Vibration — Open Access Journal

Contemporary design codes and guides for vibration serviceability assessment include some simplifications in load modelling. The same statistical distribution of the inter-pedestrian variability of the step interval (frequency) is proposed for all applications. Moreover, walking loads are considered to be periodic. The intra-pedestrian variability of the step interval is neglected. A more realistic load modelling trying to overcome the limitations of the codes is intended in this paper. Instead of a single mean value of the inter-pedestrian distribution of walking speed, a range of possible variation, which account for the real variations that occur in practice depending on the footbridge location and usage, is considered. An enhanced model is proposed in this paper to reproduce statistically both the intra- and inter-pedestrian variability of the step interval as a function of the walking speed distribution. This innovative model is then applied to study the sensitivity of the vertical response of footbridges to the variability of the step interval and to evaluate the influence of the aforementioned simplifications on the predicted characteristic responses. For this purpose, low-frequency footbridges excited by single-pedestrian crossings are chosen. The response is statistically characterized through Monte Carlo numerical simulations including 720 different configurations and 10,000 load cases in each configuration. Results of the study provide an overview of the influence of the footbridge and load parameters on the responses, which can be useful in practical applications where human–structure interactions are negligible. As for the simplifications of the codes, it is found that either using a single distribution to model the inter-pedestrian variability of the spatiotemporal parameters or neglecting the intra-pedestrian variability can lead to a significant underestimation of the characteristic response of footbridges. Full article

Wind action can induce large amplitude vibrations in the stay cables of bridges. To reduce the vibration level of these structural elements, different types of passive damping devices are usually installed. In this paper, a motion-based design method is proposed and implemented in order to achieve the optimum design of different passive damping devices for stay cables under wind action. According to this method, the design problem is transformed into an optimization problem. Thus, its main aim is to minimize the different terms of a multi-objective function, considering as design variables the characteristic parameters of each considered passive damping device. The multi-objective function is defined in terms of the scaled characteristic parameters, one single-function for each parameter, and an additional function that checks the compliance of the considered design criterion. Genetic algorithms are considered as a global optimization method. Three passive damping devices have been studied herein: viscous, elastomeric and friction dampers. As a benchmark structure, the Alamillo bridge (Seville, Spain), is considered in order to validate the performance of the proposed method. Finally, the parameters of the damping devices designed according to this proposal are successfully compared with the results provided by a conventional design method. Full article

This paper proposes a methodology to reconstruct the vertical GRFs from the registered body motion that is reasonably robust against measurement noise. The vertical GRFs are reconstructed from the experimentally identified time-variant pacing rate and a generalised single-step load model available in the literature. The proposed methodology only requires accurately capturing the body motion within the frequency range 1–10 Hz and does not rely on the exact magnitude of the registered signal. The methodology can therefore also be applied when low-cost sensors are used and to minimize the impact of soft-tissue artefacts. In addition, the proposed procedure can be applied regardless of the position of the sensor on the human body, as long as the recorded body motion allows for identifying the time of a nominally identical event in successive walking cycles. The methodology is illustrated by a numerical example and applied to an experimental dataset where the ground reaction forces and the body motion were registered simultaneously. The results show that the proposed methodology allows for arriving at a good estimate of the vertical ground reaction forces. When the impact of soft-tissue artefacts is low, a comparable estimate can be obtained using Newton’s second law of motion. Full article

This paper addresses the feasibility of an optical vibrometer that is based on the shift of the optical modes, also known as whispering gallery modes (WGMs), of a magnetorheological optical resonator. The optical resonator that is used in this study is fabricated by mixing polyvinyl chloride plastisol with magnetically polarizable particles. When a permanent magnet that is located nearby the optical resonator is moved, it induces a perturbation of the morphology of the resonator, due to the magnetostrictive effect. This change in the morphology induces a shift in the optical modes of the resonator. The shift of the optical modes can be related to the displacement of the permanent magnet. The proposed sensor concept is based on monitoring the displacement of a tiny magnet that is attached to a moving surface. The optical quality factor of the resonator used in these studies was of the order of 10⁶. The experimental results show a sensitivity of 0.32 pm/μm and a resolution that is less than 300 nm. Full article

