Random Base Excitation Research Articles

Nonstationary Characteristics of Structural Response and Fatigue Life Calculation Under Base Stationary Excitation

ABSTRACTWhen a structure is randomly excited by its installation base, significant vibration stress may be caused within it, thus causing damage to the structure. The authors find in the vibration fatigue test that when the notched slender beam specimen is excited by stationary Gaussian random base movement, the measured acceleration response and strain response of the specimen have obvious nonstationary characteristics. The vibration responses of the specimen under Gaussian and non‐Gaussian random base excitations are calculated by the finite element method and corresponding vibration fatigue tests were completed. The nonstationary characteristics of the responses from calculations and experiments are analyzed. Finally, a method for calculating the fatigue life of the specimen under nonstationary response is given, and the calculated results are compared with the measured data. The results indicate that the method proposed in this article performed excellent calculation fatigue life with measured strain data.

Energy generation through a hybrid energy harvester under random excitation

This manuscript analyses a multi-frequency based coupled piezo-electromagnetic hybrid vibration energy harvester. Most of the energy harvesting devices discussed in the literature are based on the assumption that the base excitation is harmonic. However, in general, energy harvesting devices are deployed in an ambient environment, which is random in nature. Hence, in this regard, the manuscript discusses the power harvesting capabilities of the hybrid energy harvester under random base excitation using analytical and experimental studies. Acceleration with band limited Gaussian noise has been provided as an input to the base of the harvester. Comparative studies are also made to understand the performance of the hybrid harvester over conventional standalone piezoelectric and electromagnetic harvesters under the same support excitation. Thus, the novelty of the present work is to analyse a novel design of a hybrid harvester to improve harvesting performance across a wide range of frequencies under random base excitation compared to conventional harvesters. The results demonstrate that the proposed hybrid energy harvester can yield sufficient power over a wide range of frequencies. In addition, parametric studies have also been performed to characterize the system parameters in order to enhance the performance of the harvester. Studies show that the harvested power can be enhanced by maximizing the values of mass ratio, frequency ratio, non-dimensional electromechanical coupling coefficient and minimizing the values of structural damping ratios. Finally, practical applications of the proposed device have also been reported.

Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

In the practical environment, it is very common for the simultaneous occurrence of base excitation and crosswind. Scavenging the combined energy of vibration and wind with a single energy harvesting structure is fascinating. For this purpose, the effects of the wind speed and random excitation level are investigated with the stochastic averaging method (SAM) based on the energy envelope. The results of the analytical prediction are verified with the Monte-Carlo method (MCM). The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester (BEH) realize the performance enhancement for a weak base excitation. However, as the strength of the wind increases to a particular level, the influence of the random base excitation on the dynamic responses is weakened, and the system exhibits a periodic galloping response. A comparison between a BEH and a linear energy harvester (LEH) indicates that the BEH demonstrates inferior performance for high-speed wind. Relevant experiments are conducted to investigate the validity of the theoretical prediction and numerical simulation. The experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind speeds. However, as the speed of the incoming wind is up to a particular level, the disadvantage of the BEH becomes clear and evident.

Vibration Control of Base-Excited Rotors Supported by Active Magnetic Bearing Using a Model-Based Compensation Method

Active magnetic bearings (AMBs) are a type of mechatronics product widely used in high-speed rotating machinery. Considerable research has been conducted on the vibration rejection of the AMBs-rotor systems at the base standstill. However, little attention has been paid to the case where the rotor operates under base excitations, such as turbines mounted on ships with wave excitation. The increased rotor vibration caused by base excitations is a great challenge to operational safety. To address this issue, a base acceleration feedforward compensation (BAFC) algorithm was proposed in this paper. Using the online base excitation data and the dynamic model of the rotor system, the proposed model-based algorithm determines the optimal compensation current in real time. Further, to reject the decreased compensation performance due to inaccurate modeling, a method for correcting the compensation error has been presented. Moreover, the effect of controller parameters on system stability was explored to avoid parametric instability during base excitations. By employing the BAFC algorithm in the experiments, the rotor vibration was reduced considerably under both the harmonic and random base excitations with a maximum vibration reduction of 85%, demonstrating the remarkable effectiveness of the BAFC algorithm.

