A comparison of infinite Timoshenko and Euler–Bernoulli beam models on Winkler foundation in the frequency- and time-domain

2007 ◽  
Vol 304 (3-5) ◽  
pp. 932-947 ◽  
Author(s):  
P. Ruge ◽  
C. Birk
Keyword(s):  
Time Domain ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

scholarly journals Quintic B-spline collocation method for numerical solution of free vibration of tapered Euler-Bernoulli beam on variable Winkler foundation

2021 ◽  
Vol 15 (2) ◽  
pp. 8193-8204
Author(s):  
Amin Ghannadiasl
Keyword(s):  
Free Vibration ◽  
Numerical Solution ◽  
Collocation Method ◽  
Winkler Foundation ◽  
Finite Dimensional Space ◽  
Spline Collocation ◽  
Bernoulli Beam ◽  
B Spline ◽  
Spline Collocation Method ◽  
Euler Bernoulli Beam

The collocation method is the method for the numerical solution of integral equations and partial and ordinary differential equations. The main idea of this method is to choose a number of points in the domain and a finite-dimensional space of candidate solutions. So, that solution satisfies the governing equation at the collocation points. The current paper involves developing, and a comprehensive, step-by step procedure for applying the collocation method to the numerical solution of free vibration of tapered Euler-Bernoulli beam. In this stusy, it is assumed the beam rested on variable Winkler foundation. The simplicity of this approximation method makes it an ideal candidate for computer implementation. Finally, the numerical examples are introduced to show efficiency and applicability of quintic B-spline collocation method. Numerical results are demonstrated that quintic B-spline collocation method is very competitive for numerical solution of frequency analysis of tapered beam on variable elastic foundation.

scholarly journals Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 328 ◽  
Author(s):  
Yuxin Sun ◽  
Shoubin Liu ◽  
Zhangheng Rao ◽  
Yuhang Li ◽  
Jialing Yang
Keyword(s):  
Laser Pulse ◽  
Elastic Foundation ◽  
Heat Conduction Equation ◽  
Laser Pulses ◽  
Winkler Foundation ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Vibration Equation ◽  
Motion Speed ◽  
Euler Bernoulli Beam

In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green’s function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail.

Nonlinear Vibration of Carbon Nanotube Resonators Considering Higher Modes

2015 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Multiple Scales ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Objective System ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the carbon nanotubes based on the Euler-Bernoulli beam theory is studied. The Euler-Bernoulli beam theory is implemented to find the governing equation of the vibrations of the carbon nanotube. The Pasternak and Nonlinear Winkler foundation is assumed for the objective system. It is supposed that the system is supported by hinged-hinged boundary conditions. The Galerkin procedure is employed in order to find the nonlinear ordinary differential equation of the vibration of the objective system considering two modes of vibrations. The primary and secondary resonant cases are developed for the objective system employing the multiple scales method. Influence of different factors such as length, thickness, position of applied force, Pasternak and Winkler foundation are fully shown on the primary and secondary resonance of the system.

scholarly journals Rail Joint Model Based on the Euler-Bernoulli Beam Theory

2019 ◽  
Vol 8 (2) ◽  
pp. 16-29
Author(s):  
Traian Mazilu ◽  
Ionuţ Radu Răcănel ◽  
Cristian Lucian Ghindea ◽  
Radu Iuliu Cruciat ◽  
Mihai-Cornel Leu
Keyword(s):  
Beam Theory ◽  
Joint Model ◽  
Experimental Results ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Model Based ◽  
Bernoulli Beam Theory ◽  
Proposed Model ◽  
Joint Gap ◽  
Euler Bernoulli Beam

Abstract In this paper, a rail joint model consisting of three Euler-Bernoulli beams connected via a Winkler foundation is proposed in order to point out the influence of the joint gap length upon the stiffness of the rail joint. Starting from the experimental results aiming the stiffness of the rail joint, the Winkler foundation stiffness of the model has been calculated. Using the proposed model, it is shown that the stiffness of the rail joint of the 49 rail can decreases up to 10 % when the joint gap length increases from 0 to 20 mm.

scholarly journals The Euler–Bernoulli beam on a tensionless Winkler foundation: A simple problem of receding contact

2018 ◽  
Vol 46 (4) ◽  
pp. 375-383
Author(s):  
NG Stephen ◽  
SY Ch’ng
Keyword(s):  
Beam Theory ◽  
Point Load ◽  
Simple Problem ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Simple Experiment ◽  
Receding Contact ◽  
Undergraduate Programme ◽  
Flexible Foam ◽  
Euler Bernoulli Beam

A steel ruler supported by a flexible foam foundation, modelled as an Euler–Bernoulli beam on a Winkler foundation, exhibits receding contact when subjected to a point load. The system is analysed using simple beam theory and Laplace transformation – both of which are typically covered in the first two years of a UK Mechanical Engineering undergraduate programme. The design of a simple experiment is described.

scholarly journals Dynamics and buckling loads for a vibrating damped Euler–Bernoulli beam connected to an inhomogeneous foundation

2020 ◽  
Author(s):  
Andrei K. Abramian ◽  
Sergei A. Vakulenko ◽  
Wim T. van Horssen ◽  
Dmitry V. Lukichev
Keyword(s):  
Elastic Foundation ◽  
Added Mass ◽  
Variation Principle ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Internal Resonances ◽  
Main Mode ◽  
Buckling Loads ◽  
Inhomogeneous Foundation ◽  
Euler Bernoulli Beam

AbstractIn this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle, beam buckling loads are computed for cases of harmonically perturbed types of inhomogeneities in the elastic foundation, for cases of point inhomogeneities in the form of concentrated springs in the elastic foundation, and for cases with rectangular inclusions in the elastic foundation. The investigation of the beam dynamics shows the possibility of internal resonances for particular values of the beam rigidity and longitudinal force. Such types of resonances, which are usually typical for nonlinear systems, are only possible for the beam due to its inhomogeneous foundation. The occurrence of so-called added mass effects near buckling instabilities under the influence of damping have been found. The analytical expressions for this “added mass” effect have been obtained for different damping models including space hysteresis types. This effect arises as a result of an interaction between the main mode, which is close to instability, and all the other stable modes of vibration.

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