噪声与振动控制
譟聲與振動控製
조성여진동공제
NOISE AND VIBRATION CONTROL
2014年
2期
28-33
,共6页
唐元璋%翁雪涛%楼京俊%林雄伟%张晖
唐元璋%翁雪濤%樓京俊%林雄偉%張暉
당원장%옹설도%루경준%림웅위%장휘
振动与波%非线性常微分方程%Duffing方程%傅立叶展开%谐波平衡法
振動與波%非線性常微分方程%Duffing方程%傅立葉展開%諧波平衡法
진동여파%비선성상미분방정%Duffing방정%부립협전개%해파평형법
vibration and wave%nonlinear ordinary differential equation%Duffing equation%Fourier expansion%harmonic balance method
简化了一种求取非线性常微分方程高阶谐波解的近似解析计算方法。对平方和立方非线性项的傅里叶展开过程进行改进和简化，使计算过程变为两次矩阵运算即可完成展开过程，且两次矩阵运算过程一致，易于编程。以Duffing方程为算例，计算结果与数值方法一致，运算效率有所提高。
簡化瞭一種求取非線性常微分方程高階諧波解的近似解析計算方法。對平方和立方非線性項的傅裏葉展開過程進行改進和簡化，使計算過程變為兩次矩陣運算即可完成展開過程，且兩次矩陣運算過程一緻，易于編程。以Duffing方程為算例，計算結果與數值方法一緻，運算效率有所提高。
간화료일충구취비선성상미분방정고계해파해적근사해석계산방법。대평방화립방비선성항적부리협전개과정진행개진화간화，사계산과정변위량차구진운산즉가완성전개과정，차량차구진운산과정일치，역우편정。이Duffing방정위산례，계산결과여수치방법일치，운산효솔유소제고。
A simplified computation method of the high-order harmonic solution for nonlinear ordinary differential equations is discussed. Fourier expansion procedure of the equation with quadratic or cubic terms is improved and simplified. The procedure consists of two steps of matrix operation with the same computation process so that the algorithm is easier to program than that of the previous equation. Results of the solution for the Duffing equation using this method show that the high-order harmonic solution is in good agreement with its numerical solution, but more efficient than the latter one.
