbon surface, is recorded as voltage with an oscilloscope. Cost-efficient design and operation are key objectives of this setup since only conventional equipment (coil, oscilloscope) is used, whereas filtering, amplification and similar circuits are absent. A statistical framework for extending past findings on the relationship between spectral changes in voltage and fault occurrence is introduced. Currently, different levels of beam excitation (within a frequency range) are shown to result in statistically different voltage spectral changes (frequency shifts). The principle is also valid for loads (faults) of different magnitudes and/or locations on the beam for a given excitation. Testing with either various beam excitation frequencies or different loads (magnitude/locations) at a given excitation demonstrates that voltage spectral changes are statistically mapped onto excitation levels or occurrences of distinct faults (loads). Thus, conventional beams may cost-efficiently acquire contact-less sensing and fault diagnosis capabilities using limited hardware/equipment. Full article

Shockmounts in naval applications are used to mount technical equipment onto the structure of naval vessels. The insulating effect against mechanical shock is important here, as it can excite the structure in the event of underwater explosions and otherwise cause damage to the equipment. Although knowledge of the dynamic properties of shockmounts is important to naval architects, the dynamic force-displacement characteristics of shockmounts are often tested and measured statically and/or in the harmonic field. Recently, an inertia-based method and a dynamic model for measuring the dynamic force-displacement characteristics of shockmounts was described. This paper presents a full description of a testbench for implementing this method. The testbench incorporates a drop table for excitation. The proposed setup can be configured for measuring the dynamic characteristics of elastomer and wire rope shockmounts, with shock loads in compression, tension, shear and roll directions. The advanced Kelvin–Voigt model for shockmounts is applied, showing that the dynamic force-displacement characteristics measured with this setup are qualified to generate model parameters for further use. Full article