Farshid Allahkarami - Department of Mechanical Engineering, Bijar Branch, Islamic Azad University, Bijar, Iran
Maryam Ghassabzadeh Saryazdi - Vehicle Technology Research Institute, Amirkabir University of Technology, Tehran, Iran
Hasan Tohidi - Department of Mechanical Engineering, Saqqez Branch, Islamic Azad University, Saqqez, Iran

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 theo-ry 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 re-gion 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 de-pends on the values of volume fraction indexes which causes increment or decrement of excitation frequencies.

Dynamic buckling; Bi-directional; Nonlocal theory; nanobeam.