Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

Year 2018, Volume: 6 Issue: 1, 127 - 141, 31.01.2018

Çiğdem Dinçkal

https://doi.org/10.21541/apjes.321997

Abstract

This paper is pertinent to the
analytical solutions for vibration analysis of initially stressed Nonlocal Euler-Bernoulli nano-beams. In order to take into account of small length scale effect,
this vibration problem formulation is depending upon both nonlocal
Euler-Bernoulli and also Eringen’s nonlocal elasticity theory. The boundary
conditions and governing equation are obtained by use of Hamiltonian’s
principle. These equations are solved analytically with different initial
stresses (both compressive and tensile) and boundary conditions. The effect of small
length scale and the initial stress on the fundamental frequency are
investigated.  The solutions obtained are
compared with the ones depending upon both classical Euler-Bernoulli and
Timoshenko beam theory to comprehend the responses of nano-beams under the
effect of initial stress and small scale in terms of  frequencies for both theories. The results
supply a better declaration for vibration analysis of nano-beams which are
short and stubby with initial stress.

 

Keywords

Nonlocal Euler-Bernoulli beam theory, fundamental frequency, initially stressed nano-beams, small length scale effect

Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

Abstract

This paper is pertinent to the
analytical solutions for vibration analysis of initially stressed Nonlocal Euler-Bernoulli nano-beams. In order to take into account of small length scale effect,
this vibration problem formulation is depending upon both nonlocal
Euler-Bernoulli and also Eringen’s nonlocal elasticity theory. The boundary
conditions and governing equation are obtained by use of Hamiltonian’s
principle. These equations are solved analytically with different initial
stresses (both compressive and tensile) and boundary conditions. The effect of small
length scale and the initial stress on the fundamental frequency are
investigated.  The solutions obtained are
compared with the ones depending upon both classical Euler-Bernoulli and
Timoshenko beam theory to comprehend the responses of nano-beams under the
effect of initial stress and small scale in terms of  frequencies for both theories. The results
supply a better declaration for vibration analysis of nano-beams which are
short and stubby with initial stress.

Keywords

Nonlocal Euler-Bernoulli beam theory, fundamental frequency, initially stressed nano-beams, small length scale effect

References

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