In this paper, the general governing equations of three-dimensional vibrations of an Euler-Bernoulli Beam under influences of system dynamics are derived by the Hamiltonian method. Then two fundamental cases of a cantilever beam and a rotating beam are considered. The conventional methods for vibration suppression debit to expenses and make new problems such as control spillover because they ar...

This paper features the modeling and design of a Fast Output Sampling (FOS) Feedback control technique for the Active Vibration Control (AVC) of a smart flexible aluminium cantilever beam for a Single Input Single Output (SISO) case. Controllers are designed for the beam by bonding patches of piezoelectric layer as sensor / actuator to the master structure at different locations along the lengt...

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

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 ...

A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of problems in non-differentiable fractals into corresponding continuum applying calculus (FdH3-CC) carried out. derived as a generalization using FdH3-CC under analogous assumptions ordinary and then it solved analytically. To validate spatial distribution self-similar response, three different classi...