Transverse Vibration of a Two-Span Beam Under Action of a Moving Constant Force

1950 ◽  
Vol 17 (1) ◽  
pp. 1-12
Author(s):  
R. S. Ayre ◽  
George Ford ◽  
L. S. Jacobsen
Keyword(s):  
Mechanical Model ◽  
Constant Velocity ◽  
Natural Mode ◽  
Theoretical Studies ◽  
Constant Force ◽  
Bending Stress ◽  
Transient Vibration ◽  
Simply Supported ◽  
Moving Force ◽  
Theory And Experiment

Abstract The problem relates to the transient vibration of a symmetrical, continuous, simply supported two-span beam which is traversed by a constant force moving with constant velocity. The beam is of slender proportions, flexure alone being considered. Damping is zero, and there is no mass associated with the moving force. Exact theoretical solutions for bending stress have been derived in general form. They consist of three infinite series, each related to one of three time eras as follows: (a) Where force is crossing first span; (b) is crossing second span; (c) has left the beam. Each term of a series is related to a natural mode of vibration. Quantitative theoretical studies show the variation in individual terms of the series, and also in summations of the first five terms, as the traversing velocity is varied. A mechanical model with electrical recording of stress was employed to obtain a more complete quantitative solution than was feasible analytically. The agreement between theory and experiment was reasonably good. Large magnifications of stress (of the order of 2.5) were found in the neighborhood of resonance with the fundamental mode.

Dynamic Response of a Timoshenko Beam to a Moving Force

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Paweł Śniady
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Constant Velocity ◽  
Free Vibrations ◽  
Dynamical Response ◽  
Transverse Displacement ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Moving Force

We consider the dynamical response of a finite, simply supported Timoshenko beam loaded by a force moving with a constant velocity. The classical solution for the transverse displacement and the rotation of the cross section of a Timoshenko beam has a form of a sum of two infinite series, one of which represents the force vibrations (aperiodic vibrations) and the other one free vibrations of the beam. We show that one of the series, which represents aperiodic (force) vibrations of the beam, can be presented in a closed form. The closed form solutions take different forms depending if the velocity of the moving force is smaller or larger than the velocities of certain shear and bar velocities.

scholarly journals Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Śniady Paweł ◽  
Katarzyna Misiurek ◽  
Olga Szyłko-Bigus ◽  
Idzikowski Rafał
Keyword(s):  
Constant Velocity ◽  
Stress Gradient ◽  
Nonlocal Elasticity Theory ◽  
Theory Of Elasticity ◽  
Gradient Theory ◽  
Bernoulli Beam ◽  
Simply Supported ◽  
Moving Force ◽  
Theory Application ◽  
Euler Bernoulli Beam

AbstractTwo models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.

ANSYS Simply Supported Deep Beams Based on the Study of Mechanical Properties

2013 ◽  
Vol 351-352 ◽  
pp. 782-785
Author(s):  
Yong Bing Liu ◽  
Xiao Zhong Zhang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Mechanical Model ◽  
Work Performance ◽  
Deep Beam ◽  
Analysis Software ◽  
Deep Beams ◽  
Element Analysis ◽  
Simply Supported ◽  
Force Characteristics

Established the mechanical model of simply supported deep beam, calculation and analysis of simple supported deep beams by using finite element analysis software ANSYS, simulated the force characteristics and work performance of the deep beam. Provides the reference for the design and construction of deep beams.

scholarly journals Compression behavior of simply-supported and fully embedded monolayer graphene: Theory and experiment

2016 ◽  
Vol 8 ◽  
pp. 191-200 ◽  
Author(s):  
Emmanuel N. Koukaras ◽  
Charalampos Androulidakis ◽  
George Anagnostopoulos ◽  
Konstantinos Papagelis ◽  
Costas Galiotis
Keyword(s):  
Monolayer Graphene ◽  
Compression Behavior ◽  
Simply Supported ◽  
Theory And Experiment

Morphology of Voltage-Triggered Ordered Wrinkles of a Dielectric Elastomer Sheet

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Guoyong Mao ◽  
Lei Wu ◽  
Xueya Liang ◽  
Shaoxing Qu
Keyword(s):  
High Voltage ◽  
Optical Sensor ◽  
Material Science ◽  
Dielectric Elastomer ◽  
Theoretical Studies ◽  
Science And Engineering ◽  
Future Design ◽  
Experimental And Theoretical Studies ◽  
Theory And Experiment ◽  
Good Agreement

Wrinkles widely existing in sheets and membranes have attracted a lot of attention in the fields of material science and engineering applications. In this paper, we present a new method to generate ordered (striplike) and steady wrinkles of a constrained dielectric elastomer (DE) sheet coated with soft electrodes on both sides subjected to high voltage. When the voltage reaches a certain value, wrinkles will nucleate and grow. We conduct both experimental and theoretical studies to investigate the wavelength and amplitude of the wrinkle. The results show a good agreement between theory and experiment. Moreover, the amplitude and wavelength of ordered wrinkles can be tuned by varying the prestretch and geometry of the DE sheet, as well as the applying voltage. This study can help future design of DE transducers such as diffraction grating and optical sensor.

scholarly journals Flexural Interpretation of Simply Supported Laminated Composite Beam

