We show that the Akiyama-Tanigawa algorithm and Chen’s variant for computing Bernoulli numbers can be generalized to Carlitz’s q-Bernoulli numbers. We also put these algorithms in the larger context of generalized Euler-Seidel matrices.

This paper presents a way of using He’s variational iteration method to solve free vibration problems for an Euler–Bernoulli beam under various supporting conditions. By employing this technique, the beam’s natural frequencies and mode shapes can be obtained and a rapidly convergent sequence is obtained during the solution. The results obtained are the same as the results obtained by the Adomia...

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...

Offshore wind turbines (OWTs) are dynamically loaded structures and therefore the estimation of the natural frequency is an important design calculation to avoid resonance and resonance related effects (such as fatigue). Monopiles are currently the most used foundation type and are also being considered in deeper waters (430 m) where a stiff transition piece will join the monopile and the taper...

In recent years, establishing more and more explicit, complete and accurate dynamic models for the special category of flexible link manipulators has been a formidable challenging and still open problem in robotics research. This chapter is devoted to a methodological presentation of the application of Timoshenko beam (TB) theory (TBT) concepts to the mathematical description of flexible link r...

In this paper, our aim is finding the term of generalized Euler polynomials. We also obtain some identities and relations involving the Bernoulli numbers, the Euler numbers and the Stirling numbers. AMS Mathematics Subject Classification : 11B68, 11S40, 11S80.

Abstract In this work, the Poincaré map numerical method was successfully developed to solve fourth-order differential equation that describes flexural vibrations of a beam, within Timoshenko beam theory. The Euler-Bernoulli continuity conditions were considered, which are valid for frequencies smaller than critical frequency. As an example, used design complex elastic structure, characterized ...