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## trenVibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-BeamsVibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

#### Çiğdem Dinçkal [1]

##### 129 271

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.

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.

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Primary Language en Engineering Articles Author: Çiğdem DinçkalCountry: Turkey
 Bibtex @research article { apjes321997, journal = {Akademik Platform Mühendislik ve Fen Bilimleri Dergisi}, issn = {}, eissn = {2147-4575}, address = {Akademik Platform}, year = {2018}, volume = {6}, pages = {127 - 141}, doi = {10.21541/apjes.321997}, title = {Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams}, key = {cite}, author = {Dinçkal, Çiğdem} } APA Dinçkal, Ç . (2018). Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams. Akademik Platform Mühendislik ve Fen Bilimleri Dergisi, 6 (1), 127-141. DOI: 10.21541/apjes.321997 MLA Dinçkal, Ç . "Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 (2018): 127-141 Chicago Dinçkal, Ç . "Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 (2018): 127-141 RIS TY - JOUR T1 - Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams AU - Çiğdem Dinçkal Y1 - 2018 PY - 2018 N1 - doi: 10.21541/apjes.321997 DO - 10.21541/apjes.321997 T2 - Akademik Platform Mühendislik ve Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 127 EP - 141 VL - 6 IS - 1 SN - -2147-4575 M3 - doi: 10.21541/apjes.321997 UR - https://doi.org/10.21541/apjes.321997 Y2 - 2018 ER - EndNote %0 Academic Platform Journal of Engineering and Science Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams %A Çiğdem Dinçkal %T Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams %D 2018 %J Akademik Platform Mühendislik ve Fen Bilimleri Dergisi %P -2147-4575 %V 6 %N 1 %R doi: 10.21541/apjes.321997 %U 10.21541/apjes.321997 ISNAD Dinçkal, Çiğdem . "Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 / 1 (January 2018): 127-141. https://doi.org/10.21541/apjes.321997