In this paper, a comprehensive study is presented on the effect of beam's length, shear deformation and beam's theory on the dynamic modeling of single-link flexible manipulator. At the first step, Euler-Bernoulli beams theory (EBBT) is adopted. According to this model the effect of shear deformation is neglected. So, this model is only reliable for the case of slender beam. When the beam is sh...

In this paper, surface and piezoelectric effects on the vibration behavior of nanowires (NWs) are investigated by using a Timoshenko beam model. The electric field equations and the governing equations of motion for the piezoelectric NWs are derived with the consideration of surface effects. By the exact solution of the governing equations, an expression for the natural frequencies of NWs with ...

The main purpose of this paper is to derive various Matiyasevich-Miki-Gessel type convolution identities for Bernoulli and Genocchi polynomials and numbers by applying some Euler type identities with two parameters.

The Bernoulli polynomials Bk restricted to 0, 1 and extended by periodicity have nth sine and cosine Fourier coefficients of the formCk/n . In general, the Fourier coefficients of any polynomial restricted to 0, 1 are linear combinations of terms of the form 1/n . If we can make this linear combination explicit for a specific family of polynomials, then by uniqueness of Fourier series, we get a...

Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.

We establish two general identities for Bernoulli and Euler polynomials, which are of a new type and have many consequences. The most striking result in this paper is as follows: If n is a positive integer, r + s + t = n and x + y + z = 1, then we have r s t x y n + s t r y z n + t r s z x n = 0 where s t x y n := n k=0 (−1) k s k t n − k B n−k (x)B k (y). It is interesting to compare this with...

Explicit and recursive formulas for Bernoulli and Euler numbers are derived from the Faá di Bruno formula for the higher derivatives of a composite function. Along the way we prove a result about composite generating functions which can be systematically used to derive such identities.

have numerous important applications in number theory, combinatorics, and numerical analysis, among other areas, [1–13]. It is easy to find the values G1 = 1, G3 = G5 = G7 = ··· = 0, and even coefficients are given by G2m = 2(1− 2)B2n = 2nE2n−1(0), where Bn is a Bernoulli number and En(x) is an Euler polynomial. The first few Genocchi numbers for n= 2,4, . . . are −1,−3,17,−155,2073, . . . . Th...

Abstract We recall two formulas, due to C. Jordan, for the successive derivatives of functions with an exponential or logarithmic inner function. We apply them to get addition formulas for the Stirling numbers of the second kind and for the Stirling numbers of the first kind. Then we show how one can obtain, in a simple way, explicit formulas for the generalized Euler polynomials, generalized E...

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...