Superharmonic vibrations of sandwich beams with fibre composite core layer based on the multiple scale method

This paper deals with the secondary vibration problem in the superharmonic case near the harmonic excitation of 1/3 omega(l), arising from the vibration nonlinearity that characterizes the slender and less damping laminated beam with composite material core. For this aim the multiple scale method in conjunction with the higher order zigzag theories are used to obtain the resonance responses. In the present work the nonlinear forced vibration problem of sandwich beams under harmonic excitation is solved by the multiples scales method, based by the introduction of an artificial parameter with higher order expansions, to control the nonlinear analytical solutions. The application of this method demonstrates the sensitivity of the sandwich beams with viscoelastic composite layer to the secondary superharmonic vibrations. Following, parametric study is conducted to demonstrate the vulnerability of the laminated structures to the superharmonic vibrations and to reduce as far as possible the amplitude vibrations achieved by more appropriated structural design. The results reveal the effect of the slenderness of the sandwich beams on the hardening changes. In the other hand the results demonstrate the importance of fibre orientation angle to reduce as far as possible the amplitude responses of the sandwich structures in superharmonic vibration case.