The dynamic stability of the hinged-hinged sinusoidal shallow arch with geometrical imperfection under time wise distributed load is investigated in this paper. First, the nonlinear governing equation of shallow arch is derived from the d'Alembert principle andEuler-Bernoulli assumption. And the dimensionless type of the equations, which is used to investigate the equilibrium configurations of shallow arch, is obtained by the Fourier series expansion and the Galerkin integration. Then, with the application of both the nonlinear equation and sufficient condition for stability, the stability of shallow arch with geometrical imperfection is studied. The emphasis is placed on the influences of root locus of critical points and sufficient condition for dynamic stability on the second harmonic imperfection, which is similar to the buckling mode-shape of arch structure. To compare the stability property of imperfect shallow arch with that of perfect arch, the sinusoidal shallow arch with no imperfection is studied before the analysis of effect on imperfection.
The nonlinear vibrations of cables excited by the vibration of beam were investigated. At first, a simple connection condition and boundary condition of the cable-stayed beam structure were applied. The nonlinear equations of motion of the cable-stayed beam structure were derived, and the static sag of the cable as well as the geometric nonlinearity was considered, moreover, Appling the multi-scale perturbation method, the nonlinear vibrations of cables were studied, the nonlinear vibration response of cables was analyzed by the Runge-Kutta numerical method to obtain the frequency-response curves. The results indicate that the beam small scale vibration can stimulate the cable the large scale movement when local oscillation frequency of beams is in the certain region, it affects the cable-stayed beam structure the stability and the security in the Engineering. For the system in which the damping and the frequency ratio was given, the enough low excitation amplitudes can avoid the system resonances.
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