中文摘要：

立方非线性速度反馈控制被用来抑制承受非均匀热载荷的两端简支梁的主参数共振.考虑几何非线性、线性阻尼,利用Hamilton原理得到梁大振幅振动的控制方程.应用Galerkin变分原理将控制方程转化为二阶非线性常微分方程：杜分-马休方程.在梁的均匀升温小于其静态热屈曲临界温度载荷时,应用多尺度方法得到系统一次近似解的幅-频响应方程,理论分析系统的稳态响应、稳定区域及失稳临界条件.数值讨论速度控制参数、细长比等参数对系统幅-频、激振力幅-振幅响应曲线的影响.数值结果表明速度反馈控制是有效的.

英文摘要：

Cubic nonlinear velocity feedback control law was proposed to suppress the primary parametric resonance of a beam with simple surported ends and subjected to thermal shock load.By considering the effects of geometric nonlinearity and linear damp,nonlinear dynamic governing equation for the beam was derived by using Hamilton law.In the light of Galerkin s variation principle,the nonlinear partial differential equation of the system was reduced into a second-order nonlinear ordinary equation—Duffing-Mathieu ＇s equation. The method of multiple scale is used to derive the amplitude-frequency response equation for its first approximate solution when uniform thermal load less than the static buckling critical value. Steady-state response, stable region, and the critical term of stability losing were theoretically stud- ied. Numeric method was used too to study the effect of many parameters such as control parameters, ratio of slenderness to length, damping parameter, etc on the amplitude-frequency response and phase-frequency response of the primary parametic system. The numeric result indicated that the velocity feedback control law was effective.