Vibration Examination in Three-Phase Viscoelastic Composite Curved Beams with Arbitrary Supports

In this study, the free vibration behavior of a multiscale hybrid curved beam reinforced with carbon nanotubes and glass fibers and having a viscoelastic polymer matrix has been numerically investigated. In this modeling, the elastic modulus and Poisson’s ratio of the polymer matrix are considered as exponential functions of time, and the effective modulus is evaluated using the Halpin–Tsai relationship. The governing equations of the beam are derived using the first-order shear deformation theory (FSDT) and solved using the Generalized Differential Quadrature (GDQ) numerical method. The obtained results show that increasing the mass fraction of carbon nanotubes and increasing the radius of curvature increases the effective stiffness and natural frequencies. Also, increasing the relaxation times due to the viscoelastic nature leads to a decrease in the elastic modulus and, consequently, a decrease in the natural frequencies. Furthermore, different boundary conditions have a significant effect on the dynamic response of the beam, where beams with clamped-clamped boundary conditions show the highest and beams with simply supported boundary conditions show the lowest frequency values. These results can be used in the optimal design of curved viscoelastic composite structures.