The Usefulness of Elementary Theory for the Linear Vibrations of Layered, Orthotropic Elastic Beams and Corrections Due to Two-Dimensional End Effects

1991 ◽  
Vol 58 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. M. Duva ◽  
J. G. Simmonds
Keyword(s):  
Natural Frequencies ◽  
Elementary Theory ◽  
Beam Theory ◽  
Relative Order ◽  
Bernoulli Beam ◽  
End Effects ◽  
Cantilevered Beam ◽  
Linear Vibrations ◽  
Order Of Magnitude ◽  
Euler Bernoulli Beam

With the aid of formal asymptotic expansions, we conclude not only that elementary (Euler-Bernoulli) beam theory can be applied successfully to layered, orthotropic beams, possibly weak in shear, but also that, in computing the lower natural frequencies of a cantilevered beam, the most important correction to the elementary theory—of the relative order of magnitude of the ratio of depth to length—comes from effects in a neighborhood of the built-in end. We compute this correction using the fundamental work on semi-infinite elastic strips of Gregory and Gladwell (1982) and Gregory and Wan (1984). We also show that, except in unusual cases (e.g., a zero Poisson’s ratio in a homogeneous, elastically isotropic beam), Timoshenko beam theory produces an erroneous correction to the frequencies of elementary theory of the relative order of magnitude of the square of the ratio of depth to length.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

scholarly journals Natural Frequencies and Mode Shapes of Statically Deformed Inclined Risers

2016 ◽  
Author(s):  
Feras K. Alfosail ◽  
Ali H. Nayfeh ◽  
Mohammad I. Younis
Keyword(s):  
Natural Frequencies ◽  
Equilibrium Configuration ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Galerkin Approach ◽  
Inclination Angles ◽  
Linear Vibrations ◽  
Euler Bernoulli Beam ◽  
Beam Mode ◽  
Good Agreement

In this work, we investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler-Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, a Galerkin expansion of fifteen axially loaded beam mode shapes are used to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and exact mode shapes for various values of inclination angles and applied tension. The obtained results are validated against a boundary-layer analytical solution and are found in good agreement. This constructs a basis to study the nonlinear forced vibrations of inclined risers.

Dynamic Responses of Two Beams Connected by a Spring-Mass Device

2012 ◽  
Vol 29 (1) ◽  
pp. 143-155 ◽  
Author(s):  
H.- P. Lin ◽  
D. Yang
Keyword(s):  
Natural Frequencies ◽  
Beam Theory ◽  
Free Vibrations ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Entire System ◽  
Bernoulli Beam ◽  
Continuous Beams ◽  
Experimental Validations ◽  
Euler Bernoulli Beam

AbstractThis paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring con-nection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

scholarly journals Free Vibration of a Carbon Nanotube-Based Mass Sensor

2011 ◽  
Vol 403-408 ◽  
pp. 1163-1167 ◽  
Author(s):  
Payam Soltani ◽  
Omid Pashaei ◽  
Mohammad Mehdi Taherian ◽  
Anoushiravan Farshidianfar
Keyword(s):  
Boundary Condition ◽  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Added Mass ◽  
Mass Sensor ◽  
Bernoulli Beam ◽  
Single Walled Carbon Nanotube ◽  
Euler Bernoulli Beam

In this paper, nonlocal Euler-Bernoulli beam theory is applied to investigate the dynamical behavior of a single-walled carbon nanotube (SWCNT) with an extra added nanoparticle. The SWCNT is assumed to be embedded on a Winkler-type elastic foundation with cantilever boundary condition. This configuration can be used as a nano-mass sensor which works on the basis of the changing the natural frequencies. The results show that the added mass causes an obvious increase in sensitivity of SWCNT-based nano-mass sensor, especially for stiff mediums, small nonlocal parameters, and stocky SWCNTs.

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.

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

2006 ◽  
Vol 20 (4) ◽  
pp. 467-472 ◽  
Author(s):  
Youngjae Shin ◽  
Jonghak Yun ◽  
Kyeongyoun Seong ◽  
Jaeho Kim ◽  
Sunghwang Kang
Keyword(s):  
Natural Frequencies ◽  
Bernoulli Beam ◽  
Elastic Foundations ◽  
Euler Bernoulli Beam

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.

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