In the present work, the mathematical model of a homogeneous, isotropic thermoelastic double porous micro-beam, based on the Euler-Bernoulli theory is developed in the context of Lord-Shulman [1] theory of thermoelasticity. Laplace transform technique has been used to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field and temperature distribut...

This paper features the proposed modeling and design of a Robust Decentralized Periodic Output Feedback (RDPOF) control technique for the active vibration control of smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the E...

K e y w o r d s B e r n o u l l i polynomials, Euler polynomials, Generating functions, Bernoulli numbers, Euler numbers, Addition theorem, Multiplication theorem~ Generalized Bernoulli polynomials and numbers, Generalized Euler polynomials and numbers. 1. I N T R O D U C T I O N T h e classical Bernoulli polynomials Bn(x) and the classical Euler polynomials En(x) are usual ly def ined by m e a...

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

We consider explicit expansions of some elementary and q-functions in basic Fourier series introduced recently by Bustoz and Suslov. Natural q-extensions of the Bernoulli and Euler polynomials, numbers, and the Riemann zeta function are discussed as a by-product. © 2002 Elsevier Science (USA)

This paper features the modeling and design of a Robust Decentralized Fast Output Sampling (RDFOS) Feedback control technique for the active vibration control of a smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Eul...

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

Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki’s and Matiyasevich’s identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun.

Let p be a fixed odd prime. Throughout this paper, Zp,Qp,Cp will, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp. The p-adic absolute value | |p on Cp is normalized so that |p|p 1/p. Let Z>0 be the set of natural numbers and Z≥0 Z>0 ∪ {0}. As is well known, the Bernoulli polynomials Bn x are defined by the ge...