An investigation on static, vibration and stability analyses of elastically restrained FG porous Timoshenko nanobeams

This manuscript develops for the first time a combined mathematical procedure of the static, dynamical and stability responses of functionally graded porous Timoshenko nanobeam using a higher-order elasticity theory. Fourier sine and cosine series with Stokes' transformation is used to transform ordinary differential equations into a system of algebraic equations for buckling and dynamic responses. In the buckling, vibration and static problems, Fourier cosine and sine series are used in the region, while fixed constants are selected at the boundaries and modelled separately. By discretizing the constant values at the boundaries, eigenvalue problems independent of the supporting conditions are established. The validity of the presented model is assessed through comparison with available results calculated from rigid boundary conditions by giving proper values to elastic springs. Parametric studies are performed to research the effects of the different parameters on the functionally graded porous Timoshenko nanobeams.