Abstract
The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.
Highlights
In applied and structural mechanics, for dynamic calculations of cantilever structures, a number of well-proven methods are used, both analytical ones based on the use of Krylov functions, and numerical ones, such as the grid method, the finite element method, the finite differences method [1,2,3]
The use of the analytical method based on the use of Krylov functions [4] makes it possible to study the dynamic processes of cantilevers with decent accuracy
We will use the grid method to calculate the vibrations of the cantilever bar with a dynamic vibration damper (DVD)
Summary
In applied and structural mechanics, for dynamic calculations of cantilever structures, a number of well-proven methods are used, both analytical ones based on the use of Krylov functions, and numerical ones, such as the grid method, the finite element method, the finite differences method [1,2,3]. The use of the analytical method based on the use of Krylov functions [4] makes it possible to study the dynamic processes of cantilevers with decent accuracy. The finite element method is widely used for calculating complex objects under both static and dynamic loads. In our opinion, the finite difference method is easier to use, an attempt was made in the work to apply the finite difference method to simulate the dynamics of free and forced oscillations of the cantilever. The advantages of this method include its versatility, which is much higher than that of analytical methods
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.
