Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Classification of parametrically constrained bifurcations

If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.

RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK

The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.

BIFURCATION IN A PARAMETRICALLY EXCITED TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEM WITH 1∶2 INTERNAL RESONANCE

The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO_DIMENSION TWO BIFURCATION SYSTEM (Ⅰ)

For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely,a zero_mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.

Differences between lower extremity joint running kinetics captured by marker-based and markerless systems were speed dependent

Background:The development of computer vision technology has enabled the use of markerless movement tracking for biomechanical analysis.Recent research has reported the feasibility of markerless systems in motion analysis but has yet to fully explore their utility for capturing faster movements,such as running.Applied studies using markerless systems in clinical and sports settings are still lacking.Thus,the present study compared running biomechanics estimated by marker-based and markerless systems.Given running speed not only affects sports performance but is also associated with clinical injury prevention,diagnosis,and rehabilitation,we aimed to investigate the effects of speed on the comparison of estimated lower extremity joint moments and powers between markerless and marker-based technologies during treadmill running as a concurrent validating study.Methods:Kinematic data from marker-based/markerless technologies were collected,along with ground reaction force data,from 16 young adults running on an instrumented treadmill at 3 speeds:2.24 m/s,2.91 m/s,and 3.58 m/s(5.0 miles/h,6.5 miles/h,and 8.0 miles/h).Sagittal plane moments and powers of the hip,knee,and ankle were calculated by inverse dynamic methods.Time series analysis and statistical parametric mapping were used to determine system differences.Results:Compared to the marker-based system,the markerless system estimated increased lower extremity joint kinetics with faster speed during the swing phase in most cases.Conclusion:Despite the promising application of markerless technology in clinical settings,systematic markerless overestimation requires focused attention.Based on segment pose estimations,the centers of mass estimated by markerless technologies were farther away from the relevant distal joint centers,which led to greater joint moments and powers estimates by markerless vs.marker-based systems.The differences were amplified by running speed.

Parametric instability in the pure-quartic nonlinear Schrödinger equation

We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Overshoot phenomena:Observation and simulation

High-power O-mode radio waves can excite artificial instabilities in the F region,according to experiments conducted at the European Incoherent Scatter Science Association(EISCAT)heating facility.The main instabilities include the parametric decay instability(PDI),oscillating two-stream instability(OTSI),and thermal parametric instability(TPI).The PDI and OTSI not only compete with each other,but also compete with the TPI,leading to a two-stage overshoot phenomenon:a miniovershoot occurs on a millisecond time scale after pump-on,followed by the main overshoot.We gain insight into the miniovershoot via a generalized Zakharov model,whereas the main overshoot can be observed as an enhanced plasma line overshoot phenomenon in incoherent scatter radar spectra.We can also observe that the zero-frequency ion line exists only in the initial heating period after a cold start and that the upshifted and downshifted ion lines behave irregularly in the spectra.The simulation results show that competition between the PDI and OTSI leads to an initial peak,which we named the pre-miniovershoot.The following processes,namely ion density caviton generation,and collapse and cascade in the development of the PDI,contribute to the miniovershoot phenomenon.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier

A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.

不同装载条件下小型渔船参数横摇的非定常RANS CFD仿真

Fishing boats have unique features that make them prone to changing loading conditions.When the boat leaves the port,the empty fish tank gradually fills up during fishing operations which may result in parametric roll(PR).This dangerous phenomenon that can lead to capsizing.The present study aims to understand better the behaviour of parametric roll in fishing boats and its relation to changing loading conditions.The study considers the effects of displacement and the GM/KM ratio on parametric roll,as well as the longitudinal flare distribution at the waterline.Two assessments to detect the parametric roll occurrence in early stage were carried out by using the level 1 assessment of parametric roll based on the Second Generation of Intact Stability criteria(SGIS)from International maritime Organisation(IMO)and the Susceptibility criteria of Parametric roll from the American Bureau of Shipping(ABS).Then,the CFD method is used to predict the amplitude of the parametric roll phenomenon.The results provide important insights to fishing vessel operators on how to manage loading conditions to maintain stability and avoid hazardous situations.By following the guidelines outlined in this study,fishing boats can operate more safely and efficiently,reducing the risk of accidents and improving the overall sustainability of the fishing industry.

