We prove that a Z d-action by automorphisms of a compact, abelian group is Bernoulli if and only if it has completely positive entropy. The key ingredients of the proof are the extension of certain notions of asymptotic block independence from Z-actionsto Z d-action and their equivalence with Bernoullicity, and a surprisingly close link between one of these asymptotic block independence propert...

The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct for any sample size.

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler– Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler–Bernoulli beam theory. The Ritz–Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlin...

the vibration of cable-stayed bridges subjected to the passage of high-speed trains is studied in this article. the moving train includes a number of wagons, each of which is modeled as a four-axle system possessing 48 degrees of freedom. the car model is nonlinear and three-dimensional and includes nonlinear springs and dampers of primary and secondary suspensions, dry friction between differe...

the complete 3d nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. for describing the dynamics of the system, the newtonian derivation procedure is followed. the velocity field inside the pipe formulated using hydrostatic and bernoulli equations. the hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...

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...

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...

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 ...