The influence of load correlation on vibration fatigue damage of symmetrical notched cantilever beam structures

AbstractThis paper aims to develop an innovative multiaxial fatigue criterion based on the stress invariant, in order to perform the fatigue damage analysis of engineering structures subjected to random vibrations. First, the change rule of structural vibration fatigue lifetime under different load correlation conditions is systemically studied by experiments. Then, the finite element analysis of such a structure, including the modal analysis and the spectral analysis, is implemented in order to compute the response stress power spectral density (PSD) functions at the critical fatigue‐prone location under coupled random acceleration base excitations. Finally, the influence rule of load correlation on the vibration fatigue damage of such a symmetrical structure is theoretically illustrated through formula derivation. Moreover, combined with the critical distance theory point method, the proposed time/frequency‐domain multiaxial fatigue criterion is applied for vibration fatigue lifetime evaluation of the structure. The lifetime prediction accuracy of the proposed multiaxial fatigue criterion is verified by comparing with the vibration fatigue test results.

The exact closed-form equations for optimal design parameters of enhanced inerter-based isolation systems

This paper introduces the enhanced inerter-based isolation system (EIBI) to improve broadband vibration control. Using the H2 optimization method, the exact closed-form expressions for the optimal design parameters of the EIBI, such as the frequency and viscous damping ratio, have been derived analytically. The optimal frequency and viscous damping ratios of EIBI decrease as the mass ratio of the EIBI increases. For optimal design purposes, the optimal viscous damping ratio of EIBI lies between 0.20 < ζ b < 0.30, which is practically affordable and precise to implement. The exact closed-form expressions for optimal design parameters for traditional base isolators (TBI) have also been derived using the H2 method to make a fair comparison with EIBI. When the base mass ratio of TBI increases, its optimal frequency and viscous damping ratios decrease. The response reduction capacity of each optimized novel isolator was compared to the response reduction capacity of each optimized TBI. Analysis of the frequency domain demonstrates that the response reduction capacity of the proposed EIBI is significantly 2.77% and 17.46% greater than that of the TBI subjected to harmonic and random white-noise base excitations. To verify the accuracy of the optimal closed-form expressions derived for each isolator using near-field earthquake base excitations, a numerical study employing the Newmark-beta method has been conducted. Hence, the time-history analysis reveals that the displacement and acceleration reduction capacities of EIBI are significantly superior to that of the TBI subjected to near-field earthquake base excitations by 12.86% and 24.61%, respectively. The EIBI systems are cost-effective and have greater vibration reduction capacities than TBIs.

Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used as a tunable absorber damper. This non-traditional vibration absorber is attached to a primary system that is subjected to random base excitation. An analytical study is conducted by assuming that the base excitation is white noise. In terms of vibration suppression, the objective of the optimization is to minimize the power dissipated by the primary damper and maximize the power dissipated by the absorber damper. It is found that when the primary system is undamped, the power dissipated by the absorber damper remains a constant that is related to the mass ratio. The higher the mass ratio, the higher the power dissipated. When the primary system is damped, the minimization of the power dissipated by the primary damping is equivalent to the maximization of the power dissipated by the absorber damper. The existence of the optimum solutions depends on both the mass ratio and the primary damping ratio. In terms of energy harvesting, the objective of optimization is to maximize the power harvested by the load resistor. It is found that for a given mass ratio and primary damping ratio, the optimum frequency tuning ratio required to maximize vibration suppression is slightly higher than that required to maximize the harvested power. The trade-off issue between vibration suppression and energy harvesting is investigated. An apparatus is developed to allow frequency tuning and damping tuning. Both the numerical simulation and experimental study with band-limited white noise validate the general trends revealed in the analytical study.

Comparative Study of Structural Anomaly Diagnosis Based on ANN Model Using Random Displacement and Acceleration Responses with Incomplete Measurements.

Structural anomaly diagnosis, such as damage identification, is a continuously interesting issue. Artificial neural networks have an excellent ability to model complex structure dynamics. In this paper, an artificial neural network model is used to describe the relationship between structural responses and anomalies such as stiffness reduction due to damages. Random acceleration and displacement responses as generally measured data are used as the input to the artificial neural network, and the output of the artificial neural network is the anomaly severity. The artificial neural network model is set up by training and then validated using random vibration responses with different structural anomalies. The structural anomaly diagnosis method based on the artificial neural network model using random acceleration and displacement responses is applied to a five-story building structure under random base excitations (seismic loading). Anomalies in the structure are denoted by stiffness reduction. Structural anomaly diagnosis using random acceleration responses is compared with that using random displacement responses. The numerical results show the effects of different random vibration responses used on the accuracy of predicting stiffness reduction. The actual incomplete measurements include intensive noise, finite sampling time length, and limited measurement points. The effects of the incomplete measurements on the accuracy of predicting results are also discussed.

