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This thesis proposes novel designs of phononic crystal plates (PhPs) allowing ultra-wide controllability frequency ranges of guided waves at low frequencies, with promising structural and tunability characteristics. It reports on topology optimization of bi-material-layered (1D) PhPs allowing maximized relative bandgap width (RBW) at target filling fractions and demonstrates multiscale functionality of gradient PhPs. It also introduces a multi-objective topology optimization method for 2D porous PhPs allowing both maximized RBW and in-plane stiffness and addresses the critical role of considering stiffness in designing porous PhPs. The multi-objective topology optimization method is then expanded for designing 2D porous PhPs with deformation induced tunability. A variety of innovative designs are introduced which their maximized broadband RBW is enhanced by, is degraded by or is insensitive to external finite deformation. Not only does this book address the challenges of new topology optimization methods for computational design of phononic crystals; yet, it demonstrated the suitability and applicability of the topological designs by experimental validation. Furthermore, it offers a comprehensive review of the existing optimization-based approaches for the design of finite non-periodic acoustic metamaterial structures, acoustic metamaterial lattice structures and acoustic metamaterials under perfect periodicity.



Chapter 1. Background and Research Scope

In this chapter, the characteristics of acoustic metamaterials in manipulation of elastodynamic and acoustic waves is explained. Acoustic bandgaps are introduced and the role of topology optimisation for enhancing the bandgap efficiency of PhCrs is discussed. Application of PhPs in manipulation of guided waves in thin-walled structures for design of low loss vibroacoustic devices and structural health monitoring is explained. Finally, the research scope targeting topology optimisation of PhPs is introduced.
Saeid Hedayatrasa

Chapter 2. Literature Review and Research Objectives

In this chapter the existing literature concerning optimisation of AMMs, particularly PhCrs and PhPs, are categorised and explained. The research problem and objectives are then introduced based on the shortages of literature. Finally the thesis structure and the contents of thesis chapters are detailed.
Saeid Hedayatrasa

Chapter 3. Optimisation Framework and Fundamental Formulation

The implemented optimisation framework is first discussed in this chapter. Optimisation algorithms and their characteristics are explained and compared. The advantages of GA for optimisation of PhCrs and in particular for proposed research problem are argued. Then the topology mapping and definition of binary design variables for desired 1D and 2D PhPs are presented. Finally, the FEM formulation and relevant periodic boundary conditions for modal band analysis of the PhP unit-cell are discussed.
Saeid Hedayatrasa

Chapter 4. Optimisation of Bi-material Layered 1D Phononic Crystal Plates (PhPs)

In this chapter, fundumental study is performed on topology optimisation of 1D bi-material PhP unit-cell for highest specific bandgap width of Lamb waves at prescribed filling fraction of stiff scattering inclusion. Moreover the bandgap efficiency and multiscale functionality of gradient PhP structures comprising of unit-cells with various filling fractions and optimised topologies are investigated. Specialised FEM model is developed for this purpose calculating the dispersion curves and modal band structure of guided waves in a layered medium.
Saeid Hedayatrasa

Chapter 5. Optimisation of Porous 2D PhPs with Respect to In-Plane Stiffness

The optimised topology of 1D bi-material PhPs for maximised RBW of Lamb waves and its variation with respect to filling fraction of constituents was studied in the Chap. 4. This chapter explores the optimised topology of porous PhPs with 2D periodicity for maximised bandgap width of guided waves and incorporates unit-cell’s effective stiffness in optimisation algorithm to get structurally worthy porous bandgap topologies.
Saeid Hedayatrasa

Chapter 6. Optimisation of Porous 2D PhPs: Topology Refinement Study and Other Aspect Ratios

In this chapter, an improved optimisation framework is employed for topology optimisation of PhPs and a topology refinement study is performed. The void elements of topology and relevant boundary conditions are excluded from FEM solution stage for faster fitness evaluation. Special mutation and repair operations are also implemented to smoothen the exterior boundaries of topologies and to avoid checkerboards during refinement stage.
Saeid Hedayatrasa

Chapter 7. Optimisation of Porous 2D PhPs for Deformation-Induced Tunability

Due to wide multiscale application of PhCrs it is of great value to introduce controllable phononic bandgaps to be tailored, degraded or enhanced during their function or with switchable bandgap properties. In this chapter, novel porous PhP topologies with optimised deformation induced bandgap tunability performance are introduced through a multi-objective optimisation strategy. Maximum relative bandgap width of guided waves in undeformed state and maximum deformation-induced bandgap gradient under equibiaxial stretch are the two objectives of optimisation.
Saeid Hedayatrasa

Chapter 8. Experimental Validation of Optimised Porous 2D PhPs

This chapter presents experimental validation of selected optimised porous PhPs introduced in Chap. 6. The PhP samples are manufactured by water-jetting an aluminium plate and laser cutting a PMMA plate. The performance of PhP samples in attenuation and self-collimation and focusing of guideds waves is observed and calculated dispersion properties are confirmed.
Saeid Hedayatrasa

Chapter 9. Conclusions and Recommendations for Future Work

This chapter summarises the main contributions and conclusions of the thesis and provides recommendations for future work.
Saeid Hedayatrasa


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