A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.

in this paper effects of fractured sleepers on rail track vibration under moving wheelset have been investigated. two parallel rails of the track have been modeled as euler-bernoulli beams on elastic points as rail pads. also sleepers have been modeled as visco-elastic euler-bernoulli beams. it is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. the...

The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol-Bernoulli...

Recently, λ-Bernoulli and λ-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the q-extensions of the λBernoulli and the λ-Euler numbers by using the bosonic p-adic q-integral and the fermionic p-adic q-integral. The investigation of these λ-q-Bernoulli and λ-q-Euler numbers leads to interesting identities related to these objec...

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The wheel-rail-sleepers system is simulated as a series of moving point loads on an Euler–Bernoulli beam resting on a visco-elastic half space. This paper concentrates on the railsleepers interaction system (railway system) and the fault detection. The main objective is to mathematically develop and implement a dynamic model of a railway system then the diagnosis of system defects using a Luenb...

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...

This paper analyzes the effects of structures and loads on the static bending and free vibration problems of bilayer beams. Based on static mechanical equilibrium and energy equilibrium, the static and dynamic governing equations of bilayer beam are established. It is found that the value of the thickness ratio has a significant effect on the static and dynamic responses of the beam, and the st...

Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...