Variable stiffness composite laminated beams - nonlinear free flexural vibration behavior using a sinusoidal based shear flexible structural theory accounting for Poisson’s effect

In the present work, formulation for the nonlinear free vibrational behavior of laminated variable stiffness composite beams with curvilinear fibers is made incorporating sinusoidal function for representing the transverse shear flexibility, geometrical nonlinearity, and accounting for Poisson’s effect through the constitutive equation for analyzing beams with general composite lay-up. Applying Hamilton’s principle combining with a finite element approach based on three-noded C1 beam element, the governing equations are formed through matrices. The solutions for the developed governing equations are evaluated iteratively by introducing eigenvalue analysis and the results are viewed through the frequency–amplitude relationship. A large number of design parameters like curvilinear fiber angles in a layer, number of layers, lay-up sequence, thickness ratio, etc. is assumed to visualize the nonlinear free vibration characteristics of VSCL beams. Also, for the practical situation, the influence of thermal environment and restraint elastically against beam ends rotation, to accommodate other than classical boundary conditions, hybrid beam (consisting of constant and variable stiffness layers) on the non-linear free vibrational behavior is presented. •Investigated nonlinear vibration of variable stiffness laminated composite beam reinforcement with curvilinear fibers.•Beam formulation accounts for Poisson’s effect by modifying the constitutive equations.•Employed higher-order model by sinusoidal shear deformation theory for the dynamic analysis.•Provided the nonlinear frequency–vibration amplitude relation by direct iterative method.•Presented new results for evaluating the performance of other theories and solution approaches.