Dynamics of Eccentric Shafts Under Linearly Varying Tension Rotating in a Viscous Medium

1974 ◽  
Vol 96 (4) ◽  
pp. 1285-1290
Author(s):  
V. Prodonoff ◽  
C. D. Michalopoulos
Keyword(s):  
Steady State ◽  
Beam Theory ◽  
Viscous Medium ◽  
Bernoulli Beam ◽  
Axial Coordinate ◽  
Simply Supported ◽  
Deterministic Function ◽  
Mass Eccentricity ◽  
Bending Stresses ◽  
Euler Bernoulli Beam

Using Euler-Bernoulli beam theory an investigation is made of the dynamic behavior of an eccentric vertical circular shaft rotating in viscous medium. The shaft is subjected to linearly-varying tension and has distributed mass and elasticity. The mass eccentricity is assumed to be a deterministic function of the axial coordinate. The solution is obtained by modal analysis. An example is considered wherein the shaft is simply supported at the top and vertically guided at the bottom. Steady-state deflections and bending stresses are computed for a particular eccentricity function over a range of speeds of rotation which includes a resonant frequency.

scholarly journals Composite patch reinforcement of a cracked simply-supported beam traversed by moving mass

2020 ◽  
Vol 14 (1) ◽  
pp. 6403-6415
Author(s):  
M. S. Aldlemy ◽  
S. A. K. Al-jumaili ◽  
R. A. M. Al-Mamoori ◽  
T. Ya ◽  
Reza Alebrahim
Keyword(s):  
Finite Element Method ◽  
Edge Crack ◽  
Time History ◽  
Beam Theory ◽  
Beam Deflection ◽  
Moving Mass ◽  
Bernoulli Beam ◽  
Simply Supported ◽  
Composite Patch ◽  
Euler Bernoulli Beam

In this study dynamic analysis of a metallic beam under travelling mass was investigated. A beam with an edge crack was considered to be reinforced using composite patch. Euler-Bernoulli beam theory was applied to simulate the time-history behavior of the beam under dynamic loading. Crack in the beam was modeled using a rotational spring. Dimension of the composite patch, crack length, stress intensity factor at crack tip and beam deflection are some parameters which were studied in details. Results were validated against those which were found through Finite Element Method.

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.

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.

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

Longitudinal Strength Analysis of the Grounded Barge Carrying Independent Cargo Tanks

1972 ◽  
Vol 9 (03) ◽  
pp. 333-344
Author(s):  
Finn C. Michelsen ◽  
Uilmann Kilgore
Keyword(s):  
Operational Calculus ◽  
Beam Theory ◽  
Class Ii ◽  
Class I ◽  
Strength Analysis ◽  
Bending Moments ◽  
Bernoulli Beam ◽  
Method Of Solution ◽  
Longitudinal Strength ◽  
Euler Bernoulli Beam

The problem has been treated of determining deflections and bending moments of the barge hull and independent cargo tanks combination as these occur in Class I and Class II barges during grounding. The method of solution is that of the initial parameters, which is here developed by means of operational calculus. The solution is closed and exact within the limitations of the Euler-Bernoulli beam theory.

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

2020 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Medium Frequency ◽  
Beam Structures ◽  
Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Matrix Method for Buckling Analysis of Frames Based on Hencky Bar-Chain Model

2019 ◽  
Vol 19 (08) ◽  
pp. 1950093 ◽  
Author(s):  
W. H. Pan ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Matrix Method ◽  
Structural Changes ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Chain Model ◽  
Bernoulli Beam ◽  
Various Boundary Conditions ◽  
End Restraint ◽  
Euler Bernoulli Beam ◽  
General Frames

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

Flexure-Based Two Degree-of-Freedom Legs for Walking Microrobots

2006 ◽  
Author(s):  
Ankur M. Mehta ◽  
Kristofer S. J. Pister
Keyword(s):  
Analytical Model ◽  
Design Space ◽  
Beam Theory ◽  
Degree Of Freedom ◽  
Bernoulli Beam ◽  
Comb Drive ◽  
Walking Gait ◽  
Euler Bernoulli Beam ◽  
Force Displacement ◽  
Two Degree Of Freedom

This work examines the design of legs for a walking microrobot. The parameterized force-displacement relationships of planar serpentine flexure-based two degree-of-freedom legs are analyzed. An analytical model based on Euler-Bernoulli beam theory is developed to explore the design space, and is subsequently refined to include contact between adjacent beams. This is used to determine a successful leg geometry given dimensional constraints and actuator limitations. Standard comb drive actuators that output 100 μN of force over a 15 μm bi-directional throw are shown able to drive a walking gait with three legs on a 1 cm2 silicon die microrobot. If the comb drive suspensions cannot withstand the generated reaction moments, an alternate pivot-based leg linkage is proposed.

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