Garau, Marta (2020) Dynamic chirality and failure in structured materials with applications. Doctoral thesis, Keele University.

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Abstract

We consider the vibration of two classes of discrete periodic systems and the resulting dynamic effects. We analyse elastic lattices connected to arrays of gyroscopic spinners, that confer chirality to the elastic system. It is shown in the time-harmonic regime that these systems support special dynamic phenomena at various frequencies, including interfacial waves in elastic materials attached to inhomogeneous arrays of spinners. We derive a new asymptotic model that characterises the interaction between a gyroscope and an elastic truss system in the transient regime. This asymptotic model is verified with an independent finite element simulation and the model is used to confirm the identified waveforms can be realised through a transient analysis, where initial conditions and loading of the system play a greatrole. Two advanced technological applications of gyro-elastic systems are also proposed, including a topological insulator and an elastic cloaking device for a discrete lattice. The influence of vibration on failure processes in discrete flexural systems is also studied. We consider the model of a flexural system undergoing failure at an uniform rate as a result of the action of a remote mechanical sinusoidal load. This simplified model may represent the collapse of a civil engineering structure, such as a bridge, rooftop or pipeline system, exposed to hazardous vibrations resulting from, say, an earthquake. The problem is reduced to a functional equation of the Wiener-Hopf type, through the Fourier transform, that allows for the characterisation of possible failure regimes and the dynamics of the structure undergoing failure through its solution. The model is used to predict the outcomes of a numerical scheme developed in Matlab to analyse the failure in a sufficiently long finite medium subjected to a sinusoidal load.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Contributors: Nieves, MJ (Thesis advisor)
Depositing User: Lisa Bailey
Date Deposited: 15 May 2020 14:53
Last Modified: 15 May 2020 14:53
URI: https://eprints.keele.ac.uk/id/eprint/7992

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