In this work, the dynamics of an electromagnetically suspended mass, which is very simple representation of the Hyperloop system, is studied. Linear stability analysis of the 1.5 degree-of-freedom system yields three distinct regions for the physically meaningful equilibrium point, one of which exhibits limit cycles. The limit cycle is analysed using the harmonic balance method, revealing the frequencies and amplitudes of the periodically oscillating variables. The expressions for the frequency and current allow for the determination of various geometrical and physical limits of the system. Additionally, Floquet analysis is conducted to determine the stability of the limit cycle.

The relationship between stationary solitons and energy localization in chains of nonlinear oscillators has been extensively documented in the literature. Despite the established nature of this correlation, studies providing a deep analysis of damped solitons solely subjected to external excitation are still needed, once, to the best of our knowledge, the influence of the coupling stiffness on vibration localization still needs further investigation. Contrary to systems subjected to parametric excitation, externally driven damped solitons do not have reported analytical solutions, imposing an additional computational challenge. In this context, this study aims to elucidate how the coupling stiffness can impact the localization of kinetic energy in mechanical lattices through the Nonlinear Schrödinger Equation, focusing solely on external excitation. Numerical simulations demonstrate that solitonic dynamics in oscillator chains do not necessarily require low coupling values; however, analogous to Anderson localization, the intensity of localization increases with the decrease in the coupling strength.

As one of the most crucial components in control loops, pneumatic control valves ensure product quality and personnel safety. During prolonged operation of valves, nonlinear motion caused by valve stiction often leads to oscillations in control loops. Therefore, it is crucial to analyze the valve nonlinear motion from the valve position (MV) for detecting and maintaining control loops. In this paper, we construct the valve motion model in the control loop based on the DABlib module of MATLAB/Simulink. From the perspective of phase space reconstruction, we compare and evaluate the characteristics of valve nonlinear motion in loop oscillation combined with recurrence quantitative analysis (RQA).

Stiction in control valve plays a negative role in the whole control system, thus, research on motion of stem is necessary to fix the stiction problem. Lots of researches focus more on the friction and spring force in the motion model of stem, neglecting the fluid force. However, fluid force is crucial in extremely high-pressure conditions. In this paper, the fluid force in the motion model of stem has been considered by using the Fluent UDF (User-Defined Function) method. And the response time of stem during the closing process has been calculated under step-function signal of p from actuator. By analyzing the fluid flow and stem’s motion, a turning point is observed which divides the closing process into two parts according to the feature of fluid force. Before it, the fluid force can be regarded as a constant, and after it, the fluid force is functioned as a nonlinear term. Based on this, a modified model is proposed, characterized as a piecewise function, adaptable to varying conditions.

This research extends the Enriched Multiple Scales method to nonlinear partial differential equations (PDEs), illustrating the procedure using a beam with mid-plane stretching. Enriched multiple scales was originally formulated for predicting the periodic response and stability of weakly and, in some cases, strongly nonlinear non-autonomous ordinary differential equations (ODEs). It combines multiple time dilatation and asymptotic expansions found in the conventional Multiple Scales (MS) method with a continuation, or homotopy, of the original equation’s governing operator using an embedding parameter, commonly denoted by p. The central principle of the method, as applied to ODEs, requires that the undamped linear problem homotopic to the nonlinear problem (recovered by setting p = 0) be chosen to respond at the forcing frequency (or a sub- or super-harmonic thereof), leading to secular term cancellation using the excitation frequency. For ODEs, establishing the homotopy is straight-forward since the natural frequency derives from mass-like and stiffness-like coefficients. In contrast, such a simple procedure cannot be employed for PDEs where the natural frequency is dependent not only on the coefficients found in the field equation, but also the explicit form of the imposed boundary conditions. To surmount this difficulty, we chose herein to omit the embedding parameter from the boundary conditions, and instead introduce an additional stiffness parameter in the linear problem, which is ultimately determined as part of the solution procedure. It is this stiffness parameter which guarantees the linear problem responds at the forcing frequency or a sub- or super-harmonic thereof. We demonstrate the procedure for a nonlinear beam vibration problem with mid-plane stretching and hinged-hinged boundary conditions. Additionally, we develop a local stability analysis and apply it to the periodic solutions predicted for the nonlinear beam. Comparisons to finite element simulations document strong agreement with results obtained using the enriched multiple scales procedure, even for forcing resulting in strongly nonlinear response.