Abstract:This paper proposes a novel stability criterion for nonautonomous generalized Birkhoff systems based on triple combined gradient system framework. Firstly, the differential equations and fundamental properties of four distinct gradient systems and their corresponding triple combined gradient systems are systematically discussed. Secondly, for the governing differential equations of nonautonomous generalized Birkhoff systems, a representation method based on matrix combinations is proposed, establishing four different forms of triple combined gradient representations. On this basis, the Lyapunov function can be directly derived from the corresponding triple combined gradient representation equations via given matrix combinations, thereby simplifying the stability determination process. Compared with existing methods, the proposed approach significantly reduces the difficulty associated with constructing Lyapunov functions, providing an effective tool for studying the stability of nonautonomous generalized Birkhoff systems. Finally, the validity and accuracy of the proposed method are verified through stability analysis and numerical simulations of representative examples.

Abstract:The eigenvalues of a timedelay system are infinite, and exhibit complex distributions. The classical definite integral method is an effective approach for analyzing the stability of multitimedelay systems. However, it cannot directly solve the modal frequencies, i.e., the imaginary parts of the eigenvalues of the system, and instead requires first determining the real parts and then applying additional techniques, such as twodimensional Newton iteration to solve the modal frequencies. For most stable systems, modal frequency is often of greater concern, and indirect determination introduces unnecessary steps and increases computational complexity. Therefore, this article extends the definite integral method by using a new integration path and a new characteristic root translation direction, which can directly solve the modal frequency of timedelay systems, while retaining the advantages of the classical definite integral method, such as being suitable for multi timedelay systems, simple programming, and high efficiency. The paper verifies the wide applicability and the effectiveness of the proposed method for calculating the modal frequencies of timedelay systems through two engineering examples.

Abstract:Inertial navigation systems often operate in complex mechanical environments. Under conditions of highspeed motion or severe vibration, the output of accelerometers can be affected by the base angular velocity, leading to measurement errors. Therefore, this paper investigates the formation mechanism and dynamic characteristics of the output error of the Pendulous Integrating Gyroscopic Accelerometer (PIGA) under base angular motion. First, starting from the dynamic modeling of the PIGA, a comprehensive error model incorporating the combined effects of linear acceleration, angular velocity, and angular acceleration is established. Then, based on the simultaneous consideration of threeaxis angular velocity and angular acceleration inputs, the error expression of the PIGA is derived. The generation mechanism, magnitude, and coupling relationship with system parameters of error terms related to angular motion are analyzed, revealing the key error components that significantly impact output accuracy and require compensation. Finally, based on the dynamic simulation model, the influence of base angular motion inputs on the dynamic response of the PIGA output is studied. The results show that under different combinations of angular velocity and angular acceleration inputs, the error characteristics of the PIGA output exhibit significant differences. Therefore, the effect of dynamic base angular velocity on the PIGA output is substantial and should be addressed and compensated for in practical engineering applications.

Abstract:Based on the smoothed Stribeck friction model, a nonlinear dynamic model of a twodegreeoffreedom disc braking system was established. The stability of the equilibrium points was analyzed using the RouthHurwitz criterion, and the influence of different parameters on the stability of the braking system was discussed. The Hopf bifurcation point was obtained using the Hurwitz criterion, and the first Lyapunov coefficient at the bifurcation point was calculated by introducing the projection method to determine the type of Hopf bifurcation. The theoretical analysis results were verified through numerical simulations. The study shows that when the angular velocity of the brake disc is low, the system remains stable; whereas when the angular velocity is high, increasing the attenuation factor or reducing the dynamic friction coefficient can significantly improve the stability. As the braking force increases and the angular velocity decreases, the unstable region of the system also expands; moreover a reasonable design of the stiffness ratio between the brake disc and the brake pad can optimize the stability of the system. In addition, the system undergoes subcritical Hopf bifurcation under critical parameters, whereby the stability of the equilibrium point changes, an unstable limit cycle is generated, and selfexcited vibration is triggered.

