An accurate approximate analysis of the large-amplitude asymmetric vibrations of a dielectric elastomer balloon

• Published in: Advances in mechanical engineering Vol. 17; no. 1
• Main Authors: Big-Alabo, Akuro, Abah, Chukwuebuka Francis, Briggs, Tobinson Alaso
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2025; Sage Publications Ltd; SAGE Publishing
• Subjects: Amplitudes; Asymmetry; Balloons; Design parameters; Elastomers; Electric potential; Internal pressure; Kinetic energy; Nonlinearity; Parametric analysis; Vibration; Vibration analysis; Voltage; large-amplitude vibration; Dielectric elastomer balloon; strong nonlinearity; continuous piecewise linearization method; asymmetric vibration; stability analysis
• ISSN: 1687-8132; 1687-8140
• DOI: 10.1177/16878132251314325

The vibration model of the neo-Hookean DEB has a negative index nonlinearity which poses a solution problem for perturbative methods and most non-perturbative methods. In this paper, an accurate solution of the large-amplitude asymmetric vibrations of a dielectric elastomer balloon (DEB) made up of neo-Hookean material was derived using the continuous piecewise linearization method (CPLM), which was shown to handle the negative index nonlinearity smoothly. The accuracy of the CPLM was verified using published analytical results which showed that the CPLM was significantly more accurate than the published analytical results. The CPLM solution was used to conduct parametric analysis of the large-amplitude vibration of the DEB. The results revealed that increasing either of the applied voltage or static internal pressure results to lesser stiffness response, lower frequency of vibration, lower maximum kinetic energy and shorter range of initial stretch values for stable vibrations. Hence, the applied voltage and static internal pressure can be used as design parameters for neo-Hookean DEBs capable of stable large-amplitude vibrations.