The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

This article deals with the finite element modeling and free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs). Nanostructural materials can be used to alter mechanical, thermal and electrical properties of polymer-based composite materials, because of their superior properties and perfect atom arrangem...

The present work reports the static behaviour of functionally graded rotating beam based on Timoshenko theory, which includes effect shear deformation. principle virtual displacement is applied to derive a governing equation for (FG) beam, considering centrifugal stiffening effect. B-spline collocation technique employed solve differential and material properties are function power law distribu...

"Well-posedness and stability of a semilinear Mindlin-Timoshenko plate model" I will discuss well-posedness and long-time behavior of Mindlin-Timoshenko plate equations that describe vibrations of thin plates. This system of partial differential equations was derived by R. Mindlin in 1951 (though E. Reissner also considered an analogous model earlier in 1945). It can be regarded as a generaliza...

The scale effect of carbon nanotubes (CNTs) in the macro CNT-reinforced composites (CNTRCs) is analyzed, and free vibration characteristics a composite beam resting on viscoelastic foundation were studied. By combining nonlocal theory with Eshelby–Mori–Tanaka (EMT) method, EMT constitutive equation considering CNTs CNTRCs proposed. Based Timoshenko theory, governing equations corresponding boun...

A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ...