多自由度振动系统的同相振动性

SYNCHRONOUS VIBRATION OF MULTIDEGREE-OF-FREEDOM VIBRATING SYSTEM

采用反射函数法研究了多自由度振动系统 x′=p( t) x,当 p( t) =diag( A( t) ,B( t) )时 ,给出其等价系统 y′=A( t) y,z′=B( t) z同相振动的充分必要条件 ,其中 A( t) =( aij( t) ) 2× 2 ,B( t) =( bij( t) ) 2× 2 ,y=( y1,y2 ) T,z=( z1,z2 ) T,p( t+2 ω) =p( t) ,ω>0 ,t∈R,x∈ R4 ,p( t)为连续可微的矩阵函数 .

In this paper the method of reflective function is used to study the multidegree of freedom vibrating system x ′=p(t)x . When p(t) =diag( A(t),B(t)), the sufficiency and necessary conditions of the synchronous vibration of it′s equivalence system ( y ′=A(t)y, z ′=B(t)z ) are given. Where A(t)=(a ij (t)) 2×2 , B(t)=(b ij (t)) 2×2 , y=(y 1,y 2) T, z=(z 1,z 2) T, p(t+2ω)=p(t), ω>0, t∈R, x∈R 4, p(t) continuously differentiable function.