In this paper, we have calculated the spectrum of Lyapunov exponent of the strange attractor for a single degree of freedom in elastic system with a two-state variable friction law via the method advanced by Wolf. The...In this paper, we have calculated the spectrum of Lyapunov exponent of the strange attractor for a single degree of freedom in elastic system with a two-state variable friction law via the method advanced by Wolf. The system is expressed by the following dimensionless equation:where,and f are dimensionless state variable, logarithm slip velocity and frictional stress, respectively;β1,β2,ρ,and K are dimensionless system parameters.The state of this system is chaotic when dimensionless parameters are β1=1. 00, β2=0. 84, ρ=0. 048, =0. 198 85, K=0. 0685.The Lyapunov exponent spectrum of its strange attractor has been calculated as follows:λ1=0. 0179, λ2=0, λ3=-0. 1578The dimension of this strange attractor has also been calculated as DL=D0=2.11where DL and D0 denote Lyapunov dimension and Kolmogorov dimension respectively.展开更多
文摘In this paper, we have calculated the spectrum of Lyapunov exponent of the strange attractor for a single degree of freedom in elastic system with a two-state variable friction law via the method advanced by Wolf. The system is expressed by the following dimensionless equation:where,and f are dimensionless state variable, logarithm slip velocity and frictional stress, respectively;β1,β2,ρ,and K are dimensionless system parameters.The state of this system is chaotic when dimensionless parameters are β1=1. 00, β2=0. 84, ρ=0. 048, =0. 198 85, K=0. 0685.The Lyapunov exponent spectrum of its strange attractor has been calculated as follows:λ1=0. 0179, λ2=0, λ3=-0. 1578The dimension of this strange attractor has also been calculated as DL=D0=2.11where DL and D0 denote Lyapunov dimension and Kolmogorov dimension respectively.
