Dynamic buckling of bi-directional functionally graded porous Timoshenko nanobeam
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1دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی، واحد بیجار
2پژوهشکده فناوریهای مهندسی مکانیک، دانشگاه صنعتی امیرکبیر
3دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی، واحد سقز
The present research deals with dynamic buckling of bi-directional functionally graded nanobeam considering porosity effect. It is assumed that the material characteristics of nanobeam changes ac-cording to modified power-law model along thickness and length for Even and Uneven distributions of porosity patterns which are represented by bi-directional trigonometric functions. Nonlocal theory has been used for modeling the structure and attaining strain-stresses. The motion equations are derived based on Hamilton's principle. Moreover, generalized differential quadrature method in conjunction with Bolotin method are employed to obtain instability region. The influences of Non-local parameter, power-law indexes and porosity volume fraction over the dynamic instability region are studied. According to the obtained results, it is observed that the nonlocal beam model has an under-estimate prediction for the dynamic instability regions of BD-FG nanobeam. Furthermore, it is seen that the effect of the coefficient of Even porosity on dynamic instability remarkably depends on the values of volume fraction indexes which causes increment or decrement of excitation frequencies.
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