Abstract The principles of the energy variation method are commonly utilized in mechanics. Energy is a scalar variable, so these more convenient and simple to establish equilibrium equations compared vector-based approaches (i.e. using forces displacements). present article applied theorem order set for various complicated problems. Four examples applying include differential equation Euler – B...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...

We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known new numbers.

The formulation of a bending vibration problem of an elastically restrained Bernoulli–Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli–Euler beam. This hybrid strat...

In the present analysis, an infinite Euler– Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using one parameter without damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solu...

Keywords: Trigonometric functions Hurwitz zeta function Legendre chi function Lerch zeta function Bernoulli polynomials Euler polynomials a b s t r a c t In this sequel to our recent note [D. Cvijović, Values of the derivatives of the cotangent at rational multiples of π, Appl. Math. Lett. it is shown, in a unified manner, by making use of some basic properties of certain special functions, suc...

We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

@ARTICLE{HeniklAT2012, author={J. Henikl and J. Schr\"ock and T. Meurer and A. Kugi}, title={{Infinit-dimensionaler Reglerentwurf f\"ur Euler-Bernoulli Balken mit Macro-Fibre Composite Aktoren}}, journal={at -Automatisierungstechnik}, year={2012}, volume={60}, number={1}, pages={10--19}, doi = {10.1524/auto.2012.0967}, url = {http://www.degruyter.com/view/j/auto.2012.60.issue-1/auto.2012.0967/a...