Vortex-Induced Vibration Response Bifurcation Analysis of Top-Tensioned Riser Based on the Model of Variable Lift Coefficient

Top-tensioned riser (TTR) is one of the most frequently used pieces of equipment in offshore petroleum engineering. At present, the research of its vortex-induced vibration (VIV) is mainly focused on numerical simulation with few analytical approaches. In this paper, the nonlinear dynamic equation of VIV about TTR is developed by introducing the third-order variable lift coefficient hydrodynamic model. The amplitude-frequency response equation under 1:1 primary resonance excitation is deduced based on the single mode discrete results. The nonlinear dynamic responses characteristics of the TTR vibration under the excitation of vortex-induced resonance are discussed. Bifurcation theory is used to study the singularity of the analytical solution of the riser system. The hysteresis and solitary solutions from the results of singularity analysis are found. Such results can provide guidance for the design and optimization of riser structural parameters

Lateral Superharmonic Resonance of the Rotor in 12/8 Poles Switched Reluctance Motor

Switched reluctance motor (SRM) generates a very large electromagnetic radial force when the stator windings commutate because of its doubly salient structure and magnetic saturation. Lateral vibration appears when electromagnetic radial force is applied onto the rotational rotor, which causes continual changes of airgap and further radical electromagnetic force. Nonlinear vibration of the rotor under the interaction of electromagnetic radial force and displacement becomes very complicated, which is becoming a research hotspot at present. A whole lateral vibration dynamics equation is established by finite element method. The radical force formula of single rotor tooth was deduced by integration of equivalent electromagnetic circuit and Maxwell stress method, and final functional expression of radial electromagnetic resultant when stator windings are energized with ideal square wave is also obtained. The critical speeds and vibration modes of the rotor are analyzed by Campbell diagram and lateral vibration displacement locus is solved by Newmark-Beta numerical integration method. The results show that the vibration locus of the rotor distributes in a circular domain. The frequency distribution of electromagnetic resultant relates to rotation speed, current switch frequency, and current wave, while the frequency distribution of the displacement also closely relates to the first-order critical speed of the rotor. When the rotor runs at some specific speed, lateral superharmonic resonance phenomenon appears and its displacement locus shows rich diversity. Lateral vibration characteristic of the rotor could be quickly grasped through this study, which makes vibration evaluation possible for advanced motor design

Validation study on a non-linear dynamical model of the projectile

Abstract Based on the theoretical approach of multi-body interaction dynamics, a theoretical model is constructed to simulate the nonlinear response amplification of the projectile structure. The accuracy and universality of the theoretical model were verified by comparing the response data calculated by the theoretical model with the experimental data. The results show that the theoretical model can predict the acceleration and strain response of the projectile structure more accurately, providing a non-linear dynamic analysis method for the projectile structure from the perspective of structural dynamics