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Application of Gradient Elasticity to Benchmark Problems of Beam Vibrations Application of Gradient Elasticity to Benchmark Problems of Beam Vibrations K.M. Kateb1, K.A. Alnefaie1, N.H. Abu-Hamdeh1,*, and E.C. Aifantis1,2 1Dept. of Mechanical Engineering, King Abdulaziz University Jeddah 21589, Saudi Arabia 2Lab of Mechanics and Materials, Polytechnic School, Aristotle University, Thessaloniki, 52124, Greece Abstract The Gradient.