On three-dimensional dynamics of fibre-reinforced functionally graded plates when fibres resist bending

Aydogdu, Metin; Aksencer, Tolga; Soldatos, Kostas P

Abstract

This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In this context, it (i) formulates the general dynamical problem of a rectangular plate with embedded a single family of straight fibres that possess bending resistance and are distributed in a controlled, functionally graded manner through the plate thickness, and (ii) for simple support boundary conditions, it solves the free relevant vibration problem. The problem formulation is based on principles of polar linear elastic and leads to a high-order set of Navier-type partial differential equations with variable coefficients. For simply supported edge boundaries, solution of these equations is achieved with use of a computationally efficient semi-analytical (so-called fictitious layer) mathematical method. Two types of possible inhomogeneous distributions of straight fibres are considered for computational and numerical result presentation purposes. These are both regarded as possible, realistic types of inhomogeneous redistributions of stiff fibres that in previous studies have been assumed homogeneously distributed throughout the plate body. The presented numerical results examine to a considerable extent the manner that either of the employed types of inhomogeneous fibre redistribution, in conjunction with the fibre ability to resist bending, affects the dynamic behaviour of the fibrous composite plate of interest.

Citation

Aydogdu, M., Aksencer, T., & Soldatos, K. P. (2021). On three-dimensional dynamics of fibre-reinforced functionally graded plates when fibres resist bending. Journal of Engineering Mathematics, 128(1), Article 13. https://doi.org/10.1007/s10665-021-10128-0

• Journal Article Type: Article
• Acceptance Date: Mar 17, 2021
• Online Publication Date: May 18, 2021
• Publication Date: May 18, 2021
• Deposit Date: Mar 17, 2021
• Publicly Available Date: May 19, 2022
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Science and Business Media LLC
• Peer Reviewed: Peer Reviewed
• Volume: 128
• Issue: 1
• Article Number: 13
• DOI: https://doi.org/10.1007/s10665-021-10128-0
• Keywords: Elastic plate dynamics; Fibre bending stiffness; Fibre-reinforced structures; Free vibration; Functionally graded structures; Polar elasticity
• Public URL: https://nottingham-repository.worktribe.com/output/5398971
• Publisher URL: https://link.springer.com/article/10.1007/s10665-021-10128-0
• Additional Information: Received: 13 December 2020; Accepted: 17 March 2021; First Online: 18 May 2021