Abstract
This paper is concerned with the free vibration problem for micro/nanobeams modelledafter Eringen’s nonlocal elasticity theory and Timoshenko beam theory. The small scaleeffect is taken into consideration in the former theory while the effects of transverse sheardeformation and rotary inertia are accounted for in the latter theory. The governingequations and the boundary conditions are derived using Hamilton’s principle. Theseequations are solved analytically for the vibration frequencies of beams with various endconditions. The vibration solutions obtained provide a better representation ofthe vibration behaviour of short, stubby, micro/nanobeams where the effectsof small scale, transverse shear deformation and rotary inertia are significant.The exact vibration solutions should serve as benchmark results for verifyingnumerically obtained solutions based on other beam models and solution techniques.
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