In this paper, the buckling and vibration behaviour of functionally graded flexoelectric nanobeam is examined. The vibration and buckling formulations of functionally graded nanobeam are developed by using a new theory that’s presented exclusively for flexoelecteric nano-materials. So by considering Von-Karman strain and forming enthalpy equation based on displacement, polarization and electric...

By the past two decades IPMCs have been intensively studied because of their special capabilities for actuation and sensing.This paper presents a theoretical physics based model for analyzing the behavior of IPMC sensors in fluid environments. The mechanical vibration of the IPMC strip is described by the classical Euler–Bernoulli beam theory. The model also takes in to account the physical pro...

In this paper, the free vibration behaviors and flexural sensitivity of atomic force microscope cantilevers with small-scale effects are investigated. To study the small-scale effects on natural frequencies and flexural sensitivity, the consistent couple stress theory is applied. In this theory, the couple stress is assumed skew-symmetric. Unlike the classical beam theory, the new model contain...

Let B n = b 1 +. .. + b n , n ≥ 1 where b 1 , b 2 ,. .. are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic order of the sums N n=1 d θ,D (B n), where d θ,D (B n) = #{d ∈ D, d ≤ n θ : d|B n } and D is a sequence of positive integers.

Railway structures are one of the most important structures in transportation. So the lack of precise study of their dynamic behavior leads to irreparable damages. The significant factors contributing to the accurate analysis of the dynamic behavior of railways are the type of load and foundation used in it. In this study, an Euler-Bernoulli beam subjected to a moving load on a finite depth fou...

In this paper, we give some further properties of p-adic q-L-function of two variables, which is recently constructed by Kim 2005 and Cenkci 2006 . One of the applications of these properties yields general classes of congruences for generalized q-Bernoulli polynomials, which are qextensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000 , Gunaratne 1995 , an...

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

The goal of this note is to present some new results on the application of AVI algorithms to the Simo-Marsden-Krishnaprasad beam model based on a description using rotation matrices. This follows our earlier work on the Euler-Bernoulli beam and thin-shell models with Kirchhoff-Love constraints and various boundary conditions. We consider the effect of large deflections, when the beam is subject...

Previous work showed that every pair of nontrivial Bernoulli shifts over a fixed free group are orbit equivalent. In this paper, we prove that if G 1 , G 2 are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over G 1 is stably orbit equivalent to every nontrivial Bernoulli shift over G 2. This answers a question of S. Popa.

The following result is proven. Let G 1 T 1 (X 1 , µ 1) and G 2 T 2 (X 2 , µ 2) be orbit-equivalent, essentially free, probability measure preserving actions of countable groups G 1 and G 2. Let H be any countable group. For i = 1, 2, let Γ i = G i * H be the free product. Then the actions of Γ 1 and Γ 2 coinduced from T 1 and T 2 are orbit-equivalent. As an application, it is shown that if Γ i...