Energy harvesting from railway slab-tracks with continuous slabs

2021 ◽  
pp. 107754632110542
Author(s):  
Mohammed F. M. Hussein ◽  
Jamil M. Renno ◽  
Asan G. A. Muthalif
Keyword(s):  
Energy Harvesting ◽  
Natural Frequency ◽  
Dynamic Effects ◽  
Bernoulli Beam ◽  
Single Degree Of Freedom ◽  
Dynamic Excitation ◽  
Power Spectral ◽  
Track Condition ◽  
The Mean ◽  
Euler Bernoulli Beam

This paper contributes to the literature and development of knowledge in the topic of energy harvesting by presenting the modelling and calculations of energy from vibration of railway tracks due to moving trains on floating-slab tracks with continuous slabs, considering both the quasi-static and dynamic effects. The floating-slab track is modelled as a double Euler–Bernoulli beam connected by continuous spring and damper elements. The dynamic excitation is accounted for by considering the un-sprung axles of a passing train with a number of coaches. The dynamic excitation is simulated using randomly generated unevenness from standard functions of power spectral density . The responses of rails’ beam and slab are calculated for different unevenness realizations, and then used as inputs for a base-excited single-degree-of-freedom system that models the harvester. The change in the harvested energy is investigated due to the change of natural frequency of the harvester, the change of condition of track and change of train’s velocity. The parameters used in this paper correspond to tracks and trains for Doha metro and unevenness information from the literature. The results show that more energy can be harvested by tuning the harvester’s natural frequency to the frequency of axle-track resonance. It is found that a maximum mean-energy can be harvested from the rails of 0.35 J/kg for a train moving at 100 km/h for a track with poor condition and this is obtained at the axle-track resonance frequency. For the same track condition, a reduction of about 55% and 61% is observed for train’s velocities of 70 km/h and 40 km/h, respectively. Using a track with medium and good conditions resulted in reduction of the mean harvested energy at the axle-track resonance by 73.5% and 99.9%, respectively.

Nonlinear Vibration of Nanobeam With Quadratic Rational Bezier Arc Curvature

2014 ◽  
Author(s):  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Governing Equation ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Linear Frequency ◽  
Euler Bernoulli Beam

Nonlinear vibration of nanobeam with the quadratic rational Bezier arc curvature is investigated. The governing equation of motion of the nanobeam based on the Euler-Bernoulli beam theory is developed. Accordingly, the non-uniform rational B-spline (NURBS) is implemented in order to write the implicit form of the governing equation of the structure. The simply-supported boundary conditions are assumed and the Galerkin procedure is utilized to find the nonlinear ordinary differential equation of the system. The nonlinear natural frequency of the system is found and the effects of different parameters, namely, the waviness amplitude, oscillation amplitude, aspect ratio, curvature shape and the Pasternak foundation coefficient are fully investigated. The hardening and softening responses of the natural frequency of structure are detected for variations of the shape and amplitude of the curvature waviness. It is revealed that the ratio of nonlinear to linear frequency increases with an increase in the oscillation amplitudes. It is found that by increasing the Pasternak foundation coefficient, the ratio of nonlinear to linear frequency decreases.

Effects of Boundary Flexibility in the Moving Oscillator Problem

2001 ◽  
Author(s):  
Chin An Tan ◽  
Yonghong Chen ◽  
Lawrence A. Bergman
Keyword(s):  
Natural Frequency ◽  
Eigenfunction Expansion ◽  
Transverse Direction ◽  
Interaction Force ◽  
Critical Value ◽  
Significant Implication ◽  
Bernoulli Beam ◽  
Elastically Supported ◽  
Euler Bernoulli Beam ◽  
Moving Oscillator

Abstract In this paper, the problem of an oscillator moving across an elastically supported Euler-Bernoulli beam is examined. The oscillator is modeled by a one-degree-of-freedom sprung mass and the end supports are modeled by linear springs in the transverse direction. Solution for the response of the beam is represented by an eigenfunction expansion series. Numerical results are obtained for the eigenvalues and the response of the elastically supported beam, and the interaction force (force in the oscillator spring). To guide the discussion, a critical value of the support stiffness is determined from the plot of the first natural frequency versus the support stiffness. Effects of the boundary flexibility on the maximum beam response and the maximum interaction force are discussed as a function of the speed and the oscillator frequency. The boundary flexibility is shown to have a significant implication in the design analysis of the moving oscillator problem, especially for shorter span beam structures.