The ability to characterize shocks which occur during road transport is a vital prerequisite for the design of optimized protective packaging, which can assist in reducing cost and waste related to products and good transport. Many methods have been developed to detect shocks buried in road vehicle vibration signals, but none has yet considered the nonstationary nature of vehicle vibration and how, individually, they fail to accurately detect shocks. Using machine learning, several shock detection methods can be combined, and the reliability and accuracy of shock detection can also be improved. This paper presents how these methods can be integrated into four different machine learning algorithms (Decision Tree, k-Nearest Neighbors, Bagged Ensemble, and Support Vector Machine). The Pseudo-Energy Ratio/Fall-Out (PERFO) curve, a novel classification assessment tool, is also introduced to calibrate the algorithms and compare their detection performance. In the context of shock detection, the PERFO curve has an advantage over classical assessment tools, such as the Receiver Operating Characteristic (ROC) curve, as it gives more importance to high-amplitude shocks. Full article

This study provides a forced vibration analysis to evaluate the stresses at the pedicel interfaces of the fruit-peduncle system of Coffea arabica L. var. Colombia by means of finite element analysis. The real topology of the fruit-peduncle system was developed from a proposed numerical procedure to complete a dynamic analysis. The Young’s modulus of the fruit was approximated from firmness indices for all stages of ripening. Numerical computations were performed in the frequency range of 0 to 400 Hz and three vibration modes were identified in this bandwidth. Results show that the second natural frequency (128 Hz) is acceptable for stimulating the detachment of ripe fruits because the fruit-pedicel-peduncle system induces bending in the fruit interface. As a final conclusion, we determine that dynamic excitations between 120 and 150 Hz could permit selective stimulus of ripe fruits, since other ripening stages were not stimulated in this frequency range. Full article

Tuned Mass Dampers (TMDs) are widely used for the control and mitigation of vibrations in engineering structures, including buildings, towers, bridges and wind turbines. The traditional representation of a TMD is a point mass connected to the structure by a spring and a dashpot. However, many TMDs differ from this model by having multiple mass components with motions of different magnitudes and directions. We say that such TMDs have added mass. Added mass is rarely introduced intentionally, but often arises as a by-product of the TMD suspension system or the damping mechanism. Examples include tuned pendulum dampers, tuned liquid dampers and other composite mechanical systems. In this paper, we show how a TMD with added mass can be analyzed using traditional methods for simple TMDs by introducing equivalent simple TMD parameters, including the effective TMD mass, the mass of the equivalent simple TMD. The presence of added mass always reduces the effective TMD mass. This effect is explained as a consequence of smaller internal motions of the TMD due to the increased inertia associated with the added mass. The effective TMD mass must be correctly calculated in order to predict the TMD efficiency and in order to properly tune the TMD. The developed framework is easy to apply to any given general linear TMD system with a known motion. Here, we demonstrate the approach for a number of well-known examples, including tuned liquid dampers, which are shown to use only a small fraction of the total liquid mass effectively. Full article

This research aims to analyze the vibration response of damaged rolling element bearings experimentally and to assess their degree of degradation by examining parameters extracted from the time domain. This task was accomplished in three phases. In the first phase, a test rig was carefully designed and precisely manufactured. In particular, an innovative solution for rapidly mounting and dismounting bearings on the supporting shaft was tested and used successfully. In the second phase, a specific technique of seeding defects inside the ball bearings was developed. In the last phase, damaged bearings (and healthy ones serving as a reference) were installed on the test rig, and different vibration measurements were taken. The results obtained from this work show that different parameters could be extracted from the time domain. In addition to the six common indicators (peak, root mean square, crest factor, kurtosis value, impulse factor, and shape factor), four hybrid new ones have been proposed (Talaf, Thikat, Siana and, Inthar). The experimental results confirm the well-known efficiency of kurtosis in the detection of bearing defects. However, the newly proposed parameters were found to be more responsive to defect growth. Full article

In this work, the nonlinear behaviour of a parametrically excited system with electromagnetic excitation is accurately modelled, predicted and experimentally investigated. The equations of motion include both the electromechanical coupling factor and the electromechanical damping. Unlike previous studies where only linear time-varying stiffness due to electromagnetic forces was presented, in this paper the effect of the induced current is studied. As a consequence, nonlinear parameters such as electromechanical damping, cubic stiffness and cubic parametric stiffness have been included in the model. These parameters are also observed experimentally by controlling the direct current (DC) and alternating current (AC) passed through the electromagnets. In fact, the proposed apparatus allows to control both linear and nonlinear stiffnesses and the independent effect of each parameter on the response is presented. In particular the effect of the cubic parametric stiffness on the parametric resonance amplitudes and the influence of cubic stiffness on the frequency bandwidth of the parametric resonance are shown. This model improves the prediction of parametric resonance, frequency bandwidth, and the response amplitude of parametrically excited systems and it may lead to refined design of electromagnetic actuators, filters, amplifiers, vibration energy harvesters, and magnetic bearings. Full article

