• Honam Mathematical Journal
• /
• v.46 no.4
• /
• pp.677-696
• /
• 2024

In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the 𝓓𝓖𝓒 Leonardo sequence coefficients, depending on the parameter p ∈ ℝ. This generalization gives dual quaternions with the dual-complex Leonardo sequence for 𝖕 = -1, dual quaternions with the hyper-dual Leonardo sequence for 𝖕 = 0, and dual quaternions with the dual-hyperbolic Leonardo sequence for 𝖕 = 1. The basic algebraic structures and some special characteristic relations are presented, as well as the Binet's formula, generating function, d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities.

• Structural Engineering and Mechanics
• /
• v.46 no.6
• /
• pp.869-886
• /
• 2013

This work presents an experimental methodology specially developed for the nonlinear large-amplitude free vibration analysis of a clamped-free thin-walled metal column under self-weight. The main contribution of this paper is related to the developed experimental methodology which is based on a remote sensing technique using a computer vision system that integrates, on-line, the digital image acquisition and its treatment through special image processing routines. The main importance of this methodology is that it performs large deflections measurements without making contact with the structure and thus, not introducing undesirable changes in its behavior, for instance, appreciable changes in mass and stiffness properties. This structure presents, in most cases, highly non-linear responses, which cannot be reproduced by conventional finite-element softwares due, mainly, to the simultaneous influence of geometric and inertial non-linearities. To capture the non-linearities associated with large amplitude vibration and be able to describe the buckling process, the structure is discretized as a sequence of jointed coupled elastic pendulums. The obtained numerical results are favorably compared with the experimental ones, in the pre- and post-buckling regimes.