Effects of fiber orientation and temperature on natural frequencies of a functionally graded beam reinforced with fiber

In this paper, thermal vibrations of a reinforced orthotropic beam are studied. The beam is reinforced with fibers functionally oriented and graded along the thickness direction. Uniform thermal distribution is applied throughout the beam and property of the fiber functionally graded beam considered temperature-dependent. Symmetrical, asymmetrical, and classical distributions are presented for variability of the angle of the fibers along the thickness direction. Equilibrium equations are employed to obtain the pre-stresses and equations of motion derived from first-order shear deformation theory and Hamilton principle. Generalized differential quadrature is used to solve the system of coupled differential equations. To verify the accuracy of the present analysis, compression is conducted with valid data. Results show that different parameters, such as thickness-to-radius ratio, effect of temperature variations, distribution of the angle of the fibers, and different boundary conditions, influenced the beam effect on natural frequencies.