Vibration analysis of laminated composite higher order beams under varying axial loads

The article develops a computational mathematical model to predict the dynamic response of composite laminated beam under variable axial load using a third higher order shear deformation beam theory, for the first time. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equations of composite beam are used on the basis of plane stress problem. The variable axial load is distributed along the axial direction by: constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived using Hamilton's principle. Then, the variable coefficients-differential equations of motion are discretized in spatial direction by using numerical differential quadrature method (DQM). The proposed model is verified with previous works available in literature. Parametric analyses are developed to present the influence of axial load type, orthotropy ratio, slenderness ratio, fiber orientations, and boundary conditions on the natural frequencies of composite beams. The present enhanced model can be used specially in designing of spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads. •Developed a mathematical model to predict the dynamic response of composite laminated beam under variable axial load.•The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory.•The integro-differential equations of motion are discretized in spatial direction by using numerical differential quadrature method (DQM).•The model can be used in designing of spacecrafts, naval, automotive, see pilers, helicopter and wind turbines subjected to the variable axial loads.