In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control nonaffine equations. The basic model of the system will be a Timoshenko beam supported at the ends by magnetic frictionless bearings. The effectiv...

This paper deals with the design of a periodic output feedback controller for a flexible beam structure modeled with Timoshenko beam theory, Finite Element Method, State space methods and embedded piezoelectrics concept. The first 3 modes are considered in modeling the beam. The main objective of this work is to control the vibrations of the beam when subjected to an external force. Shear piezo...

In this paper we consider the following Timoshenko system φtt − (φx + ψ)x = 0, (0, 1)× (0,+∞) ψtt−ψxx + ∫ t 0 g(t−τ)(a(x)ψx(τ))xdτ +φx +ψ+b(x)h(ψt) = 0, (0, 1)×(0,∞) with Dirichlet boundary conditions where a, b, g, and h are specific functions. We establish an exponential and polynomial decay results. This result improves and generalizes some existing results in the literature.

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...

This paper communicates an analytical study on computing the natural frequencies and in-plane deflections caused by static forces in panel walls using Euler-Bernoulli, Timoshenko, Timoshenko Goodier, Couple-stress, Micropolar-Cosserat theory. The highlights formulation of transfer matrix via state-space method spatial domain; from coupled governing equations motion that arises theory captures n...

In this study, using the non-local elasticity theory, the buckling and vibration analysis of triple- walled ZnO piezoelectric Timoshenko beam on elastic Pasternak foundation is analytically investigated under magneto-electro-thermo-mechanical loadings. Using the Timoshenko beam free body diagram, the equilibrium equation of Timoshenko nano-beam model is obtained and solved by Navier’s method fo...

We consider an elastic model for a curved rod with arbitrary threedimensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear an...