We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment when one of these points comes back to the original region. We describe the statistical distribution of these “first–return” times in various settings: when ph...

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 ...

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obt...

In this paper we study intermittency for the parabolic Anderson equation ∂u/∂t = κ∆u + γξu with u : Z d × [0, ∞) → R, where κ ∈ [0, ∞) is the diffusion constant, ∆ is the discrete Laplacian, γ ∈ (0, ∞) is the coupling constant, and ξ : Z d × [0, ∞) → R is a space-time random medium. The solution of this equation describes the evolution of a " reactant " u under the influence of a " catalyst " ξ...

We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation of the beam the fluid domain depends on time. We prove that this system is exponentially stabilizable, locally about the null solution, with an...

A smart structure cantilever beam is a distributed parameter system that employs sensors and actuators at different finite element locations on the beam and makes use of controllers that respond to inputs obtained from the sensors. The paper uses the mathematical modeling of the smart structure using finite element method and Euler Bernoulli beam assumptions. A state space model of the beam as ...

This paper deals with the active vibration control of beam like structures with distributed piezoelechic sensor and actuator layers bonded on top and bottom surfaces of the beam. A finite element model based on Euler-Bernoulli beam theory has been developed. The contribution of the piezoelectric sensor and actuator layers on the mass and stiffness of the beam is colisidered. Three types of clas...

This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) Tf @-l,rD :m Ø m , generated by a bipermutative local rule f Ix-l, ... , xrM  ⁄i-l r ai xi Hmod mL (m ¥ 2 and l, r œ +), with respect to the Bernoulli measure mp on m  defined by a probability vector p  Ip0, p1, ... , pm-1M. We prove that the measure entropy of the one-dimensional LCA Tf @-l,rD wi...