Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force

A theoretical model for the multi-span spinning beams with elastic constraints under an axial compressive force is proposed.The displacement and bending angle functions are represented through an improved Fourier series,which ensures the continuity of the derivative at the boundary and enhances the convergence.The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation.The efficiency and accuracy of the present method are validated in comparison with the finite element method(FEM)and other methods.The effects of the boundary spring stiffness,the number of spans,the spinning velocity,and the axial compressive force on the dynamic characteristics of the multi-span spinning beams are studied.The results show that the present method can freely simulate any boundary constraints without modifying the solution process.The elastic range of linear springs is larger than that of torsion springs,and it is not affected by the number of spans.With an increase in the axial compressive force,the attenuation rate of the natural frequency of a spinning beam with a large number of spans becomes larger,while the attenuation rate with an elastic boundary is lower than that under a classic simply supported boundary.

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.

Dynamic Trajectory Planning of Autonomous Lane Change at Medium and Low Speeds Based on Elastic Soft Constraint of the Safety Domain

Most current research on the trajectory planning of the autonomous lane change focuses on high-speed scenarios and assumes that the states of the surrounding vehicles keep stable during the lane change.The methods based on geometric-curve are mostly used for trajectory planning.In this paper,considering the inevitable development of the autonomous driving,the surrounding vehicles are assumed to be driven by human drivers,while the ego vehicles are able to autonomously change lanes.Representative local lane-change scenarios are then designed and analyzed in detail aiming at medium-and low-speed lane-change conditions.Additionally,in contrast with most research,dynamic trajectory planning which considers the possible state variations of the surrounding vehicles and the driver characteristics is studied and described by a fifth-order polynomial function.The safety and comfort of the dynamic trajectory planning are validated through simulation.Moreover,the elastic soft constraint of the safety domain is designed,whereby the sensitivity of the studied dynamic trajectory planning system is reduced under the premise of ensuring safety.The effectiveness of the elastic soft constraint in terms of improving comfort during the lane change is verified through simulation.The availability of the dynamic trajectory planning system with the elastic soft constraint is demonstrated with the addition of trajectory tracking based on model predictive control,showing its potential in practical applications.