DYNAMIC MODEL AND PRINCIPAL RESONANCE OF A COUPLED STRUCTURE BY SUSPENDED CABLE AND STAYED BEAM

The mathematical model for the vertical vibration of the coupled structure of a suspended-cable and stayed beam is established. The model of partial differential equations (PDEs) describes the effects of geometric nonlinearity that are induced by the large deformation and initial curvature of the mail cable. The ordinary differential equations (ODEs) are obtained from the PDEs by Galerkin method. In the principal resonance case, the first approximate analytical solutions of the ODEs are attained by the multiscale method under harmonic excitations. The results show that when the excitation frequency is close to the structure low or high natural frequency, the amplitudes of vibration appear jump phenomenon. When both low and high frequency principal resonances occur there are two cases: 1) if the amplitude and frequency of high frequency excitation are fixed, the amplitudes of the low and high frequency vibration will increase or decrease synchronously when the parameters of a low frequency excitation change; 2) if the amplitude and frequency of the low frequency excitation are fixed, the amplitudes of the low and high frequency vibration will vary in an opposite trend when the parameters of a high frequency excitation change.