Document Details

Document Type : Thesis 
Document Title :
Application of Gradient Materials Mechanics in Vibration of Beams
تطبيق تدرج ميكانيكا المواد في اهتزاز العوارض
 
Subject : Faculty of Engineering - Department of Mechanical Engineering 
Document Language : Arabic 
Abstract : Gradient approach was adopted to revisit certain engineering configurations, specifically mechanical vibrations. New results on size effects and scale-dependent behavior not captured by traditional theories were derived with applications to advanced technologies. This thesis discussed the elastic prismatic straight beams in bending and examined the one-dimensional formulation of the gradient elasticity problem using two different governing equations: the gradient elasticity bending moment equation (fourth order) and the gradient elasticity deflection equation (sixth order). Different geometric boundary and support conditions were examined and the corresponding extra gradient elasticity boundary conditions were obtained. Considering the gradient material elasticity theory, the free vibrations of a cantilever beam loaded by an end force and a simply supported beam disturbed by a concentrated force in the middle of the beam were solved via an exact, analytical approach. Exact free vibration frequencies and mode shapes were derived and presented. The difference between the gradient material elasticity solution and its equivalent classical elasticity one was revealed. The size ratio induced significant effects on vibration frequencies. For both beams, increases in the size ratio ℓ/L caused the vibration frequencies to increase which imply higher beam stiffness. Numerical examples showed the results were reduced exactly to the classical vibration solutions for vanishing size ratio ℓ/L. 
Supervisor : Prof. Dr. Nidal H. Abu-Hamdeh 
Thesis Type : Master Thesis 
Publishing Year : 1434 AH
2013 AD 
Co-Supervisor : Dr. Khalid A. Al-nefaie 
Added Date : Thursday, November 7, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
خضر محمد كاتبKateb, Kheder MohammedResearcherMaster 

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