In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper...

In this paper, a size-dependent formulation for the Bernoulli-Euler beam is developed based on a new model of couple stress theory presented by Hadjesfandiari and Dargush. The constitutive equation obtained in this new model, consists of only one length scale parameter that is capable of capturing the micro-structural size effect in predicting the mechanical behavior of the structure. Having on...

We present a computer algebra approach to proving identities on Bernoulli and Euler polynomials by using the extended Zeilberger’s algorithm given by Chen, Hou and Mu. The key idea is to use the contour integral definitions of the Bernoulli and Euler numbers to establish recurrence relations on the integrands. Such recurrence relations have certain parameter free properties which lead to the re...

Abstract A novel formulation of the weak form quadrature element method, referred to as locally adaptive is proposed develop elements for nonlinear graded strain gradient Timoshenko and Euler–Bernoulli nanobeams. The equations motion are obtained based on Hamilton principle while accounting position physical neutral axis. use Gauss points ensure full integration variational statement. develops ...

This article investigates the theoretical and numerical analysis as well applications of three-dimensional theory first strain gradient elasticity. The corresponding continuous discrete variational formulations are established with error estimates stemming from continuity coercivity within a Sobolev space framework. An implementation isogeometric Ritz–Galerkin method is provided open-source sof...

A review of contributions and views on the second spectrum of Timoshenko beam theory (TBT) over the past two decades, together with some new results, are presented. It is shown that the Timoshenko frequency equation factorises not solely for hinged–hinged end conditions, as is often claimed, but also for guided–guided and guided–hinged; these new cases may be regarded as portions of a multi-spa...

The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the correspondig solution of the Bernoulli-Euler beam.The problem of convergence is related to a Singular Perturbation Problem. The main tool in solving this problem is a weak version of a lower bound for hyperbolic polynomials.

We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known ...