Linear and nonlinear free vibration analysis of super-light composite beams with honeycomb core layer and adjustable Poisson’s ratio using multiple-scale method

An analytical procedure to analyze the linear and nonlinear vibrations of composite beams with honeycomb core layer and adjustable Poisson’s ratio subjected to axial load is presented in this study. By employing the first-order shear deformation theory, the von-Karman relations for moderately large deformation, and using the Hamilton principle, the equations of motion which are a system of coupled nonlinear partial differential equations are obtained. These equations are solved analytically using the multiple-scale method and the linear and nonlinear natural frequencies, mode shapes, and frequency–amplitude curves are extracted. Both transverse and axial frequencies are studied. By utilizing a parametric study, the effects of geometrical and mechanical parameters such as the honeycomb cell dimensions and parameters, the thickness of layers, length, axial load, different types of boundary conditions, and Poisson’s ratio on the linear and nonlinear vibrations are determined. It is observed that by employing the honeycomb structures, the mass of the structure has been significantly decreased while the frequencies will remain nearly the same or increase. To compare the results, the finite element analysis, and results from the literature are used to show the accuracy of the presented method.