Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
A Modal Reduction Scheme for the Free Vibration of Strings with Inertially Loaded Boundary
Submission Author:
Pedro Menescal Jales , RN
Co-Authors:
Pedro Menescal Jales, Rubens Gonçalves Salsa Junior, Vinícius Lamas von Sohsten
Presenter: Vinícius Lamas von Sohsten
doi://10.26678/ABCM.COBEM2023.COB2023-0457
Abstract
In structural engineering, simulations often require the solution of differential equations that may result in significant computational costs. To reduce these costs while maintaining acceptable levels of accuracy, modal reduction techniques are frequently employed. These techniques involve the exclusion of higher-order modes that typically have a negligible impact on a system's response. In this light, the objective of this work is to report a modal reduction scheme for the free vibration of a string with fixed-inertially loaded boundaries in structural engineering. The proposed scheme reduces computational costs by neglecting modes that have less impact on the system's response. In the methodology presented herein, modal participation factors are estimated by analyzing the energy distribution among modal coordinates, and errors between the approximated and analytical responses are assessed using a signal-to-noise ratio. Modes that embrace the most energetical values are selected to measure the approximate general solution. These factors are combined and their influence on the error is considered, mode-by-mode, until it reaches acceptable values. Thus, a satisfactory approximation of the string behavior could be provided. The nature of the boundary conditions is used to derive modes that satisfy modified orthogonality relationships. Then, modal expansion is used to uncouple the partial differential equation of motion into modal equations, consisting of independent ordinary differential equations that could be solved for the modal coordinates. To demonstrate the effectiveness of the proposed scheme, three examples are provided. The first example validates the methodology by exciting only one mode of the string. The second example involves releasing a linearly stretched string, while the third example concerns the release of a string plucked at its midpoint. The modal reduction scheme presented in this study offers an effective approach to reducing computational costs while maintaining accuracy in simulating the free vibration of a string with fixed-inertially loaded boundaries.
Keywords
modal reduction, modal analysis, strings, orthogonality, modal participation
