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Abstract
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In this thesis, comprehensive studies on the size-dependent nonlinear free vibration and thermal post-buckling behaviour rotating pre-twisted functionally graded (FG) microbeams and microplates in thermal environment are presented. The material properties are assumed to be temperature dependent and graded in the thickness direction. At first, the discretized nonlinear governing equations are derived based on the modified strain gradient theory (MSGT) in conjunction with the first-order shear deformation theory (FSDT) of beams and four-variable refined plate theory under the von K?rm?n geometric nonlinearity assumptions using Hamilton's principle and Chebyshev-Ritz method. The resulting nonlinear equations under different boundary conditions are solved iteratively by employing methods such as direct, Newton-Raphson and Broyden. After validating the approach, the effects of angular velocity, twist angle, length scale parameters, thickness-to-length ratio, hub radius, material gradient index and boundary conditions on nonlinear, linear free vibration and thermal post-buckling behavior of rotating pre-twisted FG microbeams and microplates are investigated.
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