Saeid Hedayatrasa

Numerical modeling of wave propagation in functionally graded materials using time-domain spectral Chebyshev elements

Numerical modeling of the Lamb wave propagation in functionally graded materials (FGMs) by a two-dimensional time-domain spectral finite element method (SpFEM) is presented. The high-order Chebyshev polynomials as approximation functions are used in the present formulation, which provides the capability to take into account the through thickness variation of the material properties. The efficiency and accuracy of the present model with one and two layers of 5th order spectral elements in modeling wave propagation in FGM plates are analyzed. Different excitation frequencies in a wide range of 28-350 kHz are investigated, and the dispersion properties obtained by the present model are verified by reference results. The through thickness wave structure of two principal Lamb modes are extracted and analyzed by the symmetry and relative amplitude of the vertical and horizontal oscillations. The differences with respect to Lamb modes generated in homogeneous plates are explained. Zero-crossing and wavelet signal processing-spectrum decomposition procedures are implemented to obtain phase and group velocities and their dispersion properties. So it is attested how this approach can be practically employed for simulation, calibration and optimization of Lamb wave based nondestructive evaluation techniques for the FGMs. The capability of modeling stress wave propagation through the thickness of an FGM specimen subjected to impact load is also investigated, which shows that the present method is highly accurate as compared with other existing reference data. Spectral time-domain Chebyshev element is developed for wave propagation in FGMs.Phase velocity dispersion properties of FGM structures are studied using one and two layers of 5th order spectral elements.Different excitation frequencies in a wide range of 28-350 kHz are analyzed.Impact stress wave propagation through the thickness of FGM specimen is investigated.

Numerical study and topology optimization of 1D periodic bimaterial phononic crystal plates for bandgaps of low order Lamb waves

The optimum topology of bimaterial phononic crystal (PhCr) plates with one-dimensional (1D) periodicity to attain maximum relative bandgap width of low order Lamb waves is computationally investigated. The evolution of optimized topology with respect to filling fraction of constituents, alternatively stiff scattering inclusion, is explored. The underlying idea is to develop PhCr plate structures with high specific bandgap efficiency at particular filling fraction, or further with multiscale functionality through gradient of optimized PhCr unitcell all over the lattice array. Multiobjective genetic algorithm (GA) is employed in this research in conjunction with finite element method (FEM) for topology optimization of silicon-tungsten PhCr plate unitcells. A specialized FEM model is developed and verified for dispersion analysis of plate waves and calculation of modal response. Modal band structure of regular PhCr plate unitcells with centric scattering layer is studied as a function of aspect ratio and filling fraction. Topology optimization is then carried out for a few aspect ratios, with and without prescribed symmetry, over various filling fractions. The efficiency of obtained solutions is verified as compared to corresponding regular centric PhCr plate unitcells. Moreover, being inspired by the obtained optimum topologies, definite and easy to produce topologies are proposed with enhanced bandgap efficiency as compared to centric unitcells. Finally a few cases are introduced to evaluate the frequency response of finite PhCr plate structures produced by achieved topologies and also to confirm the reliability of calculated modal band structures. Cases made by consecutive unitcells of different filling fraction are examined in order to attest the bandgap efficiency and multiscale functionality of such graded PhCr plate structures.

Optimal design of tunable phononic bandgap plates under equibiaxial stretch

Design and application of phononic crystal (PhCr) acoustic metamaterials has been a topic with tremendous growth of interest in the last decade due to their promising capabilities to manipulate acoustic and elastodynamic waves. Phononic controllability of waves through a particular PhCr is limited only to the spectrums located within its fixed bandgap frequency. Hence the ability to tune a PhCr is desired to add functionality over its variable bandgap frequency or for switchability. Deformation induced bandgap tunability of elastomeric PhCr solids and plates with prescribed topology have been studied by other researchers. Principally the internal stress state and distorted geometry of a deformed phononic crystal plate (PhP) changes its effective stiffness and leads to deformation induced tunability of resultant modal band structure. Thus the microstructural topology of a PhP can be altered so that specific tunability features are met through prescribed deformation. In the present study novel tunable PhPs of this kind with optimized bandgap efficiency-tunability of guided waves are computationally explored and evaluated. Low loss transmission of guided waves throughout thin walled structures makes them ideal for fabrication of low loss ultrasound devices and structural health monitoring purposes. Various tunability targets are defined to enhance or degrade complete bandgaps of plate waves through macroscopic tensile deformation. Elastomeric hyperelastic material is considered which enables recoverable micromechanical deformation under tuning finite stretch. Phononic tunability through stable deformation of phononic lattice is specifically required and so any topology showing buckling instability under assumed deformation is disregarded. Nondominated sorting genetic algorithm (GA) NSGA-II is adopted for evolutionary multiobjective topology optimization of hypothesized tunable PhP with square symmetric unit-cell and relevant topologies are analyzed through finite element method. Following earlier studies by the authors, specialized GA algorithm, topology mapping, assessment and analysis techniques are employed to get feasible porous topologies of assumed thick PhP, efficiently.

Conclusions and Recommendations for Future Work

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

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.

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.

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.

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.

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.

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.