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...

Abstract In this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory further development and extension space-fractional (non-local) Euler–Bernoulli model (s-FEBB) to Timoshenko (s-FTB) one by proper taking into account shear deformation. Furthermore, detailed parametric study on influence le...

The elastic foundation beam theory has been widely used in civil engineering, including railway, tunnel, and building foundations. With the development of fabricated structures, more beams need to be prestressed. In order explore frame with anchor-cable slope reinforcement project, this article, prestress is applied both ends beam. Then, according calculation method internal force deformation u...

This paper deals with stability of solution for a one-dimensional model Rao?Nakra sandwich beam Kelvin?Voigt damping and time delay given by ??1?1?????? ? ??(??? + ?? ??????) ?????????? ??????????( , ??) = 0, ??3?3?????? ????????? ?????????????? ????(??? ??????)?? 0. A is an engineering that consists three layers: two stiff outer layers, bottom top faces, more compliant inner layer called ?core...

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...

Mechanical foundations and pavements design need a perfect prediction of the response of the material to reach a reliable and safe structure. This work deals with the thermoelastic response of microbeams rested on a two-parameter viscoelastic foundation due to a magnetic field in the context of the dual - phase lag thermoelasticity model. The solutions of the governing equations are attained us...

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This paper presents the elastic buckling of homogeneous beams with a pair of piezoelectric layers surface bonded on both sides of the beams. The displacement field of beam is assumed based on the Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of applied voltage, dimensionless geometrical parameter and piezoelectric thi...

A Timoshenko beam theory for layered orthotropic beams is presented. The theory consists of a novel combination of three key components: average displacement and rotation variables that provide the kinematic description of the beam, stress and strain moments used to represent the average stress and strain state in the beam, and the use of exact axially-invariant plane stress solutions to calibr...

In this study, free vibration analysis of carbon nanotubes is investigated based on Timoshenko beam theory. Discrete singular convolution (DSC) method is used for free vibration problem of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in the literature. It is shown that reasonable accurate results are obtained. Keywords-Carbon Nanotubes...