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研究了热环境中功能梯度圆板在横向简谐激励作用下的非线性动力响应和动应力问题。针对陶瓷-金属功能梯度圆板,考虑几何非线性、材料物理性质参数随温度变化及材料组分沿厚度方向按幂律分布的情况,应用虚功原理给出了热载荷与横向简谐载荷共同作用下的非线性振动偏微分方程。在固支无滑动的边界条件下,利用伽辽金法得到了达芬型非线性强迫振动方程。通过数值算例,给出了关于体积分数指数的分岔图,相图、Poin-care映射等响应图以及动应力变化规律图,讨论了材料体积分数指数和温度场对功能梯度圆板非线性动力响应的影响。结果表明:热环境中功能梯度圆板随体积分数指数的变化可使系统出现周期响应、倍周期响应和混沌响应。功能梯度圆板中心处动应力在系统发生分岔或出现混沌响应时出现大幅变化,而且在混沌响应时具有不可预测性。
The nonlinear dynamic response and the dynamic stress of the functionally graded circular plate under the harmonic excitation in the transverse direction are studied. Aiming at the geometric-nonlinearity of ceramic-metal functionally graded circular plates, the parameters of physical properties of materials vary with the temperature and the material components are distributed according to the power law in the direction of thickness. By applying the principle of virtual work, Nonlinear Vibration Partial Differential Equations under. Under the condition of no-slip boundary between solid and branch, DaVincan nonlinear forced vibration equation is obtained by Galerkin method. The bifurcation diagram, phase diagram, Poin-care mapping response diagram and dynamic stress variation law of the volume fraction index are given through the numerical examples. The effects of the material volume fraction index and the temperature field on the nonlinearity of the functional gradient disc Effect of dynamic response. The results show that the change of volume fraction index of functionally graded disk in thermal environment can make the system appear periodic response, doubling period response and chaotic response. The dynamic stress at the center of the functionally gradient disk changes greatly when the system is bifurcated or chaotic, and it is unpredictable in the chaotic response.