Vibration, Volume 2, Issue 1 (March 2019) – 10 articles

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently. Full article

In brake systems, some dynamic phenomena can worsen the performance (e.g., fading, hot banding), but a major part of the research concerns phenomena which reduce driving comfort (e.g., squeal, judder, or creep groan). These dynamic phenomena are caused by specific instabilities that lead to self-excited oscillations. In practice, these instabilities can be investigated using the Complex Eigenvalues Analysis (CEA), in which positive real parts of the eigenvalues are identified to characterize instable regions. Measurements on real brake test benches or tribometers show that the coefficient of friction (COF), $\mu$ , is not a constant, but dynamic, system variable. In order to consider this aspect, the Method of Augmented Dimensioning (MAD) has been introduced and implemented, which couples the mechanical degrees of freedom of the brake system with the degrees of freedom of the friction dynamics. In addition to this, instability prediction techniques can often determine whether a system is stable or instable, but cannot eliminate the instability phenomena on a real brake system. To address this, the current work deals with the quantification of the relevant polymorphic uncertainty of the friction dynamics, wherein the aleatory and epistemic uncertainties are described simultaneously. Aleatory uncertainty is concerned with the stochastic variability of the friction dynamics and incorporated with probabilistic methods (e.g., a Monte Carlo simulation), while the epistemic uncertainty resulting from model uncertainties is modeled via fuzzy methods. The existing measurement data are collected and processed through Data Driven Methods (DDM) for the identification of the dynamic friction models and corresponding parameters. Total Variation Regularization is used for the evaluation of derivatives within noisy data. Using an established minimal model for brake squealing, this paper addresses the question of probabilities for instabilities and the degree of certainty with which this conclusion can be made. The focus is on a comparison between the conventional Coulomb friction model and a dynamic friction model in combination with the MAD. This shows that the quality of the predictive accuracy improves dramatically with the more precise friction model. Full article

This paper proposes an innovative solution to suppress torsional vibrations in any rotating machinery with a variable frequency of excitation, or a variable natural frequency. The adaptive torsional tuned vibration absorber (ATTVA) was designed using an integrated electromagnetic circuit, which can adapt its natural frequency to match the varying natural frequency of any Multi Degree of Freedom (MDOF) rotating system. A two degree of freedom rotating system was modeled along with the integrated ATTVA using the bond graph modeling technique. Simulation results showed that torsional vibrations can be easily attenuated by controlling the capacitance shunted to the voice coil circuit. The ATTVA was designed, fabricated and evaluated on a test rig in the laboratory. Test results revealed good matching between the mathematical model and the experimental data. Experiments were performed with different configurations of the ATTVA, and the experimental results showed reasonable suppression in vibration magnitude at the desired frequency. Full article

This paper investigates the coupled mechanics of a fluid-conveying microtube embedded inside an elastic medium and subject to a pretension. The fluid-structure interaction model of the microsystem is developed based on Lagrange’s equations for the open system of a clamped-clamped microtube. A continuation model is used to examine the nonlinear mechanics of this microsystem prior to and beyond losing stability; the growth and the response in the supercritical regime is analysed. It is shown that the microtube stays stable prior to losing stability at the so-called critical flow velocity; beyond that point, the amplitude of the buckled microsystem grows with the velocity of the flowing fluid. The effects of different system parameters such as the linear and nonlinear stiffness coefficients of the elastic medium as well as the length-scale parameter and the slenderness ratio of the microtube on the critical speeds and the post-buckling behaviour are analysed. Full article

Synchronised motion is an important requirement for two cooperating humanoid robot arms. In this work a cooperative scenario is considered where two humanoid robot arms (using 4DOF each, namely Shoulder Flexion Joint, Shoulder abduction Joint, Humeral rotation joint and Elbow Flexion Joint) motion are synchronized. The master robot arm is controlled by a sliding mode controller and the slave robot arm is synchronized using a basic PD plus adaptive control, employing the position and velocity errors between the master and the slave. During the operation, if a joint of the slave robot arm saturates or malfunctions (for instance, Elbow flexion joint does not respond or free swinging), consequently, slave robot arm will go into chaos (i.e., chaotic motion of the end effector). In this case, a chaos controller kicks in to recover and re-synchronize the motion of the slave robot arm end effector. This re-synchronization is extremely important to complete the task in hand to address any safety issues arising from any joint malfunction of the slave robot. Effectiveness of the scheme is tested in simulation using Bristol Robotics Laboratory Humanoid BERT II arms. Full article

Cardiovascular disease is a major cause of death worldwide. New diagnostic tools are needed to provide early detection and intervention to reduce mortality and increase both the duration and quality of life for patients with heart disease. Seismocardiography (SCG) is a technique for noninvasive evaluation of cardiac activity. However, the complexity of SCG signals introduced challenges in SCG studies. Renewed interest in investigating the utility of SCG accelerated in recent years and benefited from new advances in low-cost lightweight sensors, and signal processing and machine learning methods. Recent studies demonstrated the potential clinical utility of SCG signals for the detection and monitoring of certain cardiovascular conditions. While some studies focused on investigating the genesis of SCG signals and their clinical applications, others focused on developing proper signal processing algorithms for noise reduction, and SCG signal feature extraction and classification. This paper reviews the recent advances in the field of SCG. Full article

Tracking triangular or staircase trajectories is a challenge for a piezo-driven nanopositioner due to vibration problems. The piezo-driven nanopositioner is a lightly-damped system because of its mechanical construction. These reference trajectories are high-frequency components that tend to excite the mechanical resonance of the nanopositioner, causing vibration and thus affecting the accuracy. The Integral Resonant Controller (IRC) is employed to damp the resonance and thereby furnish a larger gain margin for a high-gain tracking controller to be implemented. The IRC, however, introduces a low-frequency pole. Due to other control issues, such as hysteresis nonlinearity, Integral (I) or Proportional Integral (PI) tracking control is used as a tracking loop to address uncertainties (hysteresis). The traditional method using a PI controller has a limited positioning bandwidth. This paper presents the strategic zero placement of the PI controller to enhance the positioning bandwidth, thereby overcoming the limitations of tracking error. Using experimental validations to confirm the feasibility of the proposed method, it is shown that significant improvement regarding bandwidth and disturbance rejection are reported. Full article

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics. Full article

Innovative design and technological advancements in the construction industry have resulted in an increased use of large, slender and lightweight floors in contemporary office buildings. Compounded by an ever-increasing use of open-plan layouts with few internal partitions and thus lower damping, floor vibration is becoming a governing limit state in the modern structural design originating from dynamic footfall excitations. This could cause annoyance and discomfort to building occupants as well as knock-on management and financial consequences for facility owners. This article presents a comprehensive review pertinent to walking-induced dynamic loading of low-frequency floor structures. It is intended to introduce and explain key walking parameters in the field as well as summarise the development of previous walking models and methods for vibration serviceability assessment. Although a number of walking models and design procedures have been proposed, the literature survey highlights that further work is required in the following areas; (1) the development of a probabilistic multi-person loading model which accounts for inter- and intra-subject variabilities, (2) the identification of walking paths (routes accounting for the effect of occupancy patterns on office floors) coupled with spatial distribution of pedestrians and (3) the production of a statistical spatial response approach for vibration serviceability assessment. A stochastic approach, capable of taking into account uncertainties in loading model and vibration responses, appears to be a more reliable way forward compared to the deterministic approaches of the past and there is a clear need for further research in this area. Full article