Drosopoulos, Georgios.Jeawon, Yajur.2025-07-032025-07-0320242024https://hdl.handle.net/10413/23805Doctoral Degree. University of KwaZulu-Natal, Durban.Industries naturally strive to improve processes, materials, and material applications in order to raise the quality of the resource under consideration. This thesis focuses on proposing a numerical scheme to optimize and maximize the natural frequency response generated in 3-phase nanocomposite laminated plates through the use of graphene nanoplatelets (GPLs) and fibre reinforcement in terms of glass and carbon fibres. Many industries are now interested in conducting research on graphene reinforcement to form superior composites with the intention that the research may lead to a number of useful present-day and future initiatives. The natural frequency of nanoreinforced composite laminated plates has been researched in published articles by using techniques such as the Halpin-Tsai model and rule of mixtures to derive micromechanical equations and the Hamiltonian approach to acquire the equations of motion which are later solved via governing equations to obtain the natural frequency of the system. The current study uses MATLAB coding techniques to implement a Finite Element Model to accurately analyse the frequency response of a nanocomposite plate, the effective material properties of which are found using the micromechanical equations that are further discussed in this study. The composite plate's kinematics are developed using the first order shear deformation theory (FSDT). By using micromechanical equations the properties of a 2-phase composite, reinforced with graphene nanoplatelets (GPLs) located in the matrix, can be calculated. After the effective material properties have been calculated for this graphene-reinforced composite, the same micromechanical equations are applied once again for the introduction of fibre reinforcement (glass or carbon fibre) thereby forming a 3-phase nanocomposite laminate reinforced with graphene and fibres. The study builds itself around two major aspects which are the maximum generated natural frequencies and the optimized natural frequencies for a defined set of parameters including graphene content, fibre reinforcement type and content, boundary conditions, fibre orientation, number of layers in the laminate and thickness ratio. The first investigation focuses on optimizing a hybrid, multi-scale graphene/fibre reinforced composite laminate plate in order to provide an optimal design solution resulting in a superior natural frequency and ultimately reducing the probability of resonance. Resonance occurs when the natural frequency of an object aligns with the vibration frequency of the excitation source. When resonance occurs it can lead to structural failure of the object. In this study a Sequential Quadratic Programming Algorithm is used to optimize the fundamental frequency. The Sequential Quadratic Programming Algorithm was chosen based on the extensive use and validity in numerous research studies and the successful application thereof. A Matlab function is used to implement the SQP optimization, called fmincon. In the central Matlab code this function is used, and the developed finite element analysis code calculating the natural frequencies for the composite laminate is called as a Matlab subroutine by this SQP function. No convergence problems were identified in these optimization simulations. The results of this research revealed that adding graphene nanoplatelets (GPLs) improved the fundamental frequency of the composite and that maximum GPLs content in all layers is not always the optimal solution. Every simulation produces both the optimized fundamental frequency and the design efficiency, which is represented as the ratio of the maximum fundamental frequency that corresponds to optimal design divided by the reference frequency of the laminate that results from uniform properties. The second research paper expands on the ideas of the first by altering the plate geometry to define a cantilever support condition for a 45° skew laminated composite plate. The second study formulates an optimization scheme for a skew cantilever plate subject to similar constraints applied to the rectangular plate and provides a comparison of their natural frequencies. By investigating skew plates and various boundary conditions the research data adapted to form solutions for a broad spectrum of industry wide applications. In the second study the findings showed that a more economical design, with lower fibre volume content, could be produced by distributing the graphene and fibres optimally throughout the plate's thickness. Secondly, the skew laminate's design efficiency appeared to decline despite the apparent increase in natural frequency when compared to the results for a rectangular laminate. The third study investigates the natural frequency of a rectangular laminated composite plate with functionally graded (FG) reinforcement material. Functionally graded materials are composites that have two or more constituent materials with contents that are changed gradually or continuously so as to maximize the composite’s strength properties. Five distinct graphene reinforcement distribution patterns applied along the thickness direction of the laminate were used in the functionally graded application to identify the distribution that produced the maximum natural frequency. The distribution patterns considered in this investigation are Type ‘V’, Type ‘A’, Uniform (UD), Type ‘O’ and Type ‘X’. The analysis model was defined as in the previous studies for a rectangular laminated plate with the exception of the optimization scheme as this research was formulated to investigate the apparent maximum natural frequency of the laminated composite. In the majority of the simulations, the defined distribution pattern was assigned to each layer and investigated for variable constraints similar to the previous studies. Additionally, a simulation was done for a layerwise distribution of the FG patterns with different patterns assign in the subsequent layers. The data obtained from the analysis showed the Type ‘X’ distribution produces the maximum natural frequency when lower fibre content is used (<5 glass and <7.8% carbon) in combination with graphene as the reinforcement materials. On the other hand, the largest natural frequencies are produced by the uniform distribution when the fibre content rises above the specified levels. This research introduces 3-phase material optimization framework and defines a design efficiency factor that quantifies the output of optimization. Results indicate that graphene nanoparticles, when introduced into the matrix of the nanocomposite, produced much higher natural frequencies as compared to conventional fibre reinforced laminates. The results also showed that carbon fibres that were utilized as reinforcement perform better in maximizing the natural frequency compared to glass fibres. It is noted that optimization results in increased reinforcement contents in the outer layers of the laminate and reduced or no reinforcement in the inner layers, indicating that this is the optimal distribution of reinforcement with respect to the observed fundamental frequency. Increasing the number of design variables also improved the fundamental frequency. In terms of the skew laminate versus the rectangular laminate, the observation was made that the fundamental frequency was larger for a skew laminate than a rectangular laminate but the design efficiency decreased compared to the rectangular laminate. The thesis also suggests optimal functionally graded distributions along the thickness, in terms of maximizing natural laminate frequencies. Industrial applications in civil, aerospace, mechanical and energy sectors can adopt some of these outcomes, towards a cost-effective design of advanced nanocomposite materials.enHalpin-Tsai model.Hamiltonian.MATLAB.Thesis