Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
SPRINGS WITH PROPORTIONAL STIFFNESS TO THE APPLIED FORCE
Submission Author:
Alexandre de Macêdo Wahrhaftig , BA , Brazil
Co-Authors:
Julia Good Lima Dantas, Cibele Mota Menezes, Vanessa Cruz Pacheco, Alexandre de Macêdo Wahrhaftig
Presenter: Julia Good Lima Dantas
doi://10.26678/ABCM.COBEM2021.COB2021-0024
Abstract
The studies on springs gained notoriety after the publication of “Lectures of Potentia Restitutive, or Spring Explaining the Power of Spring” by the English physicist Robert Hooke, in 1678, which deals with the fundamentals of the elasticity of materials, providing an important basis for understanding the body´s strain as a function of the stress at which they are subjected. Following Hooke's work, solids came to be understood as deformable bodies, similar to springs, which elongation or shortening could be predicted based on the law established by him, that of the proportionality between the applied force and the response of the spring (or the solid) in terms of the presented displacement. To establish the cause-and-effect relationship a proportionality constant called stiffness or spring coefficient was foreseen. In this work, however, the concept that defines a spring stiffness is established no longer as a function of the induced displacement but through the applied force on the system, an assumption that can be, adequately evaluated through the theory of vibration of the mechanical systems. In this regard, a model consisting of a simply supported beam submitted to a normal force that tends to reduce its frequencies is used to verify the assumed hypothesis. Connected to the system, there is a translational spring positioned according to its longitudinal direction, which stiffness is allowed to vary with the intensity of the applied force. The spring, or analogous device, therefore, acts in order to keep the natural frequency of the beam unmodified. The model was computationally elaborated by the finite element method. The results obtained prove the constancy of the natural frequency of the beam, even when the system is under the action of a force that tends to reduce its structural stiffness and, consequently, to change the frequency of vibration of the system.
Keywords
variable stiffness, spring, Vibration, Frequency, finite elements method
