In this paper we study the dynamic behavior of an isotropic KirchhoffLove beam and investigate the equilibrium position of an Euler-Bernoulli beam. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, we simulate the behavior by means of variational integrators and, in particular, AVIs (Asynchronous Variational Integrators). We place special emphasis on the geometric structure ...

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...

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...

The problem of computing the exact value of ∑ 1/n is so classical (dating back to 1644) that it even has a name of its own: the Basel problem. The city of Basel was the hometown both of the famous brothers Jakob and Johann Bernoulli, who made serious but unsuccessful attempts to solve the problem, and to the prodigious mathematician Leonhard Euler, who found the first solution in 1735, see [3]....

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 Euler-Bernoulli uniform elastically supported beam model with incorporated dissipation mechanisms is dealt with. Conditions are given to ensure oscillatory character of solutions.

Abstract In this work, we study the vibration control of a flexible mechanical system. The dynamic problem is modeled as viscoelastic nonlinear Euler–Bernoulli beam. To suppress undesirable transversal vibrations beam, adopt at right boundary This law simple to implement. We prove uniform stability system using material, multiplier method and some ideas introduced in [20]. It shown that large r...