中文摘要：

为考查假设模态法应用于壁板非线性颤振响应时域分析的可行性,分别采用时域方法和频域方法研究了超声速飞行器壁板的非线性颤振响应,并从壁板的颤振幅值、颤振频率和颤振型态三个方面对时域和频域分析结果的一致性作了较详细的比较.首先,基于von Karman应变-位移关系和Mindlin板理论建立考虑几何非线性的壁板力学模型,应用一阶活塞理论分析壁板上单面承受的超声速准定常气动力,基于虚功原理和有限单元法推导壁板的运动微分方程.然后,用壁板的线性固有模态作为假设模态,减缩系统的自由度而得到降阶模型.采用四阶龙格-库塔法对降阶模型作时域数值积分,得到壁板的非线性颤振响应.另一方面,假设壁板的极限环颤振为简谐振荡,可对壁板的非线性刚度作等效线性化处理,进而在频域中直接在有限元（未降阶）模型的基础上分析壁板的颤振幅值、颤振频率和颤振型态.数值分析表明,当极限环颤振为简谐振荡时,时域方法和频域方法的计算结果符合一致.本文最后讨论了时域法和频域法应用在壁板非线性颤振分析中各自的优点和局限性.

英文摘要：

The nonlinear flutter responses of heated panels in supersonic airflow are studied.The aeroelastic model of three-dimensional panels considering thermal effect is established by the use of von Karman large deflection strain-displacement formulations,quasi-steady first-order piston theory aerodynamics and the principle of virtual work.A Mindlin-type three-node finite element（MIN3） discretization is performed in deriving the governing equations which are solved in frequency domain through the use of the linearized updated mode with a nonlinear time function approximation（LUM/NTF） method.For time domain analysis,the discretized dynamic equations of motion are transformed into nonlinear coupled-mode equations by using the proper linear modal coordinates.The amplitude and frequency of panel flutter response is calculated using both frequency domain method and time domain numerical integration.The numerical results show that the efficient frequency domain method can be used to predict nonlinear panel flutter characteristics when the flutter response is demonstrated as a simply harmonic limit cycle oscillation.