composites provide design flexibility because many of them can be moulded into complex shapes.  carbon fibre-reinforced epoxy composites exhibit excellent fatigue tolerance with high specific strength and stiffness. these properties led to their numerous advanced applications ranging from military and civil aircraft structures to consumer products. the modelling of beams undergoing arbitrarily ...

The goal of this note is to present some new results on the application of AVI algorithms to the Simo-Marsden-Krishnaprasad beam model based on a description using rotation matrices. This follows our earlier work on the Euler-Bernoulli beam and thin-shell models with Kirchhoff-Love constraints and various boundary conditions. We consider the effect of large deflections, when the beam is subject...

The axially translating flexible link in flexible manipulators with a prismatic joint can be modeled using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, we present a nondimensional form of the Euler-Bernoulli beam equation using the concept of g...

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical so...

A system of serially connected string and Euler-Bernoulli beam with coupled linear feedback control and sliding model control is studied in the present paper. The system is formulated by partial differential equations with the boundary conditions. The eigenvalues and eigenfunctions of the system operator are discussed in the appropriate Hilbert spaces. A sliding model control is applied to the ...

In this paper, we consider parameter estimation techniques for detecting changes of a nonlinear nature in an Euler-Bernoulli beam model. The nonlinear stiiness used provides a very simple model of damage, and the adaptive estimation algorithm is used to track the onset of the nonlinearity. Using Lyapunov redesign methods, extended and applied to innnite dimensional systems, a stable learning sc...

For linear partial differential equations, there exist well-developed classical methods of their analytical solution, which, in particular, includes the separation of variables, different integral transforms, Fourier series and their generalizations. At the same time, the study of symmetry properties of such equations is important, first of all, for the development of methods of symmetry analys...

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...