Large amplitude free vibration of hemp fiber-reinforced laminated composite plates using generalized differential quadrature method

In recent years, natural fiber-reinforced composite (NFRC) materials have gained significant attention in applications due to their eco-friendly nature, biodegradability, low cost, lightweight, and satisfactory mechanical properties. Bast, flax, jute, and hemp are among the most popular natural fibers in composite applications. In this study, the pure and hybrid (with glass and carbon fibers) use of hemp fibers in the large amplitude (nonlinear) free vibration of laminated composite plates is investigated. The large amplitude free vibration equation is derived using the virtual work principle. Nonlinear Green-Lagrange strains are utilized in the derivation. Spatial derivatives in the free vibration equation are calculated using the Generalized Differential Quadrature (GDQ) method. The nonlinear free vibration equation is solved using a direct iterative procedure. Effects of stacking sequence, aspect ratio, and boundary conditions on the frequency of linear and nonlinear free vibration are also investigated. Linear modal analysis results indicate that carbon/hemp fiber-reinforced hybrid composite plates have slightly higher natural frequency values than carbon/glass fiber-reinforced hybrid composite plates for CHCHC (C: carbon, H: hemp) and CHHHC stacking sequences, regardless of the aspect ratio and boundary conditions. For nonlinear modal analyses, carbon/glass and carbon/hemp hybrid composite plates exhibit very similar frequency ratio ( ω N L / ω L ) values for CGCGC (G: glass) and CHCHC stacking sequences, as well as for the stacking sequences of CGGGC and CHHHC.