Research of Precise Time Integration Method and its Derived Formats on Helicopter Rotor Dynamics

The aeroelastic coupling dynamic equation of helicopter rotor is essentially a set of nonlinear and inhomogeneous equations with large rigidity, in which the inhomogeneous term is a function of blade motion and aerodynamic load. In this paper, the precise time integration method and its derived formats are introduced to solve the rotor blade dynamic equation, and the Duhamel integral item can be calculated by various numerical methods. In terms of computational accuracy and numerical stability, the precise Kutta method and high precision direct integration method (HPD method) are carefully selected to compare with classical Runge–Kutta method numerically. HPD method is used to solve the rotor blade dynamic equation, and the transient response of the rotor blade is examined by Newmark and implicit trapezoidal methods. Results indicate that HPD method dominates the classical Runge–Kutta method in step size independence, and gets close to implicit methods in numerical stability and accuracy for dynamic equation of helicopter rotor blade.

Research on Dynamic Response of Bridge Subjected to Kinds of Load

A vehicle-bridge system is simplified as a model of Euler-Bernoulli beam subjected to kinds of load. Dynamic behavior of the beam is researched in this paper. Several equations of the beam traversed by static or moving load and mass are given. Some of these equations are time-varying nonlinear. In order to avoid the problem of instability solving the equations, precise time integration method is used. Results show that the transversal deflection of the mid-span of the beam is greater when a harmonic force or a mass is traveling on the bridge at a lower velocity or by accelerating.