Vibration analysis of deploying laminated beams with generalized boundary conditions in hygrothermal environment

The free vibration of a deploying laminated beam in hygrothermal environment with a constant axial velocity is studied. The model of this system is given within the framework of the Euler-Bernoulli beam theory and von Karman nonlinear strain theory. The nonlinear dynamic equilibrium equation with generalized boundary conditions is established based on the Hamilton's principle with considering the combined effects of the axial motion, transverse vibration and hygrothermal environment. Based on the Galerkin method, a set of ordinary differential equations is obtained. The numerical results of the discretization equation are performed adopting the eigenvalue method and Newmark method. In addition, the dynamic stability is discussed, and extensive numerical calculations are performed to illustrate the effects of varying extension velocities, temperature, humidity and ply angles on frequencies.