Effectiveness analysis of structural anomaly diagnosis based on ANN model

Assessing and localizing damages are an important problem in structural engineering. Artificial neural networks (ANN) have an excellent pattern recognition capability. In this paper, a structural anomaly diagnosis method based on ANN model using displacement response signals is proposed to assess and localize damages, and applied to a five-story frame structure under random base excitation. The random displacement responses are used as the input to ANN for detecting structural damages, which differ from conventional methods such as using modal parameters extracted from responses. The ANN model is set up by training and then validation using random displacement responses. Damages in a structure are denoted by stiffness degradation. Detection results are mainly affected by incomplete measurement due to intensive noise, finite sampling time length and measured degree of freedom (DOF). Numerical results show the effects of the incomplete measurement on the accuracy of predicting damages based on the proposed method.

Time History Analysis of Sturctures Subjected to Random Base Excitation by a Substructuring Method

Time History Analysis of Sturctures Subjected to Random Base Excitation by a Substructuring Method

A novel semi-active switching control scheme for magnetorheological elastomer-based vibration isolator under dynamic input saturation

It is still a challenge to guarantee a robust performance of magnetorheological elastomer (MRE)-based isolators under complex and frequency-varying base excitation, due to the highly nonlinear dynamic behavior of the MRE. The dynamic behavior of the MRE-based isolator should be considered properly in the control law to ensure the effectiveness of the MRE-based isolator. In this research study, first a dynamic modeling of an MRE-based isolator is established to formulate the actuation (transmitted) force of the MRE-based isolator. The MRE induced actuation force is limited to a dynamic input saturation and depends on the applied magnetic field density, geometry of the MRE layers, viscoelastic properties of the MREs and system states. Subsequently, a novel semi-active switching control scheme, which adopts the fastest convergence speed of driving the virtual energy toward zero based on Lyapunov theory, is proposed to improve the mitigation performance of the MRE-based isolator. The proposed control law requires less modeling information and does not require a time-consuming adjustment of control parameters, thereby possessing a broad application prospect in MRE-based isolators. Finally, the performance of the MRE-based isolator using the developed control strategy is compared with those based on passive control with different levels of constant magnetic field density, ON–OFF control and PD control under the harmonic, random and bump shock base excitation. The results show a robust and superior performance of the developed vibration control strategy.

Damage detection and fatigue life estimation under random loads: A new structural health monitoring methodology in the frequency domain

AbstractThis paper presents a methodology for structural health monitoring of fatigue cracks under stationary random loads. The methodology is composed of two parts: an empirical correlation to monitor the evolution of damage indices and a numerical scheme for fatigue life estimation. The damage indices are based on the variation of the vibrational response of the structure due to crack propagation. Two damage metrics are studied, and the methodology is verified for a cantilever beam subjected to random base excitation. The case study validates the effectiveness of the methodology and shows that both metrics have the potential for damage detection. For the numerical estimation of the fatigue life, the proposed framework uses the probability density function of the stress, which is obtained from frequency‐domain methods, and an equivalent stress approach based on the Walker's equation for fatigue crack growth. Excellent agreement is found between the predicted fatigue life and the experimental values.

Parametric Uncertainty and Random Excitation in Energy Harvesting Dynamic Vibration Absorber

Abstract An energy harvesting dynamic vibration absorber (EHDVA) is studied to suppress undesirable vibrations in a host structure as well as to harvest electrical energy from vibrations using piezoelectric transduction. This work studies the feasibility of using vibration absorber for harvesting energy under random excitation and in presence of parametric uncertainties. A two degrees-of-freedom model is considered in the analytical formulation for the host along with the absorber. A separate equation is used for energy generation from piezoelectric material. Two studies are reported here: (i) with random excitation where the base input is considered to be Gaussian and (ii) parametric uncertainty is considered with harmonic excitation. Under random base excitation, the analytical results show that, with the proper selection of parameters, harvested electrical energy can be increased along with the reduction in vibration of the host structure. Graphs are reported showing tradeoff between harvested energy and vibration control. Whereas, Monte Carlo simulations are carried out to analyze the system with parametric uncertainty. This showed that the mean harvested power decreases with an increase in uncertainties in the natural frequency as well as damping ratio. In addition, optimal electrical parameters for obtaining maximum power for the case of uncertain parameters are also reported in this study.

