Analysis of Large Membrane Vibrations Using Fractional Calculus
Year: 2025
Type: article
Abstract: The study of vibration equations of large membranes is crucial in various scientific and engineering fields. Analyzing the vibration equations of bridges, roofs, and spacecraft structures helps in designing structures that resist excessive oscillations and potential failures. Aircraft wings, parachutes, and satellite components often behave like large membranes. Understanding their vibration characteristics is essential for stability, efficiency, and durability. Studying large membrane vibration involves solving partial differential equations and eigenvalue problems, contributing to advancements in numerical methods and computational physics. In this paper, the Elzaki transformation decomposition method and the Shehu transformation decomposition method, along with inverse Elzaki and inverse Shehu transformations, are used to investigate the fractional vibration equation of a large membrane. The solutions are obtained in terms of Mittag–Leffler functions.
Source: Fractal and Fractional
Authors: Nihar Ranjan Mallick, Snehashish Chakraverty, Rajarama Mohan Jena
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W4409012155