عنوان	Free vibration analysis of the macro-micro-nano plates and shells made of a material with functionally graded porosity: A closed-form solution
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Functionally graded porous material,plates and shells,free vibration,analytical closed-form solution
چکیده	This article deals with introducing a closed-form solution for considering thevibration of macro-micro-nano plates and shells made of unit material withfunctionally graded porosity (FGP). Classic continuum theory beside modifiednonlocal strain gradient theory are used at macro and micro/nano scales,respectively. The governing equations are obtained in the frame work of thirdorder plate and shell theories. In the solution procedure, a differential oper-ator is defined and by using it, five equations of motion are converted to thefive algebraic equations. Then, by satisfying the equations of boundary condi-tions and achieving the nonzero solution, the frequencies are extracted.
پژوهشگران	پویان طالبی زاده (نفر اول)، حمزه صالحی پور (نفر دوم)، داوود شاهقلیان (نفر سوم)، امین شهسوار (نفر چهارم)، مرتضی کریمی (نفر پنجم)