Analytical solution to vibrational analysis and response of smart laminated composite beams with experimental and finite element validation

Abstract

This thesis discusses the vibrational behaviour of laminated composite beams, which are widely used in many industrial applications due to their lightweight and superior mechanical, corrosion, and wear resistance properties. Besides, since composite laminated materials provide more flexibility to tailor the material properties to reach specific design goals, they are attractive selections in numerous applications. Remarkably, three types of advanced laminated composite structures are investigated in this thesis. The first type is smart laminated structures, in which a sensor or actuator is integrated into the surface of the beam to control or improve the overall vibrational response of the whole structure. The second type is the functionally graded laminates, in which the material properties along the thickness is uniformly varied to fulfil a different design requirement at different surfaces of the structure. The Third part is generally orthotropic laminates, which is widely used as an adaptive structure, in which the structure passively mitigates the effect of loading fluctuation by passively adapting its shape. These advanced laminated structures are extensively used in high-tech industries, including propulsion, aerospace, and medical, where understanding the accurate vibrational characteristics and response of the structure is highly essential. Equivalent single-layer models (ESL), including classical shear deformation theory (CLT) and first-order shear deformation theories (FSDT), are used to simulate the complicated 3D behaviour of the laminate into 2D equivalent single-layer models, which is applicable to thin and thin o moderately thick beams. Specifically, an analytical solution is developed to discover the accurate and reliable solution for vibrational analysis of laminated beams with step change of geometry or material properties subjected to a combination of different boundary conditions anywhere thorough the beam. To provide accurate results, the developed models consider the second moment of inertia of the section, lateral movement of the beam related to Poisson and bending Poisson effects. More importantly, the extension-bending and bend-twist coupling are appropriately integrated into the model, crucial to obtaining accurate results. Thus, the developed models provide versatile tools to precisely analyse the vibration behaviour of laminated structures in practical applications where step changes due to the integration of sensors, actuators, or reinforcement are usually unavoidable. First, to find the analytical solution, Hamilton's principle was used to find the governing equation and boundary condition equations of the laminated beam. Then, The state-space model was employed to find the dynamic stiffness matrix of the problem, which is solved using a two-stage iterative algorithm. To assess the applicability of the provided solution method, the vibrational behaviour of several different laminated structures is validated with the published papers. Additionally, finite element models are developed to investigate the accuracy of the proposed method for more complicated cases. Furthermore, several experiments are conducted to evaluate the accuracy of the proposed analytical closed-form solution experimentally. Comparisons reveal that the provided solution can provide accurate and reliable results for a broad range of engineering applications. Finally, parametric studies are conveyed to find the effect of different parameters on the vibrational behaviour of the laminated composite structures. Show more