Solving imprecisely defined vibration equation of large membranes
Abstract
Purpose
Vibration of large membranes has great utility in engineering application such as in important parts of drums, pumps, microphones, telephones and other devices. So, to obtain a numerical solution of this type of problems is necessary and important. In general, in existing approaches, involved parameters and variables are defined exactly. Whereas in actual practice, it may contain uncertainty owing to error in observations, maintenance-induced error, etc. So, the main purpose of this paper is to solve this important problem numerically under fuzzy and interval uncertainty to have an uncertain solution and to study its behaviour.
Design/methodology/approach
In this study, the authors have considered a new approach is known as double parametric form of fuzzy number to model uncertain parameters. Along with this a semianalytical approach, i.e. variational iteration method, has been used to obtain uncertain bounds of the solution.
Findings
The variational iteration method has been successfully implemented along with the double parametric form of fuzzy number to find the uncertain solution of the vibration equation of a large membrane. The advantage of this approach is that the solution can be written in a power series or a compact form. Also, this method converges rapidly to obtain an accurate solution. Various cases depending on the functional value involved in the initial conditions have been studied and the behaviour has been analysed. Applying the double parametric form reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.
Originality/value
The vibration equation of large membranes has been solved under fuzzy and interval uncertainty. Uncertainties have been considered in the initial conditions. New approaches, i.e. variational iteration method along with the double parametric form, have been applied to solve the vibration equation of large membranes.
Keywords
Acknowledgements
The first author would like to acknowledge the Grant No. 106112016CDJCR291209 sponsored by the Chongqing University, China, under the scheme of special fundamental research projects for the central universities. Also, the third author thanks the China Postdoctoral Science Foundation, Government of P. R. China for funding under the Project No: 2016M592648.
Citation
Tapaswini, S., Mu, C., Behera, D. and Chakraverty, S. (2017), "Solving imprecisely defined vibration equation of large membranes", Engineering Computations, Vol. 34 No. 8, pp. 2528-2546. https://doi.org/10.1108/EC-04-2017-0118
Publisher
:Emerald Publishing Limited
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