On the Effects of Structural Coupling on Piezoelectric Energy Harvesting Systems Subject to Random Base Excitation

The current research investigates the novel approach of coupling separate energy harvesters in order to scavenge more power from a stochastic point of view. To this end, a multi-body system composed of two cantilever harvesters with two identical piezoelectric patches is considered. The beams are interconnected through a linear spring. Assuming a stochastic band limited white noise excitation of the base, the statistical properties of the mechanical response and those of the generated voltages are derived in closed form. Moreover, analytical models are derived for the expected value of the total harvested energy. In order to maximize the expected generated power, an optimization is performed to determine the optimum physical and geometrical characteristics of the system. It is observed that by properly tuning the harvester parameters, the energy harvesting performance of the structure is remarkably improved. Furthermore, using an optimized energy harvester model, this study shows that the coupling of the beams negatively affects the scavenged power, contrary to the effect previously demonstrated for harvesters under harmonic excitation. The qualitative and quantitative knowledge resulting from this analysis can be effectively employed for the realistic design and modelling of coupled multi-body structures under stochastic excitations.

Measurement of full-field displacement time history of a vibrating continuous edge from video

Video of a vibrating structural component provides dense continuous spatial information of motion compared to contact based sensors which are more localized. In order to harness such quantitative information, various Computer Vision based methods have been studied in the past few years. Computer vision algorithms that implement sparse optical flow, tracks the displacement of few selected texture rich patches of pixels corresponding to salient points of the structure, in subsequent frames of the video starting from the initial frame. The obtained displacement response of individual, spatially discrete, points of the structure denotes the Lagrangian representation of motion. Such vision based measurement already proved its potential in replacing the need for a contact based vibration measuring sensors. However, full-field vibration response of a structural component, in its operating condition, is vital for identifying heterogeneous mechanical properties as well as localize damages. In order to obtain full-field, spatially dense, vibration response, a large number of sensors are needed to be attached throughout the specimen’s surface, making it impractical. In such scenarios, the technique of Digital Image Correlation (DIC) is used to measure Lagrangian representation of motion using Computer Vision algorithms which implements dense optical flow. In DIC, the presence of much required rich optical textures is ensured by adding speckle paint on the surface of the specimen which can be easily tracked over subsequent frames of the video. But its application is limited to laboratory setups that cannot be implemented for full-scale real-world structural components that vibrate in its operating condition. Continuous edge of a moving object is a rich optical feature whose motion perpendicular to its orientation can be tracked in Lagrangian coordinates using optical flow. In this paper, a novel method of measuring full-field displacement response of a vibrating continuous edge of a structural component is proposed from its video. The proposed method computes both horizontal and vertical components of the Lagrangian displacement of each pixel of the edge for every frame in the video with sub-pixel accuracy. The method consists of applying d’Alembertian of Gaussian filter on the spatiotemporal video signal to convert the edge information into zero crossing signal which is tracked over time using the optical flow of edge. Intermittent and sparse noise in the obtained full-field displacement signal is removed using Robust Principal Component Analysis. Further, experimental validation of the proposed method is presented for two kinds of structures, one a cantilever beam, another a two-story steel frame, both undergoing harmonic as well as random base excitation. The results obtained using the proposed method is validated with the displacement measured using Laser Doppler Vibrometer at a particular point of the edge. Further, the analytical derivations of the proposed method along with the effect of the filter parameters on the edge signal are presented in the Appendix. In order to validate the efficacy of the method on real-world structures, part of the vibrating cable of Tacoma Narrows bridge is tracked from its video, moments before its collapse. The results show high correspondence between the actual motion of the cable and traced motion of its edge, over time. The proposed method reveals the absolute as well as relative displacement response of the cable along with the dominating frequencies of the cable’s vibration.

