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Yayın An essential approach to the architecture of diatomic molecules: 1.Basic theory(Optical Soc Amer, 2004-11) Yarman, Nuh TolgaWe consider the quantum-mechanical description of a diatomic molecule of electronic mass m(0e), internuclear distance R-0, and total electronic energy E-0e. We apply to it the Born-Oppenheimer approximation, together with the relation E(0e)m(0e)R(0)(2) similar to h(2) (which we established previously), written for the electronic description (with fixed nuclei). Our approach yields an essential relationship for T-0,T- the classical vibration period, at the total electronic energy E-0e; i.e., T-0 = [4pi(2)/(rootn(1)n(2)h)] rootgM(0)m(e) R-0(2). Here, At,0 is the reduced mass of the nuclei; m(e) is the mass of the electron; g is a dimensionless and relativistically invariant coefficient. roughly around unity (this quantity is associated with the particular electronic structure under consideration; thus, it remains practically the same for bonds bearing similar electronic configurations); and n(1) and n(2) are the principal quantum numbers of electrons making up the bond(s) of the diatomic molecule in hand: because of quantum defects, they are not integer numbers. The above relationship holds generally, although the quantum numbers n(1) and n(2) need to be refined. This task is undertaken in our next article, yielding a whole new systematization regarding all diatomic molecules.Yayın A hollow cylinder problem in microstretch theory(Springer-Verlag, 2011) İnan, Esin; Kırış, AhmetA hollow cylinder micro-damaged tube under pressure problem is discussed. Micro damage is modeled with Eringen's microstretch theory and the displacement and its comparison with classical result are given.Yayın Free vibration of composite sandwich beams with microstretch viscoelastic core(Springer Science and Business Media Deutschland GmbH, 2021) Aydınlık, Soner; Kırış, Ahmet; İnan, EsinIn the present work, we studied a sandwich beam which is made of two thin stiff layers on top and bottom and a microstretch viscoelastic core in the middle. Here, the top and the bottom stiff layers are considered as elastic, while the inner part is taken as microstretch viscoelastic material. The free vibration of this composite beam is investigated. Differential transform method is used for the solution. The values of the frequencies obtained for microstretch case are found greater than the classical ones, as it is expected. Besides, the minimum differences between the classical frequencies and deviated classical frequencies due to the microstretch core are getting bigger for the large loss factors.
