scholarly journals Extremely Large Oscillations of Cantilevers Subject to Motion Constraints

2018 ◽  
Vol 86 (3) ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh
Keyword(s):  
Numerical Simulations ◽  
Large Amplitude ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Motion Constraints ◽  
Resonance Response ◽  
Large Amplitude Oscillation ◽  
First Time ◽  
Euler Bernoulli Beam ◽  
Motion Constraint

The nonlinear extremely large-amplitude oscillation of a cantilever subject to motion constraints is examined for the first time. In order to be able to model the large-amplitude oscillations accurately, the equation governing the cantilever centerline rotation is derived. This allows for analyzing motions of very large amplitude even when tip angle is larger than π/2. The Euler–Bernoulli beam theory is employed along with the centerline inextensibility assumption, which results in nonlinear inertial terms in the equation of motion. The motion constraint is modeled as a spring with a large stiffness coefficient. The presence of a gap between the motion constraint and the cantilever causes major difficulties in modeling and numerical simulations, and results in a nonsmooth resonance response. The final form of the equation of motion is discretized via the Galerkin technique, while keeping the trigonometric functions intact to ensure accurate results even at large-amplitude oscillations. Numerical simulations are conducted via a continuation technique, examining the effect of various system parameters. It is shown that the presence of the motion constraints widens the resonance frequency band effectively which is particularly important for energy harvesting applications.

Damping of Vibrations of Layered Elastic-Viscoelastic Beams

1993 ◽  
Vol 46 (11S) ◽  
pp. S305-S311 ◽  
Author(s):  
Richard B. Hetnarski ◽  
Ray A. West ◽  
Joseph S. Torok
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Bernoulli Beam ◽  
Viscoelastic Effects ◽  
Viscoelastic Layers ◽  
Euler Bernoulli Beam ◽  
Damping Of Vibrations ◽  
Fourth Order Differential Equation

A five-layer cantilever beam consisting of an elastic core, two symmetric viscoelastic layers, and two elastic constraining layers is considered. The viscoelastic effects are incorporated in the Euler-Bernoulli beam theory. If the contraction and extension of the constraining layers is neglecterd a fourth order differential equation of motion is received. Inclusion of contraction and extension of the constraining layers results in a more accurate sixth order differential equation. Appropriate boundary conditions are derived. Laplace transforms are used extensively. Both the analytical solution and the numerical results are presented.

scholarly journals Effects of Time-Varying Fluid on Dynamical Characteristics of Cantilever Beams: Numerical Simulations and Experimental Measurements

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Mingyu Shao ◽  
Chicheng Ma ◽  
Shuaizhao Hu ◽  
Chuansong Sun ◽  
Dong Jing
Keyword(s):  
Numerical Simulations ◽  
Beam Theory ◽  
Mass Effect ◽  
Added Mass ◽  
Experimental Measurements ◽  
Time Varying ◽  
Cantilever Beams ◽  
Dynamical Characteristics ◽  
The Mathematical Model ◽  
Euler Bernoulli Beam

In order to obtain the effects of time-varying fluid on dynamical characteristics of cantilever beams, this paper gives a comprehensive study of cantilever beams vibrating in a fluid with variable depth. The mathematical model of the cantilever beams in time-varying fluid is derived by combining Euler–Bernoulli beam theory and velocity potential theory, and the influence of the time-varying fluid is discussed. Then, a two-way fluid-structure interaction (FSI) numerical simulation procedure is proposed to calculate the transient responses of the beam. The validity and accuracy are verified according to the comparison among theoretical analysis, numerical simulations, and experimental measurements. Results show that, besides the added mass effect, a damping-like term is also induced due to the motion of the fluid, which is proportional to the moving velocity of the fluid. Both the added mass and the added damping increase with the increment of the width of the beam. The surrounding fluid near the free end affects the beam more significantly. As a negative damping is caused while the fluid decreases, resulting in a much slower decay of the time responses. Therefore, the added damping should not be neglected in the analysis of the FSI problems with time-varying fluid.

scholarly journals Thermoelectric Sensor Coupled Yagi–Uda Nanoantenna for Infrared Detection

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 527
Author(s):  
Waleed Tariq Sethi ◽  
Olivier De Sagazan ◽  
Mohamed Himdi ◽  
Hamsakutty Vettikalladi ◽  
Saleh A. Alshebeili
Keyword(s):  
State Of The Art ◽  
Infrared Detection ◽  
Single Element ◽  
Center Wavelength ◽  
Resonance Response ◽  
Thermal Measurements ◽  
Radiation Induced ◽  
Thermoelectric Sensor ◽  
Junction Array ◽  
First Time

