Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 27, No. 6 (June 2014) 979-990   

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  ANALYTIC APPROACH TO FREE VIBRATION AND BUCKLING ANALYSIS OF FUNCTIONALLY GRADED BEAMS WITH EDGE CRACKS USING FOUR ENGINEERING BEAM THEORIES
 
K. Sherafatnia, G. H. Farrahi and S. A. Faghidian
 
( Received: September 20, 2013 – Accepted: December 12, 2013 )
 
 

Abstract    A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed in this research. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments connected by two mass-less springs (extensional and rotational). Then the equations of motion for the free vibrations and buckling analysis are established and solved analytically for clamped-free boundary conditions. A detailed parametric study is performed to examine the influences of the location and depth of the crack, material properties and slenderness ratio of the beam on the free vibration and buckling characteristics of cracked FGM beams for each of the four engineering beam theories.

 

Keywords    Functionally graded materials; Engineering beam theories; Open edge crack; Vibration analysis; Buckling analysis.

 

چکیده    در پژوهش حاضر ارتعاشات آزاد و آنالیز پایداری تیرهای دارای ترک لبه ای و ساخته شده از مواد FG با استفاده از چهار تئوری تیر اویلر-برنولی، رایلی، تئوری برشی و تیموشنکو بررسی شده اند. رفتار مادی تیر در راستای ضخامت آن بصورت نمایی فرض شده و ترک لبه ای نیز به کمک دو فنر بدون جرم کششی و پیچشی مدلسازی شده است. معادلات حاکم بر ارتعاشات آزاد و تحلیل کمانش تیر به کمک روش انرژی بدست آمده و به صورت تحلیلی برای شرایط مرزی یکسر درگیر حل شده اند. هم چنین تاثیرات مکان و عمق ترک، خواص مادی و نسبت رعنایی تیر بر فرکانس طبیعی و شکل مود های ارتعاشات آزاد و مشخصه های کمانشی تیر نیز با استفاده از هر یک از چهار تئوری مهندسی تیر کاملا بررسی شده اند.

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