Design and experimental investigation of ultra-low frequency vibration isolation during neonatal transport

To resolve the tough issue of ultra-low frequency vibration isolation during neonatal transport, a new incubator with quasi-zero-stiffness (QZS) isolators is proposed. In the new incubator, the infant housing unit is supported by the QZS isolators to mitigate mechanical vibration being transmitted from the ambulance floor to the infant. Each of the QZS isolators is devised by combining a pair of permanent magnet rings and a coil spring, and the design parameters are realized by the equivalent magnetic charge method. Both the prototypes of the QZS isolator and incubator are manufactured, and their vibration isolation performances are tested. The results show that the QZS isolator can fulfil vibration isolation from 2 Hz, and the incubator with four such QZS isolators is effective from 3.2 Hz under the designated payload. Most importantly, the acceleration response of the infant model in the housing unit is much lower than the base excitation, when the incubator is driven by a random base excitation with frequency bandwidth from 2 Hz to 15 Hz.

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with nonlinear energy sink (NES) are investigated. The linear system is excited by a harmonic and random base excitation, consisting of a mass block, a linear spring, and a linear viscous damper. The NES is composed of a mass block, a linear viscous damper, and a spring with ideal cubic nonlinear stiffness. Based on the generalized harmonic function method, the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system. The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions. The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities, the transmissibility transition probability density, and the percentage of the energy absorption transition probability density of the linear oscillator. The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio. The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters, which will affect the stability of the system.

Tuned tandem mass dampers-inerters with broadband high effectiveness for structures under white noise base excitations

By integrating the tuned tandem mass dampers (TTMD) with two inerters, the tuned tandem mass dampers-inerters (TTMDI) with high effectiveness and wide frequency spacing (i.e., high robustness) have been proposed in this paper. It is expected that the frequency spacing of the TTMDI will be comparable with that of the multiple tuned mass dampers. In order to reveal the fundamental performance of the TTMDI, it is attached to a single degree of freedom (SDOF) structure under random Gaussian white noise base excitations. Closed-form expressions for calculating the dimensionless displacement variances are thereupon derived for the SDOF structure–TTMDI system. The optimization criterion is determined as the minimization of the dimensionless displacement variances. Employing the gradient-based optimization technique, the effects of varying the key parameters on the performance of the TTMDI are scrutinized in order to probe into its superiority. Evaluation of the performance of the TTMDI includes that of its effectiveness, strokes, stiffness, damping coefficient, distributions of the inertance coefficients, frequency spacing, and frequency response of the controlled structure. For purposes of further comparison, the optimum results of the TTMD and tuned mass damper-inerter (TMDI) are also included into consideration. Results clearly demonstrate that the TTMDI outperforms both the TTMD and TMDI because of several advantages, particularly high effectiveness and broadband characteristics. Therefore, the TTMDI is deemed to be a broadband high effectiveness control device. Furthermore, the TTMDI only needs a linking dashpot and is capable of decentralizing a large inertance coefficient, thus showing its simplicity and easier implementation.

Nonlinear Whirling Motion of Monopile Offshore Wind Turbines Subjected to Harmonic and Seismic Base Excitations

The triggering mechanism and the vibration patterns of the nonlinear whirling motion of monopile offshore wind turbines subjected to unidirectional base excitations are investigated both theoretically and experimentally via a 64:1 scaled model of the prototype NREL-5MW monopile offshore wind turbine. For motion, two nonlinear coupled integro-differential equations containing cubic nonlinearities due to curvature and inertia are solved by both analytical and numerical methods. Harmonic and random seismic base excitations with different amplitudes and frequencies are considered in the analysis to understand the instability mechanism. Extensive shake table tests show that the experimental results have good qualitative agreements with the theoretical results, and as observed in eight load cases, the nonlinear whirling motions of nacelle do exist and tend to be induced by large harmonic excitations with structural resonant frequency.

Response analysis of random base excitation ona magnetic bearing rotor system

The magnetic bearing-rotor system is subject to various external disturbances in practical application. Under certain control conditions, the random response characteristics of the magnetic bearing-rotor system are a particular concern. This paper analyzes the response characteristics of base of the magnetic bearing subjected to acceleration random excitation in the horizontal direction. First, the magnetic bearing-rotor system model is deduced. Then, the random response of the rotor under acceleration random excitation is derived. The probability of the collision of the rotor between the auxiliary bearing is calculated and the example is given. The paper conclusion provides a theoretical basis for the collision detection and prediction of the magnetic bearing-rotor system.