Abstract

This article aims to obtain the dynamic elastic analysis of a steel tube tower for horizontal axis wind turbine using finite elements of bar (own code) and finite elements of bark and solids (modeling in ANSYS). For this, a theoretical foundation is presented that consists in the development of the movement equation from the Lagrange equation. Next, the modal overlay method is presented for solving the matrix motion equation and for obtaining the dynamic response of the tower. In the second part of this article, the development is presented for the assembly of the mass and damping matrices of the tower modeled with its own code in finite elements of the bar. In the part of results, initially, the rigidity, mass and damping matrices are exposed for a certain level of discretization of the modeled tower with finite elements of bar. Then, the results of the modal analysis were done for both the finite element shell model, with and without flexible base, and the finite element model of the bar, in which the modes and the frequencies of vibration of the tower in all the models are presented. Finally, the responses of the tower were analyzed: in the direction of the wind flow, when submitted by a vector of resonant forces to its 1st mode of vibration, representing the floating part of the wind; and, in the transverse direction to the wind flow due to the von Kárman cadenced vortex detachment. The results of the modal analysis made for both the finite element shell model, with and without flexible base, and the finite element model of the bar are similar, especially in the first mode of vibration of the tower. Therefore, the model represented by finite elements (FE) of bar can be used as representative of the dynamic behavior of the tower when it is subjected to the resonant excitations at its fundamental frequency.

Abstract

A new alternative is presented for the estimation of modal mass, in order to scale the vibration modes obtained from operational modal analysis tests, using optimization techniques, in the frequency-independent proportional damping situation (structural or hysteretic), achieving optimal results even with the presence of a high level of noise in the signal.

After a brief exposition of the theoretical foundations, and the limitations in the current state of the art, the determination of modal parameters is analyzed in a coupled dynamic system, using optimization techniques.

To illustrate the procedure, two examples of application are presented: first, for the case of an elementary beam model of small dimensions; and then, to confirm the capacity of the proposed method to be applied to real civil structures, said capacity is illustrated by a numerical simulation, on a very slender bridge currently in service, and with a very complex internal geometry of its main beam.

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This paper shows a revision of the text Structural Dynamics Applied to the Seismic Design of Professor Luis Enrique García Reyes, from the Universidad de los Andes, Bogotá, Colombia, in which the most relevant appraisals of its content are collected. Although it has been published in 1998, the subject matter is still valid, and due to the form and sequence in which the contents are presented, it is easy for an undergraduate student in engineering to understand in most of its chapters, being used as text book in the subject Dynamics of Structures of the Universidad Politécnica Salesiana del Ecuador.

Abstract

The investigation of modeling the time evolution of a folding wing during the morphing process and the dynamic characteristics analysis is carried out. The governing equations with uniform form are developed from the integration of floating frame method in multi-body dynamics and component mode synthesis in structural dynamics. The time-dependent aerodynamic force is taken into the governing equations. The equation achieves the time-dependent coupling between structure and aerodynamics and avoids the data transmission and low efficiency, which holds true for the multi-segmented folding wing. The relative parameters in constraint equations are easily modified to be applied to both slow and fast-varying processes for a folding wing. Also, the influence of the velocity and attack angle on transient responses can be investigated. Transient response analysis shows that slower morphing means more stable transient responses. The flexibility of the folding wing has the significant influence on transient responses. To some extent, the aerodynamic force can be beneficial to the morphing process.

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