Abstract
In this work, planar free vibrations of a single physical pendulum are investigated both experimentally and numerically. The laboratory experiments are performed with pendula of different lengths, for a wide range of initial configurations, beyond the small angle regime. In order to approximate the air resistance, three models of damping are considered—involving the three components of the resistive force: linear (proportional to velocity), quadratic (velocity-squared) and acceleration-dependent (proportional to acceleration). A series of numerical experiments is discussed, in which the damping coefficients are estimated by means of several computational methods. Based on the observed efficiency, a gradient method for optimization is treated as the main tool for determination of a single set of damping parameters, independent of the system’s initial position. In the model of resistive force, the term proportional to acceleration, associated with the empirical Morison equation, seems to be indispensable for the successful approximation of the real pendulum motion.
Highlights
The proper selection of a damping model and estimation of damping parameters is an essential problem in the area of dynamic simulation and analysis of real mechanical systems
The laboratory experiments are performed with pendula of different lengths, for a wide range of the initial swing angle—without the assumption of small oscillations
Results obtained for L 1⁄4 100 mm, k 1⁄4 3 and the linear damping. (Color figure online) coefficients a1 and a2, the optimization problem has been solved by means of two methods: the successive search in combination with the intersection technique, and the gradient method
Summary
The proper selection of a damping model and estimation of damping parameters is an essential problem in the area of dynamic simulation and analysis of real mechanical systems. The basic models, especially the viscous damping or—a kind of its extension—the proportional damping, can serve as an equivalent or ‘‘resultant’’ representation of the internal, and structural and external damping [2, 3, 7, 27] Such an approach with the limited interest in the actual damping sources and mechanisms can be mainly justified by the fact that the amount of energy dissipated within numerous real systems is very small (heavy machines and structures, conventional materials etc.).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