Multi-Objective Optimization of Aluminum Alloy Electric Bus Frame Connectors for Enhanced Durability

The widespread adoption of aluminumalloy electric buses,known for their energy efficiency and eco-friendliness,faces a challenge due to the aluminum frame’s susceptibility to deformation compared to steel.This issue is further exacerbated by the stringent requirements imposed by the flammability and explosiveness of batteries,necessitating robust frame protection.Our study aims to optimize the connectors of aluminum alloy bus frames,emphasizing durability,energy efficiency,and safety.This research delves into Multi-Objective Coordinated Optimization(MCO)techniques for lightweight design in aluminum alloy bus body connectors.Our goal is to enhance lightweighting,reinforce energy absorption,and improve deformation resistance in connector components.Three typical aluminum alloy connectors were selected and a design optimization platform was built for their MCO using a variety of software and methods.Firstly,through three-point bending experiments and finite element analysis on three types of connector components,we identified optimized design parameters based on deformation patterns.Then,employing Optimal Latin hypercube design(OLHD),parametric modeling,and neural network approximation,we developed high-precision approximate models for the design parameters of each connector component,targeting energy absorption,mass,and logarithmic strain.Lastly,utilizing the Archive-based Micro Genetic Algorithm(AMGA),Multi-Objective Particle Swarm Optimization(MOPSO),and Non-dominated SortingGenetic Algorithm(NSGA2),we explored optimized design solutions for these joint components.Subsequently,we simulated joint assembly buckling during bus rollover crash scenarios to verify and analyze the optimized solutions in three-point bending simulations.Each joint component showcased a remarkable 30%–40%mass reduction while boosting energy absorption.Our design optimization method exhibits high efficiency and costeffectiveness.Leveraging contemporary automation technology,the design optimization platform developed in this study is poised to facilitate intelligent optimization of lightweight metal components in future applications.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

Measuring Causal Effect with ARDL-BART: A Macroeconomic Application

Modeling dynamic systems with linear parametric models usually suffer limitation which affects forecasting performance and policy implications. This paper advances a non-parametric autoregressive distributed lag model that employs a Bayesian additive regression tree (BART). The performance of the BART model is compared with selection models like Lasso, Elastic Net, and Bayesian networks in simulation experiments with linear and non-linear data generating processes (DGP), and on US macroeconomic time series data. The results show that the BART model is quite competitive against the linear parametric methods when the DGP is linear, and outperforms the competing methods when the DGP is non-linear. The empirical results suggest that the BART estimators are generally more efficient than the traditional linear methods when modeling and forecasting macroeconomic time series.

Evaluation of Rainfall Tendency for the Twentieth Century over Indira Sagar Region in Central India

The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.

Reflections and mirror effect of parametrically-excited solitons at a boundary

Some of the up-to-date experimental results on the parametrically-excited solitons in arectangular trough of water are provided, including the periodical reflection of a soliton at an end wall of a trough, the collision dynamics of two solitons of like polarity and the existence of mirror effect at boundaries. Attempts are made to explain the observed phenomena and a conception of virtual solitons is proposed.

FORCED SOLITARY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR TANK

A new mode of nonpropagating solitary waves in circular tank, which are forcedly ex-cited in tbe vertical direction, is described. The waveform is measured and the data accordwell with the hyperbolic secant function.Analyses of the vibration modes of the wave showthat the mode is not a pure mode of circular container. A wax cone was inserted in themiddle of tank in order to keep down the plateau. The hysteresis phenomenon of excitation ofsolitary wave has been observed as well.