In this study, flapwise bending vibration analysis of a tapered Timoshenko beam mounted on the periphery of a rotating rigid hub is performed. The governing differential equations of motion for pure bending are derived using the Hamilton’s principle and solved using the Differential Transform Method, DTM. During the derivation of the equations, effects of rotary inertia, shear deformation and h...

The present paper is concerned with the free vibration analysis of double-walled carbon nanotubes embedded in an elastic medium and based on Eringen's nonlocal elasticity theory. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The governing equations of motion which are coupled with each other via the van der Waals interla...

Associated with a skew-symmetric linear operator on the spatial domain [a, b] we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated with this Dirac structure is an infinite-dimensional system. We parameterize the boundary port variables for which the C0semigroup associate...

The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms...

In recent years, establishing more and more explicit, complete and accurate dynamic models for the special category of flexible link manipulators has been a formidable challenging and still open problem in robotics research. This chapter is devoted to a methodological presentation of the application of Timoshenko beam (TB) theory (TBT) concepts to the mathematical description of flexible link r...

We calculate the tensile and shear moduli of a series of boron nitride nanotubes and their piezoelectric response to applied loads. We compare in detail results from a simple molecular mechanics (MM) potential, the universal force field, with those from the atomistic finite element method (AFEM) using both Euler-Bernoulli and Timoshenko beam formulations. The MM energy minimisations are much mo...

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 ...