In this paper, a non-modal parametric method to identify structural damage using a regularized autoregressive moving average time series model under environmental excitation is proposed in combination with the virtual impulse response function. This method can use the structural vibration response to determine the damage caused to the structure during environmental excitation. Firstly, the virtual impulse response function is obtained by using the structural vibration response. Then, a regularized ARMA time series model is used to fit the virtual impulse response function. Based on the change of auto-regression coefficients in the regularization model under different damage cases, the structural damage is identified. The authors derive the regularization equation of an ARMA time series model to solve the problems in a time series model and obtain the regularization coefficient. Finally, this method is applied to a three-degrees-of-freedom chain structure and a three-floor shear structure of the Los Alamos National Laboratory (LANL). The experimental results show that the method based on the regularized ARMA time series model under environmental excitation can effectively identify the structural damage, which is a reliable method for damage identification. The regularized ARMA time series model can accurately extract signal features and has invaluable application prospects in the field of structural health monitoring. Full article

In this paper, a finite element model is coupled to an homogenisation theory in order to predict the energy harvesting capabilities of a porous piezoelectric energy harvester. The harvester consists of a porous piezoelectric patch bonded to the root of a cantilever beam. The material properties of the porous piezoelectric material are estimated by the Mori–Tanaka homogenisation method, which is an analytical method that provides the material properties as a function of the porosity of the piezoelectric composite. These material properties are then used in a finite element model of the harvester that predicts the deformation and voltage output for a given base excitation of the cantilever beam, onto which the piezoelectric element is bonded. Experiments are performed to validate the numerical model, based on the fabrication and testing of several demonstrators composed of porous piezoelectric patches with different percentages of porosity bonded to an aluminium cantilever beam. The electrical load is simulated using a resistor and the voltage across the resistor is measured to estimate the energy generated. The beam is excited in a range of frequencies close to the first and second modes using base excitation. The effects of the porosity and the assumptions made for homogenisation are discussed. Full article

This paper focuses on vibration suppression and energy harvesting using a non-traditional vibration absorber referred to as model B. Unlike the traditional vibration absorber, model B has its damper connected between the absorber mass and ground. The apparatus used in the study consists of a cantilever beam attached by a mass at its free end and an electromagnetic energy harvester. The frequency tuning is achieved by varying the beam length while the damping tuning is realized by varying the harvester load resistance. The question addressed is how to achieve the best performance under transient responses. The optimum tuning condition for vibration suppression is based on the Stability Maximization Criterion (SMC). The performance of energy harvesting is measured by the percentage of the harvested energy to the input energy. A computer simulation is conducted. The results validate the optimum parameters derived by the SMC. There is a trade-off between vibration suppression and energy harvesting within the realistic ranges of the frequency tuning ratio and damping ratio. A multi-objective optimization is conducted. The results provide a guideline for obtaining a balanced performance. An experimental study is carried out. The results verify the main findings from the computer simulation. This study shows that the developed apparatus is capable of achieving simultaneous vibration suppression and energy harvesting under transient responses. Full article

This paper presents an analytical approach for the development of a new wideband piezoelectric energy harvesting system. The proposed model is based on Adomian decomposition method to derive the dynamic response of the general non-uniform smart structures under external environmental excitations over a wide frequency domain efficiently harvesting the subsequent vibrational energy. The steady-state response of a nonlinearly tapered piezoelectric harvester subjected to harmonic base motion is obtained, and the higher potential electromechanical outputs compared with traditional uniform harvester are analytically derived. Afterward, a group of nonlinearly tapered cantilevers with the same volume and length but different taper ratios and surface bonded piezoelectric layers are assembled together in order to build a broadband piezoelectric energy harvester. Through numerical studies, it is proven that with the proposed non-uniform configuration, the new energy harvester design can function effectively and efficiently with high voltage output over a wide frequency range. The designed wideband harvester can automatically activate one of the non-uniform bimorphs to resonate at particular ambient vibration frequencies and eventually reach the maximum electromechanical output. Based on the proposed theoretical model, an optimum structural design for the wideband piezoelectric energy harvester in the required operational frequency range can be efficiently achieved. Full article

Metamaterials are materials with an artificially tailored internal structure and unusual physical and mechanical properties such as a negative refraction coefficient, negative mass inertia, and negative modulus of elasticity, etc. Due to their unique characteristics, metamaterials possess great potential in engineering applications. This study aims to develop new acoustic metamaterials for applications in semi-active vibration isolation. For the proposed state-of-the-art structural configurations in metamaterials, the geometry and mass distribution of the crafted internal structure is employed to induce the local resonance inside the material. Therefore, a stopband in the dispersion curve can be created because of the energy gap. For conventional metamaterials, the stopband is fixed and unable to be adjusted in real-time once the design is completed. Although the metamaterial with distributed resonance characteristics has been proposed in the literature to extend its working stopband, the efficacy is usually compromised. In order to increase its adaptability to time-varying disturbance, several semi-active metamaterials have been proposed. In this study, the incorporation of a tunable shape memory alloy (SMA) into the configuration of metamaterial is proposed. The repeated resonance unit consisting of SMA beams is designed and its theoretical formulation for determining the dynamic characteristics is established. For more general application, the finite element model of this smart metamaterial is also derived and simulated. The stopband of this metamaterial beam with different configurations in the arrangement of the SMA absorbers was investigated. The result shows that the proposed model is able to predict the unique dynamic characteristics of this smart metamaterial beam. Moreover, the tunable stopband of the metamaterial beam with controlling the state of SMA absorbers was also demonstrated. Full article

The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices. Full article

The objective of this work is to use natural frequencies for the localization and quantification of cracks in beams. First, to study the effect of the crack on natural frequencies, a finite element model of Euler–Bernoulli is presented. Concerning the damaged element, the stiffness matrix is calculated by the theory of fracture mechanics, by inverting the flexibility matrix. Then, in order to detect damage, we are going to show that the shape given by the change in the natural frequencies is as function of the damage position only. Thus, the crack is located by the correlation between the shape of the measured frequencies and those obtained by the finite elements, where the position that gives the calculated shape which is the most similar to the measured one, indicates the crack position. After the localization, an inverse method will be applied to quantify the damage. Finally, an experimental application is presented to show the real applicability of the method, in which the crack is introduced by using an Electrical Discharge Machining. The results confirm the applicability of the method for the localization and the quantification of cracks. Full article

A novel characterization method for discrete saw filters’ vibrational sensitivity is presented. The proposed approach allows the characterization of filters under vibrations and the extraction of a behavioural model. Filters are assumed to be transducers so that external induced vibrational energy is partially transformed in an undesired simultaneous amplitude and phase modulation of the input RF signal. When the filter is mechanically excited with vibrations, it introduces spurious amplitude and phase modulation to the input signal that can potentially affect the link quality. Full article

The use of suspension preview information obtained from a quarter vehicle model (QvM) to control an active seat has been shown by the authors to be very promising, in terms of improved ride comfort. However, in reality, a road vehicle will be subjected to disturbances from all four wheels, and therefore the concept of preview enhanced control should be applied to a full vehicle model. In this paper, different preview scenarios are examined, in which suspension data is taken from all or limited axles. Accordingly, three control strategies are hypothesized—namely, front-left suspension (FLS), front axle (FA), and four wheel (4W). The former utilises suspension displacement and velocity preview information from the vehicle suspension nearest to the driver’s seat. The FA uses similar preview information, but from both the front-left and front-right suspensions. The 4W controller employs similar preview information from all of the vehicle suspensions. To cope with friction non-linearities, as well as constraints on the active actuator displacement and force capabilities, three optimal fuzzy logic controllers (FLCs) are developed. The structure of each FLC, including membership functions, scaling factors, and rule base, was sequentially optimised based on improving the seat effective amplitude transmissibility (SEAT) factor in the vertical direction, using the particle swarming optimisation (PSO) algorithm. These strategies were evaluated in simulation according to ISO 2631-1, using different road disturbances at a range of vehicle forward speeds. The results show that the proposed controllers are very effective in attenuating the vertical acceleration at the driver’s seat, when compared with a passive system. The controller that utilised suspension preview information from all four corners of the car provided the best seat isolation performance, independent of vehicle speed. Finally, to reduce the implementation cost of the “four suspension” controller, a practical alternative is developed that requires less measured preview information. Full article

The use of a piezoelectric transducer to monitor the tuning of a musical instrument string has been investigated. It has been shown that the transverse resonance frequencies of the string can be identified by electrical measurements on a low-cost actuator/sensor, sufficiently discreetly to be done during a performance. This frequency measurement approach can be used as the basis for a tuning control mechanism to maintain a musical instrument string at the required pitch, without it having to be plucked or played. Such a system would be of direct benefit to harp players in particular, who have no other means to adjust a mistuned string during a performance. Some of the practical issues and implications of adding such a tuning control system to the harp are considered. Full article