Dynamic Properties of the Elliptic Hyperbolic Parabolic Cable Network
As the basis of response analysis of flexible cable net under seismic load, the dynamic properties of the elliptic hyperbolic parabolic cable network are investigated. First, the shape function, the vibration displacement function and the external excitation function for the elliptic hyperbolic parabolic cable network are established through contact conditions. Subsequently the dynamics equations for elliptic hyperbolic parabolic cable network are got by assuming the support system as a continuum membrane. Then Galerkin's method is used to discrete the dynamics equations into ordinary differential equations and the
approximate solutions to free and forced vibrations of cable net are respectively received by L-P method and KBM method. Lastly, with an example, the influences of temperature, amplitude, and initial tension on the nonlinear free vibration, and the influences of the factors, such as temperature, amplitude of external excitation and circuit frequency of external excitation on the non-resonant forced vibration are discussed. The example shows as follows: (1) the nonlinear vibration frequency is higher than linear vibration frequency, and that vibration frequency decreases with the increase of temperature, and increases with the increase of amplitude and initial tension; (2) the stationary vibration of the elliptic hyperbolic parabolic cable network under harmonic excitation is the simple harmonic vibration with the same period as external excitation; (3) there is little influence of temperature on the structure time-history curve, and with the increase of amplitude of external excitation, the vibration amplitude will increase, but the vibration frequency and
dynamic coefficient remain changeless; (4) as to the influence of circuit frequency of external excitation on the amplitude of time-history curve, it was mainly embodied with dynamic coefficient, with the increase of dynamic coefficient, the vibration amplitude will increase, and the vibration frequency is the same with the excitation frequency.
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