抄録
Though various types of eigenvalue solvers for rotordynamics exist, they only provide solutions for specific parameters, e.g., for several selected rotational speeds. Since these solutions are discrete, it is occasionally difficult for us to make continuous transitions depending on the changes in parameters.
Our tracking solver is capable of providing the continuous behaviour of the solution caused by a varying parameter. Letting the parameter be the time t, the solution is obtained as a time function λ(t) of a state variable λ which is regulated by the sliding mode control so as to be placed on an unknown exact path of f(λ,t)=0. Once the state variable starts from an exact initial value, the state variable consistently indicates exact values thereafter. The principle of this tracking solver is extended to a 2D orbital tracking solver for f(x,y)=0.
To demonstrate the effectiveness of this method, we selected several case studies; complex eigenvalue analysis, algebraic equations with exponential functions, a critical speed map, 2D drawing of resonance curves.