We present an experimental demonstration of a thermoelectric sensor coupled with a nanoantenna as an alternative option for detecting infrared energy. Two nanoantenna design (single element and an array) variations based on Yagi-Uda technology and one separate nano-thermoelectric junction array were fabricated and tested. The nanoantennas were tuned to operate and respond at a center wavelength of 1550 nm (193.5 THz) optical C-band window, but they also exhibited a resonance response when excited by lasers of various wavelengths (650 nm and 940 nm). The radiation-induced electric currents in the nanoantennas, coupled with a nano-thermoelectric sensor, produced a potential difference as per the Seebeck effect. With respect to the uniform thermal measurements of the reference nanoantenna, the experiments confirmed the detection properties of the proposed nanoantennas; the single element detected a peak percentage voltage hike of 28%, whereas the array detected a peak percentage voltage hike of 80% at the center wavelength. Compared to state-of-the-art thermoelectric designs, this was the first time that such peak percentage voltages were experimentally reported following a planar design based on the Seebeck principle.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory

2021 ◽  
pp. 239779142110633
Author(s):  
Reza Ebrahimi
Keyword(s):  
Nonlocal Parameter ◽  
Power Spectra ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Effective Control ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Force ◽  
Spectra Analysis ◽  
Chaotic Vibrations ◽  
Euler Bernoulli Beam

The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.

Fatigue Life Prediction of Drill-String Subjected to Random Loadings

2014 ◽  
Author(s):  
Jiahao Zheng ◽  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
Fatigue Life ◽  
Time History ◽  
Beam Theory ◽  
Drill String ◽  
Finite Element Models ◽  
Bernoulli Beam ◽  
Stress Cycles ◽  
Rainflow Counting ◽  
Euler Bernoulli Beam ◽  
Random Nature

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Experimental and Theoretical Study of a Dual-Beam Piezoelectric Energy Harvester With Misaligned Magnets

2018 ◽  
Author(s):  
Wei-Jiun Su ◽  
Hsuan-Chen Lu
Keyword(s):  
Energy Harvester ◽  
Theoretical Study ◽  
Beam Theory ◽  
Main Beam ◽  
Bernoulli Beam ◽  
Potential Wells ◽  
Piezoelectric Energy ◽  
Dual Beam ◽  
Frequency Sweeps ◽  
Euler Bernoulli Beam

In this study, a dual-beam piezoelectric energy harvester is proposed. This harvester consists of a main beam and an auxiliary beam with a pair of magnets attached to couple their motions. The potential energy of the system is modeled to understand the influence of the potential wells on the dynamics of the harvester. It is noted that the alignment of the magnets significantly influences the potential wells. A theoretical model of the harvester is developed based on the Euler-Bernoulli beam theory. Frequency sweeps are conducted experimentally and numerically to study the dynamics of the harvester. It is shown that the dual-beam harvester can exhibit hardening effect with different configurations of magnet alignments in frequency sweeps. The performance of the harvester can be improved with proper placement of the magnets.

scholarly journals Influence of Frequency on the Resolution of Magnetostrictive Bio-Inspired Whisker Sensors

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ran Zhao ◽  
Bo-wen Wang ◽  
Quan-guo Lu ◽  
Jian-wu Yan ◽  
Xiao-cui Yuan
Keyword(s):  
Vibration Frequency ◽  
Dynamic Testing ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
Experimental System ◽  
Flow Sensors ◽  
Maximum Resolution ◽  
Sensing Model ◽  
Euler Bernoulli Beam ◽  
Good Agreement

Magnetostrictive biomimetic whiskers have been used as tactile and flow sensors. Compared to other types of whiskers, such whiskers have the advantage of being able to perform static and dynamic measurements. For dynamic measurement, the whisker’s resolution changes with varying vibration frequency; however, the mechanism for this influence has not been studied yet. Thus, the aim of this study is to investigate the resolution–frequency correlation. First, the structure and operation principle of the whisker were analyzed. Then, the Euler–Bernoulli beam theory was employed to establish the sensing model of the magnetostrictive whisker. Finally, the mapping relationship between sensor resolution and frequency was obtained. The eigenfrequency analysis was implemented by FEM to obtain the frequency response of the whisker. A vibration experimental system was built for dynamic testing. The experimental results were in good agreement with the theoretical calculations. Furthermore, it was noted that the resolution was positively correlated with frequency, and the maximum resolution was attained at the natural frequency (two peak values appeared at the first-order and second-order eigenfrequencies). Our research reveals the manner in which a whisker sensor’s resolution is affected by the vibration frequency. The theoretical model can be used to predict the resolution of magnetostrictive whisker sensors.

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