Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Beam Structures

This work deals with the study of vibration behavior of the Functionally Graded Timoshenko Beam that has been reinforced with Carbon Nanotubes (CNTs), which is subjected to thermal and mechanical loads. The constituent materials of the functionally graded beam are alumina as the matrix material and single walled CNTs as the reinforcement material. The volumetric fraction varies according to power law along the thickness. The temperature dependent (TD) and temperature independent (TID) material properties of the beam are determined by employing Mori-Tanaka method and extended rule of mixture along the thickness direction. Timoshenko beam theory is used to study the dynamic behavior of the beam. The finite element method is employed to discretize the model and Hamilton’s principal is used to derive the equation of motion . Vibration analysis has been carried out to study the response of Temperature dependent and independent material properties on the dynamic behavior of the beam. The results show that CNT volume fraction and Temperature dependent material properties has substantial effect on the vibration characteristic of the beam

Advanced Composite Materials and Structures

Composite materials are used to produce multi-objective structures such as fluid reservoirs, transmission pipes, heat exchangers, pressure vessels due to high strength and stiffness to density ratios and improved corrosion resistance. The mathematical concepts can be used to simulate and analyze the generated mechanical and thermal properties of composite materials regarding to the desired performances in actual working conditions.  To solve and obtain the exact solution of the developed nonlinear differential equations in the composite materials, analytical methods can be applied. Mechanical and thermal analysis of complex composite structures can be numerically analyzed using the Finite Element Method (FEM) to increase performances of composite structures in different working conditions. To decrease failure rate and increase performances of composite structures under complex loading system, thermal stress and effects of static and dynamic loads on the designed shapes of composite structures can be analytically investigated. The stresses and deformation of the composite materials under the complex applied loads can be calculated by using the FEM method in order to be used in terms of safety enhancement of composite structures. To increase the safety level as well as performances of the composite structures in different working conditions, crack development in elastic composites can be simulated and analyzed. To develop and optimize the process of composite deigning in terms of mechanical as well as thermal properties under different mechanical and thermal loading conditions, the advanced machine learning systems can be applied. A review in recent development of composite materials and structures is presented in the study and future research works are also suggested. Thus, to increase performances of composite materials and structures under complex loading systems, advanced methodology of composite designing and modification procedures can be provided by reviewing and assessing recent achievements in the published papers

Plate Vibration under Irregular Internal Supports

10.1016/S0020-7683(01)00241-4International Journal of Solids and Structures3951361-138

The fourier spectral element method for vibration analysis of general dynamic structures

The Fourier Spectral Element Method (FSEM) was proposed by Wen Li on the vibration of simple beams (Li, 1999), and was extended to the vibration of rectangular plates (Li, 2004). This dissertation proposes a revised formulation on the vibration of rectangular plates with general boundary conditions, and extends the FSEM on the vibration of general triangular plates with elastic boundary supports. 3-D coupling formulation among the plates and beams is further developed. A general dynamic structure is then analyzed by dividing the structure into coupled triangular plates, rectangular plates, and beams. The accuracy and fast convergence of FSEM method is repeatedly benchmarked by analytical, experimental, and numerical results from the literature, Laboratory test, and commercial software. The Key feature of FSEM method is that the approximation solution satisfies both the governing equation and the boundary conditions of the beam (plates) vibration in an exact sense. The displacement function composes a standard Fourier cosine series plus several supplementary functions to ensure the convergence to the exact solution including displacement, bending moment, and shear forces, etc. All the formulation is transformed into standard form and a set of stored matrices ensure fast assembly of the studied structure matrix. Since the matrix size of the FSEM method is substantially smaller than the FEA method, FSEM method has the potential to reduce the calculation time, and tackle the unsolved Mid-frequency problem