Free Vibration of Edge Cracked Functionally Graded Microscale Beams Based on the Modified Couple Stress Theory

Küçük Resim Yok

Tarih

2017

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

World Scientific Publ Co Pte Ltd

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange's equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

Açıklama

Anahtar Kelimeler

Open edge crack, modified couple stress theory, functionally graded materials, microbeam, free vibration

Kaynak

International Journal Of Structural Stability And Dynamics

WoS Q Değeri

Q2

Scopus Q Değeri

Q1

Cilt

17

Sayı

3

Künye