Theoretical and Experimental Research of Viscoelastic Damping Limb-Like-Structure Device with Coupling Nonlinear Characteristics

The nonlinear characteristic of vibration control systems has attracted increasing attention for its advantage in improving structural performance. In this paper, a new type of viscoelastic damping limb-like-structure (VE-LLS) device is proposed by combing the viscoelastic (VE) damper and limb-like-structure (LLS) together, which possesses coupling nonlinearity characteristic caused by geometric and material factors, as well as a remarkable advantage in improving the control performance. First, to explore the nonlinear geometrical effects on the static stiffness of the VE-LLS device, a formula is derived from static stiffness, and the results are discussed. Second, dynamic analysis is performed of the proposed device considering the coupling geometrical and material nonlinearities in frequency domain, with the real-time effect of frequency and temperature on the mechanical properties of the viscoelastic damper considered in solving the nonlinear vibration equation. The harmonic balance method (HBM) is used to solve the nonlinear dynamic equation. Then, the displacement transmissibility of the VE-LLS device is calculated and assessed. The results indicate that the proposed device possesses excellent vibration isolation performance, and the geometric parameters of the viscoelastic damper have significant nonlinear effect on the performance. Finally, an experiment is carried out of the VE-LLS device to verify the accuracy of the static stiffness analysis. The results show that the theoretical results agree well the experimental ones, and that the theoretical results have high accuracy and reliability.

Oscillation Criteria of Second-Order Dynamic Equations on Time Scales

In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation. λ(s)Ψ1φΔ(s)y(φ(s))ΔΔ+η(s)Φ(y(τ(s)))=0,s∈[s0,∞)T. By employing generalized Riccati transformation and inequality scaling technique, we establish some oscillation criteria.

On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.

Torque distribution method based on vibration instability of PS-HEV transmission system

The power-split hybrid electric vehicle has multiple working modes, which can be switched to different working mode according to different working conditions. The main switching process involved in the vehicle driving is the switch from the pure electric mode to the hybrid driving mode. This paper studies the mode switching process involved in the power-split hybrid electric vehicle driving process, and a nonlinear dynamic equation of the electromechanical coupling of the corresponding transmission system is established. Then the multi-scale method is employed to solve the dynamic equation, and the amplitude-frequency response curve is drawn. According to the curve, the effects of load, mechanical input excitation of the engine and motor electromagnetic excitation on the electromechanical coupling torsional vibration of the transmission system are studied. The engine and motor torque distribution schemes are obtained by analyzing the amplitude-frequency response curve of the torsional vibration characteristics of the system. The analysis results show that the vibration instability phenomenon of the transmission system can be avoided by establishing the nonlinear dynamic equation of the transmission system, analyzing the vibration characteristics of the vibration system, and optimizing the torque distribution of a PS-HEV at different working modes.

Bifurcation and Chaotic Analysis for Cable Vibration of a Cable-Stayed Bridge

Cable-stayed bridges are of the most unique and cost-effective designs in modern bridge engineering. A key feature of these structures is that the cables or stays run directly from the tower to the deck. The nonlinear dynamic behavior of these cables can significantly affect the resilience and safety of the bridge. In this context, a deeper understanding of the bifurcation and chaotic mechanisms of cable vibration is highly desirable. Accordingly, in this study the nonlinear dynamic equation of a planar cable is derived for quantitative and qualitative analysis. The nonlinear system is solved asymptotically, using the conventional perturbation and two-timing scale methods, to study the periodic motion of the cables. The obtained solutions are primarily affected by the control parameters and the initial conditions. The asymptotic solutions are also simulated numerically. It is found that the chaotic behavior of cables is greatly affected by the governing parameters, including the cable dimensions, vibration amplitude, damping effect, and excitation frequency. Finally, seven state variables of the nonlinear system are analyzed to investigate the occurrence of bifurcation.

Formation of the Capillary Ridge on the Free Surface Dynamics of Second-Grade Fluid Over an Inclined Locally Heated Plate

The formation of capillary ridges is the typical features of thin viscous or viscoelastic fluids over a locally heated plate. This ridge leads to the nonuniformity in the thin film coating. In this work, the formation of capillary ridges on the free surface of thin second-grade non-Newtonian fluid flowing over an inclined heated plate is discussed. The flow is modelled by two-dimensional laws of conservation of mass, momentum, and energy with corresponding boundary conditions at the plate and the free surface. An evolution equation for the description of the liquid thin film height is derived from the two-dimensional balance equations using the long-wave approximation. The resulting nonlinear dynamic equation is discretised implicitly on a uniform grid using the finite volume method. The obtained results on the capillary ridge in the free surface are discussed for the different flow parameters. It is noted that the capillary ridge height is higher for the second-grade viscoelastic fluid in comparison to the Newtonian one. This study can be a starting point to investigate the influence of second-grade viscoelastic parameter on the free surface instability and other phenomena of interest.

The Nonlinear Single Controller of DGEN380 Aero Engine Design

The advanced nonlinear sliding mode control method of DGEN380 aero engine is presented in this paper. This aero engine is a small high bypass ratio turbofan engine by which the nonlinear control approach of the aero engine is invested. And this paper focuses on the power management function of the aero engine control system which includes steady control and transient control. The mathematical model of DGEN380 aero engine is built by a set of nonlinear dynamic equation that is validated by experimental data. The single controller based on sliding mode approach is designed that can keep some certain thrust levels during steady state and maintain repeatable performance during transient operation from one requested thrust level to another. The single controller can offset the impact of the signal noise and harmonic disturbance at a certain power point. And the dynamic performance of the single controller is satisfactory at the transient process. The experiment is conducted by aero engine test bench for the single control.

Impacts of Backlash on Nonlinear Dynamic Characteristic of Encased Differential Planetary Gear Train

A multifreedom tensional nonlinear dynamic equation of encased differential planetary gear train with multibacklash and time-varying mesh stiffness was developed in the present research. The nonlinear dynamic response was obtained by solving the formulated nonlinear dynamic equation, and the impacts of backlash on dynamic characteristics of the gear train were then analyzed by combining time process diagram, phase diagram, and Poincaré section. The results revealed that bilateral shock in meshing teeth was caused due to smaller backlash, thus causing dramatic changes in meshing force; hence, the gears were found to be in a chaotic state. Further, during stable motion state, no contact between intermeshing teeth with bigger backlash was noticed; thus, they were in a stable quasiperiodic motion state in the absence of teeth exciting force. Therefore, in order to avoid a bilateral shock in gears as well as to maintain gear teeth lubrication, a slightly bigger backlash is required. The backlash change in any transmission stage caused significant impacts on gear force and the motion state of its own stage; however, the impact on gear force of another stage was quite small, whereas the impact on the motion state of another stage was quite large.