On the Fundamental Transverse Vibration Frequency of a Free-Free Thin Beam With Identical End Masses

2007 ◽  
Vol 129 (5) ◽  
pp. 656-662 ◽  
Author(s):  
A. Erturk ◽  
D. J. Inman
Keyword(s):  
Natural Frequency ◽  
Extreme Case ◽  
Frequency Equation ◽  
Mode Frequency ◽  
Bernoulli Beam ◽  
Thin Beam ◽  
Microelectromechanical System ◽  
First Order ◽  
Order Polynomial ◽  
Euler Bernoulli Beam

Current research in vibration-based energy harvesting and in microelectromechanical system technology has focused renewed attention on the vibration of beams with end masses. This paper shows that the commonly accepted and frequently quoted fundamental natural frequency formula for a beam with identical end masses is incorrect. It is also shown that the higher mode frequency expressions suggested in the referred work (Haener, J., 1958, “Formulas for the Frequencies Including Higher Frequencies of Uniform Cantilever and Free-Free Beams With Additional Masses at the Ends,” ASME J. Appl. Mech. 25, pp. 412) are also incorrect. The correct characteristic (frequency) equation is derived and nondimensional comparisons are made between the results of the previously published formula and the corrected formulation using Euler–Bernoulli beam assumptions. The previous formula is shown to be accurate only for the extreme case of very large end mass to beam mass ratios. Curve fitting is used to report alternative first order and second order polynomial ratio expressions for the first natural frequency, as well as for the frequencies of some higher modes.

scholarly journals Energy harvesting from cavity flow oscillations

2021 ◽  
pp. 1045389X2110149
Author(s):  
Varun Thangamani ◽  
Foo Ngai Kok
Keyword(s):  
Energy Harvesting ◽  
Natural Frequency ◽  
Cavity Flow ◽  
High Amplitude ◽  
Time Frequency ◽  
Feedback Model ◽  
Power Spectral ◽  
Flow Oscillations ◽  
Grazing Flow ◽  
Cavity Flow Oscillations

This study investigates the energy harvesting prospects of self-sustained flow oscillations emanating from grazing flow over a rectangular cavity by employing experimental and computational methods. Two cavity geometries with length-to-depth ratios of 2 and 3, exposed to an incoming flow of 30 m/s, were selected for the purpose. The power spectral density of the baseline cavity flows showed the presence of high-amplitude peaks whose frequencies agreed to those estimated from Rossiter’s feedback model. For energy harvesting, a piezoelectric beam was placed perpendicular to the aft wall and its natural frequency tuned to match closely with the dominant frequencies of the cavity flow oscillations. From the experiments, an average and maximum instantaneous power of 21.11 and 284.18 µW was recorded for the cavity with L/ D = 2 whereas for the cavity with L/ D = 3 the corresponding values were 32.16 and 403.46 µW respectively. Time-frequency analysis showed the forcing of the beam at the cavity oscillation frequency and the substantial increase in the amplitude of beam vibrations when this frequency was close to the natural frequency of the beam.

scholarly journals Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

2018 ◽  
Vol 26 (1) ◽  
pp. 125-139
Author(s):  
Ghiocel Groza ◽  
Ana-Maria Mitu ◽  
Nicolae Pop ◽  
Tudor Sireteanu
Keyword(s):  
Natural Frequency ◽  
Hysteretic Behavior ◽  
Beam Model ◽  
Driving Frequency ◽  
Bernoulli Beam ◽  
Mathematical Methods ◽  
Transverse Vibrations ◽  
Taylor Series Method ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

Abstract The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered subjected to the boundary conditions To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]).

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