Size-dependent internal resonances and modal interactions in nonlinear dynamics of microcantilevers

Ghayesh, Mergen and Farokhi, Hamed (2018) Size-dependent internal resonances and modal interactions in nonlinear dynamics of microcantilevers. International Journal of Mechanics and Materials in Design, 14 (1). pp. 127-140. ISSN 1569-1713

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Abstract

The size-dependent internal energy transfer in the nonlinear dynamical behaviour of a microcantilever with an intermediate spring-support is investigated. A geometric size-dependent nonlinearity due to large changes in the curvature is taken into account in the longitudinal and transverse motions. Based on the modified couple stress theory, the potential energy of the system is developed; the kinetic energy is also constructed in term of the displacement field. The energy terms are balanced with the potential energy stored in the intermediate spring-support. The centreline-inextensibility assumption is applied leading to the continuous model of the system involving nonlinear inertial components as well as size-dependent nonlinear curvature components. Based on a weighted-residual technique, the continuous model is reduced and the resultant truncated model is solved via use of a continuation technique. The linear component of the truncated model is solved through an eigenvalue extraction method in order to verify the occurrence of internal energy transfer and modal interaction mechanisms. For the system tuned to internal resonances, the highly nonlinear dynamical response is obtained, taking into account both inertial and geometric (due to large rotations) nonlinearities. It is shown that taking into account the length-scale parameter changes the internal energy transfer mechanisms significantly.

Item Type:	Article
Uncontrolled Keywords:	Microbeam, Internal resonance, Nonlinear dynamics, Modal interactions
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Becky Skoyles
Date Deposited:	08 Aug 2018 09:51
Last Modified:	11 Oct 2019 19:45
URI:	http://nrl.northumbria.ac.uk/id/eprint/35218

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