2020 ◽  
Vol 8 (5) ◽  
pp. 3559-3565
Keyword(s):  
Shear Deformation ◽  
Composite Beam ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Shear Stresses ◽  
Bending Stress ◽  
Simply Supported ◽  
Laminated Composite Beam ◽  
Laminated Composite Beams

In this Paper, the analysis of simply supported laminated composite beam having uniformly distributed load is performed. The solutions obtained in the form of the displacements and stresses for different layered cross ply laminated composite simply supported beams subjected uniformly distributed to load. Different aspect ratio consider for different results in terms of displacement, bending stress and shear stresses. The shear stresses are calculated with the help of equilibrium equation and constitutive relationship. Using displacement field including trigonometric function of laminated composite beams are derived from virtual displacement principle. There are axial displacement, transverse displacement, bending stress and shear stresses. In addition, Euler-Bernoulli (ETB), First order shear deformation beam theory (FSDT), Higher order shear deformation beam theory (HSDT) and Hyperbolic shear deformation beam theory (HYSDT) solution have been made for comparison and better accuracy of solutions and results of static analyses of laminated composite beams for simply supported laminated composite beam.

Response of a Simply Supported Timoshenko Beam to a Purely Random Gaussian Process

1958 ◽  
Vol 25 (4) ◽  
pp. 496-500
Author(s):  
J. C. Samuels ◽  
A. C. Eringen
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Equation ◽  
Mean Square ◽  
Bending Stress ◽  
Random Loading ◽  
Simply Supported ◽  
The Mean ◽  
Timoshenko Beam Equation ◽  
Classical Beam Theory

Abstract The generalized Fourier analysis is applied to the damped Timoshenko beam equation to calculate the mean-square values of displacements and bending stress, resulting from purely random loading. Compared with the calculations, based on the classical beam theory, it was found that the displacement correlations of both theories were in excellent agreement. Moreover, the mean square of the bending stress, contrary to the results of the classical beam theory, was found to be convergent. Computations carried out with a digital computer are plotted for both theories.

An Excitation Spectrum Criteria for the Vibration-Induced Fatigue of Small Bore Pipes

2002 ◽  
Author(s):  
Pierre Moussou
Keyword(s):  
Natural Frequency ◽  
Excitation Spectrum ◽  
Endurance Limit ◽  
Maximum Velocity ◽  
Young Modulus ◽  
Mode Shapes ◽  
Natural Mode ◽  
Velocity Spectrum ◽  
Bending Stress ◽  
Euler Beam

The purpose of the study is to determine an easy-to-use criterion to evaluate the risk of vibration induced fatigue of small bore pipes. The failure mechanism considered is the resonant amplification of a stationary broadband excitation of the main pipe by natural modes of the small bore pipe, leading to bending stresses above the fatigue limit of the steel. Based on the Euler beam theory, a simple model is built up for the natural mode shapes of the small bore pipe close to its root. It is shown that the velocity spectrum at the root of the small bore pipe is equal to the RMS value of the bending stress multiplied by a function of the natural frequency, the damping coefficient, the speed of elastic waves in the steel, the Young modulus and a non-dimensional factor weakly depending on the geometry of the small bore pipe. A maximum velocity spectrum can then be deduced, assuming that a small bore pipe vibrates mainly on its natural mode shapes. The maximum excitation spectrum is defined for each frequency ƒ as the one which would generate a maximum bending stress equal to the endurance limit of the steel, would the small bore pipe have a natural frequency equal to ƒ. Using envelope values of the dimensional factor, the stress intensification factor, the peak factor and the endurance limit of the steel, one obtains the following maximum velocity spectrum for the stainless steel: v<6mm/s/sqrt(ƒ) and the following maximum velocity spectrum for the ferritic steel: v<2.7mm/s/sqrt(ƒ) The velocity spectrum criterion appears less penalizing than the 12 mm/s criterion and more conservative than the strict enforcement of the ANSI-OM3 standard. Comparisons with former studies show that the velocity spectrum criterion leads to the correct fatigue diagnosis.

Protection of Continuous Structures Against Vibrations by Active Damping

1983 ◽  
Vol 105 (3) ◽  
pp. 374-381
Author(s):  
E. Luzzato ◽  
M. Jean
Keyword(s):  
Control System ◽  
Mechanical Model ◽  
Approximation Problem ◽  
Active Damping ◽  
Simply Supported ◽  
Viscoelastic Structure ◽  
Flexural Vibrations ◽  
Dimension Space ◽  
Damping Of Vibrations ◽  
General Method

In this paper, we deal with the problem of active damping of vibrations of a continuous viscoelastic structure, and a general method of computation of the control system is developed. We define a mechanical model for this structure, the sources of perturbing vibrations, the control system, and different absorption criteria. The problem is set in an infinite dimension space, and an approximation problem is derived in n dimension spaces. Two methods of resolution are proposed for this approximation problem, and the solutions are compared. An example is given for the case of flexural vibrations in beams. Numerical results simulating the behavior of flexural vibrations in a rectangular plate, which is simply supported along the whole boundary, are presented for three different absorption criteria, thus permitting a quick evaluation of the comparative effectiveness of the chosen criteria.

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