scholarly journals Transverse Vibration of Clamped-Pinned-Free Beam with Mass at Free End

2019 ◽  
Vol 9 (15) ◽  
pp. 2996 ◽  
Author(s):  
Jonathan Hong ◽  
Jacob Dodson ◽  
Simon Laflamme ◽  
Austin Downey
Keyword(s):  
Transverse Vibration ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
High Rate ◽  
Harsh Environments ◽  
Mode Shapes ◽  
Engineering Systems ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Free Beam

Engineering systems undergoing extreme and harsh environments can often times experience rapid damaging effects. In order to minimize loss of economic investment and human lives, structural health monitoring (SHM) of these high-rate systems is being researched. An experimental testbed has been developed to validate SHM methods in a controllable and repeatable laboratory environment. This study applies the Euler-Bernoulli beam theory to this testbed to develop analytical solutions of the system. The transverse vibration of a clamped-pinned-free beam with a point mass at the free end is discussed in detail. Results are derived for varying pin locations and mass values. Eigenvalue plots of the first five modes are presented along with their respective mode shapes. The theoretical calculations are experimentally validated and discussed.

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.

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.

Transverse Vibration of Non-Uniform Euler-Bernoulli Beam, Using Differential Transform Method (DTM)

2011 ◽  
Vol 110-116 ◽  
pp. 2400-2405
Author(s):  
K. Torabi ◽  
H. Afshari ◽  
E. Zafari
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Method ◽  
Transverse Vibration ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Special Cases ◽  
Linear Differential ◽  
Euler Bernoulli Beam

Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Comparing results with the cases which exact solution have been presented, shows that DTM is a strong method especially for solving quasi-linear differential equations.

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.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

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.

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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