This paper proposes a numerical methodology for the prediction of the first three modes of vibration of an electric motor fixed on a rigid base. A deep literature review supported the production of four ad hoc prototy...This paper proposes a numerical methodology for the prediction of the first three modes of vibration of an electric motor fixed on a rigid base. A deep literature review supported the production of four ad hoc prototypes that aided the development of the proposed approach. Tests carried out with the prototypes led to the procurement of the modal parameters be used to calibrate the numerical models, as well as the FRF （frequency response function） curves be used to validate the numerical solution. The validated model allowed structural changes to be then promoted on the prototypes, in order to make them more robust to variations in manufacturing and assembling processes. The mentioned adjustments and structural changes were accomplished by means of a process of structural optimization using Genetic Algorithm. The solution was developed based on the commercial finite element code ANSYS. The practical results obtained in this study show that a numerical model for modal analysis of an electric motor fixed on a rigid base with errors less than 3% for the first three modes of vibration can be achieved, allowing positive structural changes to be performed in the machine design that result in the minimization of manufacturing reworks associated with the dynamic behavior of the studied motor.展开更多
A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potent...A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.展开更多
Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a loca...Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a local Musielak-Orlicz Hardy space h￠（Nn） by the local grand maximal function, and a local BMO-type space bmo￠（Nn） which is further proved to be the dual space of h￠（Nn）. As an application, the authors prove that the class of pointwise multipliers for the local BMO-type space bmo￠（Nn）, characterized by Nakai and Yabuta, is just the dual of LI（Rn） ＋ hФ0 （Rn）, where Ф is an increasing function on （0, co） satisfying some additional growth conditions and Ф0 a Musielak-Orlicz function induced by Ф. Characterizations of h￠（Rn）, including the atoms, the local vertical and the local nontangential maximal functions, are presented. Using the atomic char- acterization, the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of h￠（Rn）, from which, the authors further deduce some criterions for the boundedness on h￠（Rn） of some sublinear operators. Finally, the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on h￠（Rn）.展开更多
文摘This paper proposes a numerical methodology for the prediction of the first three modes of vibration of an electric motor fixed on a rigid base. A deep literature review supported the production of four ad hoc prototypes that aided the development of the proposed approach. Tests carried out with the prototypes led to the procurement of the modal parameters be used to calibrate the numerical models, as well as the FRF （frequency response function） curves be used to validate the numerical solution. The validated model allowed structural changes to be then promoted on the prototypes, in order to make them more robust to variations in manufacturing and assembling processes. The mentioned adjustments and structural changes were accomplished by means of a process of structural optimization using Genetic Algorithm. The solution was developed based on the commercial finite element code ANSYS. The practical results obtained in this study show that a numerical model for modal analysis of an electric motor fixed on a rigid base with errors less than 3% for the first three modes of vibration can be achieved, allowing positive structural changes to be performed in the machine design that result in the minimization of manufacturing reworks associated with the dynamic behavior of the studied motor.
文摘A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.
基金supported by National Natural Science Foundation of China(Grant No.11171027)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a local Musielak-Orlicz Hardy space h￠（Nn） by the local grand maximal function, and a local BMO-type space bmo￠（Nn） which is further proved to be the dual space of h￠（Nn）. As an application, the authors prove that the class of pointwise multipliers for the local BMO-type space bmo￠（Nn）, characterized by Nakai and Yabuta, is just the dual of LI（Rn） ＋ hФ0 （Rn）, where Ф is an increasing function on （0, co） satisfying some additional growth conditions and Ф0 a Musielak-Orlicz function induced by Ф. Characterizations of h￠（Rn）, including the atoms, the local vertical and the local nontangential maximal functions, are presented. Using the atomic char- acterization, the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of h￠（Rn）, from which, the authors further deduce some criterions for the boundedness on h￠（Rn） of some sublinear operators. Finally, the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on h￠（Rn）.