Abstract:This study investigates a galloping system integrated with a series of piezoelectric dynamic vibration absorbers (PDVAs), achieving the dual functions of vibration suppression and energy harvesting. The incremental harmonic balance method (IHBM) is employed to derive the periodic solutions of the galloping suppression system equipped with different vibration absorbers, and the results are validated through numerical simulations. Comparative analyses of wind speeddisplacement curves, wind speedvoltage characteristics, phase portraits, and timehistory responses demonstrate excellent agreement between the IHBM and numerical solutions. Notably, under identical computational conditions, the IHBM exhibits significantly higher computational efficiency than numerical methods, providing a more efficient analytical approach for the analysis of galloping systems. Furthermore, parametric studies are conducted to evaluate the influence of PDVA parametersincluding mass, stiffness,and damping on both the primary system’s vibration suppression performance and the output voltage. The comparative assessment elucidates the effects of these parameters on vibration mitigation, thereby guiding the optimal design of absorbers through appropriate parameter selection.

Abstract:With the wide application of large flexible solar wings in new generation spacecraft, the demand for realtime monitoring of the displacement field induced by rigidflexible coupling dynamics is becoming increasingly prominent. Aiming at the limitation that the existing displacement field reconstruction studies are mostly based on the static working conditions and are difficult to adapt to the complex dynamic excitation of the spacecraft, this paper proposes a dynamic displacement field reconstruction method based on the hybrid coordinate method and the assumed modal method. By analyzing the rigidflexible coupled spacecraft dynamics model, a highprecision reconstruction algorithm for the global displacement field of the solar wing is constructed by combining the modal analysis techniques. The method can realize realtime reconstruction of the dynamic displacement field under the coupling conditions of attitude maneuver and flexible vibration with only a small amount of sensing data. The results show that the proposed method can realize highprecision reconstruction of the global displacement field of the solar wing under dynamic excitation.

Abstract:As a critical fluidconveying component in mechanical structures, the stability and safety of fluidconveying pipes during operation are of particular importance. Taking a fluidconveying pipe as an example, this paper investigates the passive boundary control of the pipe by coupling an Inertial nonlinear energy sink at its elastic boundary. Firstly, the nonlinear control equations of a fluidconveying pipe with elastic supports coupled with an inertial-based nonlinear energy sink are derived using the generalized Hamilton’s principle. Subsequently, the natural frequencies and mode shapes of the fluidconveying pipe are obtained. Then, the control equations are discretized using the Galerkin truncation method, and the steadystate response of the coupled system is solved through numerical simulation based on the RungeKutta method. Finally, the influence of key parameters of the vibration absorber on the vibration reduction effect of the structure is discussed. The results indicate that the coupled inertial nonlinear energy sink exhibits effective vibration control for the fluidconveying pipe without altering its inherent dynamic characteristics. The parameters of the inertialbased nonlinear energy sink have different effects on the vibration suppression performance: there exists an optimal damping coefficient, while increasing the inertance and the cubic nonlinearity enhances the vibration mitigation.

Abstract:Fuel sloshing within aircraft fuel tanks can generate significant forces and moments on the tank walls, thereby affecting the aircraft’s dynamic characteristics. To enable accurate and efficient prediction of sloshinginduced forces and moments, this study develops an equivalent pendulum mechanical model based on the finite element method. The study focuses on fuel within auxiliary and wing tanks at a 50% fill ratio. Using this model, the sloshing forces, moments, and the motion of the fuel’s center of mass are predicted under three typical flight conditions: pitch, roll, and yaw. The predicted results are further compared with those from computational fluid dynamics simulations, demonstrating the accuracy of the proposed model in capturing the dynamic response of fuel sloshing.

Abstract:The nonreciprocity of energy transfer, particularly strong nonreciprocity, achieved within a wider range of excitation parameters, can enhance the performance of nonreciprocal devices. The influences of bistable elements on the energy transfer mode and the modulation of nonreciprocity are investigated. Initially, the dynamic equation for a system incorporating linear stiffness, cubic stiffness, and bistable components is derived. The semianalytical solutions for this system are obtained using the complexificationaveraging and least square methods. The numerical solutions are obtained via the RungeKutta method. Then, the accuracy of the analysis procedure is confirmed through a comparison of semianalytical and numerical solutions. Building on this, the nonreciprocal characteristics of the system under harmonic excitation and the effects of excitation amplitude are analyzed. The results show that regardless of the presence of the bistable component, the nonlinear system undergoes a transition from the reciprocal to a nonreciprocal state and then back to the reciprocal state. However, the bistable component significantly alters the nonreciprocal characteristics. Furthermore, it is found that an appropriate negative stiffness in the bistable system can effectively decrease the excitation amplitude threshold for activating the nonreciprocal state.