用改进平均法求解自由衰减振动  

Solving free damped vibration with an improved averaging method

作　　者：何松林[1] 黄焱[1] 

机构地区：[1]昆明学院物理科学与技术系,云南昆明650031

出　　处：《振动与冲击》2011年第1期227-229,共3页Journal of Vibration and Shock

基　　金：2009年云南省教育厅科学研究基金项目(09Y0344)

摘　　要：为了提高平均法求解非线性振动的精度,必须考虑阻尼对振动周期的影响,提出可将待解微分方程的圆频率与派生方程圆频率的差异函数表示为阻尼系数的多项式。通常只需取方程中一阶导数项的系数作为差异函数,就可在较大范围内提高平均法解的精度。利用改进平均法具体求解了线性阻尼衰减振动和杜芬型衰减振动,并与精确解或数值解进行了比较,证明改进平均法确实是有效的。In order to improve the accuracy of a nonlinear vibration solution obtained with a averaging method, the effect of damping on the vibration period must be considered. The different function of the circular frequencies between the differential equation to be solved and its derived equation was expressed as a polynomial of the damping coefficient. Usually taking the damping coefficient as the different function would improve the accuracy of the averaging method. The linear damped vibration and the Duffing-type damped vibration were solved with an improved averaging method proposed by the authors. It was proved that the improved averaging method is effective to improve the accuracy of the solution by comparing its solutions with the exact solution of the linear damped vibration and the numerical solution of the Dulling-type damped vibration.

关 键 词：非线性振动 阻尼系数 改进平均法 

分 类 号：O322[理学—一般力学与力学基础]