The Nonlinear Vibration Analysis Of Composite Thin-cylindrical Shell

The basic vibration of cantilever thin-cylindrical composite shells subjected to transverse external force at the free end has been studied in the paper. The effect of1:1internal vibration was taken into account. Numerical method, average method and method of multiple scales were used to analyze the effects of different parameters on the frequency response curves. The concrete contents and conclusions were as follows:Firstly, a nonlinear wave vibration equation considering the geometric nonlinearity was established by using Donnell’s shallow shell theory. After comparing the linear natural frequencies under the boundary of cantilever, two of the natural frequencies were found to close to1:1, there might be internal vibration. Differential equations on mode coordinate were got by using the method of Galerkin. The Runge-Kutta method was used to solve the equations numerically, the internal vibration was proved to be exist through the frequency response curves. The frequency response curves were greatly influenced by the magnitude of the exciting force and elastic modulus, while the influence of damping coefficients could be ignored.Then, the dynamic characteristics of thin-cylindrical shells with fixed elastic modulus were studied by average method and method of multiple scales on the mode coordinate. According to the results, the small parameter, coordination parameter, the magnitude of the exciting force and nonlinear terms coefficients had significant influence on the frequency-response curves, while damping coefficients had little influence on them. The stability and bifurcation of the frequency response curves were turn to be very complicated. The transition to the instability was exhibited in frequency-response curves by saddle-node bifurcation or Hopf bifurcation.Through the comparison of the results, it’s seen that there was a very good agreement among results of three different methods. The causes generated the errors were discussed. It’s found that the dynamic modulus and forms of frequency disturbance had a great influence on the response amplitude.