We consider the Cauchy problem for the Euler-Bernoulli equation of the vibrating beam and solve it in Gevrey classes under appropriate Levi conditions on the lower order terms.

The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

This paper features the proposed modeling and design of a Robust Decentralized Periodic Output Feedback (RDPOF) control technique for the active vibration control of smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the E...

We study the stability of an interconnected system of Euler−Bernoulli beam and heat equation with boundary coupling, where the boundary temperature of the heat equation is fed as the boundary moment of the Euler−Bernoulli beam and, in turn, the boundary angular velocity of the Euler−Bernoulli beam is fed into the boundary heat flux of the heat equation. We show that the spectrum of the closed-l...

This paper features the modeling and design of a Robust Decentralized Fast Output Sampling (RDFOS) Feedback control technique for the active vibration control of a smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Eul...

In this article we prove some relations between two-variable q-Bernoulli polynomials and two-variable q-Euler polynomials. By using the equality eq (z)Eq (−z) = 1, we give an identity for the two-variable qGenocchi polynomials. Also, we obtain an identity for the two-variable q-Bernoulli polynomials. Furthermore, we prove two theorems which are analogues of the q-extension Srivastava-Pinter add...

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

In this paper we study the reliability of calculations of the structural reliability. It compares the exact reliability expression within the Bernoulli-Euler column theory with its counterpart obtained via the finite difference expression in the buckling context.

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.