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研究了椭圆平面的双曲抛物面线性强化材料索网的非线性振动.在考虑温度变化的基础上,建立了椭圆平面的双曲抛物面线性强化材料索网非线性振动控制方程,采用Galerkin原理及改进的L-P法求出了索网非线性振动的近似解,结合算例讨论分析了温度、线性强化、振幅等因素对索网非线性振动的影响,为椭圆平面双曲抛物面索网的抗震设计提供了理论依据.算例表明,椭圆平面双曲抛物面索网固有频率随着温度的升高而减小,其振动具有较强的非线性,自振频率随着振幅发生变化,其非线性振动呈现“硬弹簧”特性,非线性自振频率高于线性频率,线性强化状态时的非线性振动自振频率低于线性弹性状态时的非线性振动自振频率.
The nonlinear vibration of oval planar hyperbolic parabolic linear reinforcing material cable net is studied. Based on the change of temperature, a nonlinear hyperbolic parabolic linear stiffening material cable nonlinear governing equation is established. The Galerkin principle and its improvement LP method was used to find the approximate solution of the nonlinear vibration of the cable network. The effects of temperature, linearity, amplitude and other factors on the nonlinear vibration of the cable network were discussed in conjunction with an example to provide the seismic design of the elliptic planar hyperbolic parabolic net The theoretical basis is given.Examples show that the natural frequency of elliptic plane hyperbolic parabolic net decreases with the increase of temperature and the vibration has strong nonlinearity and the natural frequency changes with the amplitude, “Hard spring ” characteristic, the nonlinear natural frequency is higher than the linear frequency, and the natural frequency of the nonlinear vibration under the linearly enhanced state is lower than the nonlinear natural frequency under the linear elastic state.