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.

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.

DYNAMIC STABILITY OF A BEAM ON AN ELASTIC FOUNDATION INCLUDING STRESS WAVE EFFECTS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250017 ◽  
Author(s):  
YING LIU ◽  
G. LU
Keyword(s):  
Dynamic Stability ◽  
Elastic Foundation ◽  
Stress Wave ◽  
Axial Load ◽  
Elastic Beam ◽  
Beam Theory ◽  
Stress Wave Propagation ◽  
Bernoulli Beam ◽  
Wave Effects ◽  
Euler Bernoulli Beam

This paper examines the dynamic stability of an elastic beam on the elastic foundation, in which the stress wave effect is taken into account. Based on Euler–Bernoulli beam theory, the dynamic response of the elastic beam on the elastic foundation to a small transverse perturbation is analyzed. By considering the stress wave propagation in the beam and the constraint of the elastic foundation, the critical bifurcation condition of elastic beam is derived, and the critical axial load of the elastic beam is predicted. Furthermore, the effects of the elastic foundation and the beam length on buckling condition are discussed by using numeric examples. Finally, an approximate solution of critical axial load for elastic beam on the elastic foundation is provided, which may be used to investigate elastic beam buckling problem.

Mathematical Analysis for Wave Propagation Characteristics of Fluid-Filled Nonlocal Carbon Nanotubes

2013 ◽  
Vol 444-445 ◽  
pp. 209-213
Author(s):  
Yang Yang
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Fluid Velocity ◽  
Nonlocal Effect ◽  
Variation Principle ◽  
The Novel ◽  
Bernoulli Beam ◽  
Nonlocal Models ◽  
Walled Carbon Nanotubes ◽  
Euler Bernoulli Beam

The analytical nonlocal Euler-Bernoulli beam models for wave propagation in fluid-filled single-walled carbon nanotubes are established employing variation principle. The analytical nonlocal governing equations are derived and used in wave propagation analysis. Comparing with partial nonlocal Euler-Bernoulli beam models used previously, the novel analytical nonlocal models predict stiffness enhancement of CNT and wave decaying at high wavenumber or high nonlocal effect area. Though the novel analytical model is less sensitive than partial nonlocal model when fluid velocity is high, it simulate much high nonlocal effect than the corresponding partial model in many cases.

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