Initial Inclination Research Articles

An estimate of resident time of the Oort Cloud new comets in planetary region

We describe the result of our numerical orbit simulation which traces dynamical evolution of new comets coming from the Oort Cloud. We combine two dynamical models for this purpose. The first one is semi-analytic, and it models an evolving comet cloud under galactic tide and encounters with nearby stars. The second one numerically deals with planetary perturbation in the planetary region. Although our study does not include physical effects such as fading or disintegration of comets, we found that typical dynamical resident time of the comets in the planetary region is about 108 years. We also found that the so-called planet barrier works when the initial orbital inclination of the comets is small. A numerical result concerning the temporary transition of the comets into other small body populations such as transneptunian objects or Centaurs is discussed.

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

Dynamics of Two Planets near a 2:1 Resonance: Case Studies of Known and Synthetic Exosystems on a Grid of Initial Configurations

The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo simulations and an empirically inferred population distribution of period ratios, we prove that this apparent dearth of near-resonant systems is not statistically significant. The excess of systems with period ratios in the wider vicinity of the 2:1 resonance is significant, however. Long-term WHFast integrations of a synthetic two-planet system on a grid period ratios from 1.87 through 2.12 reveal that the eccentricity and inclination exchange mechanism between non-resonant planets represents the orbital evolution very well in all cases, except at the exact 2:1 mean motion resonance. This resonance destroys the orderly exchange of eccentricity, while the exchange of inclination still takes place. Additional simulations of the Kepler-113 system on a grid of initial inclinations show that the secular periods of eccentricity and inclination variations are well fitted by a simple hyperbolic cosine function of the initial mutual inclination. We further investigate the six known two-planet systems with period ratios within 2% of the exact 2:1 resonance (TOI-216, KIC 5437945, Kepler-384, HD 82943, HD 73526, HD 155358) on a grid of initial inclinations and for two different initial periastron longitudes corresponding to the aligned and anti-aligned states. All these systems are found to be long-term stable except HD 73526, which is likely a false positive. The periodic orbital momentum exchange is still at work in some of these systems, albeit with much shorter cycling periods of a few years.

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

Nonlinear interactions of an n-layer X-shape low-frequency vibration isolator equipped with a nonlinear vibration absorber at 1:1 internal resonance: analytical and numerical investigations

This work addresses, for the first time, the nonlinear dynamics of an n− layers bioinspired X− shape low-frequency vibration isolation system equipped with a nonlinear vibration absorber. The comprehensive mathematical model governing the two-degree-of-freedom system has been derived using Lagrangian mechanics. The method of averaging was applied to obtain an accurate analytical solution for the derived mathematical model. Utilizing the established analytical solution, the dynamical characteristics of the X− shape vibration isolator have been explored both as a single-degree-of-freedom system and after coupling with the proposed vibration absorber, as a two-degree-of-freedom system. The influence of different system parameters, including the number of structure layers, the initial inclination angle, the X− shape rod length, and the absorber stiffness and damping coefficients, on the vibration isolation performance has been investigated. The main findings indicate that while the single-degree-of-freedom X− shape low-frequency vibration isolator performs well in eliminating low-frequency vibration excitations, it exhibits strong vibration levels when the base excitation frequency exceeds the structure's natural frequency. Additionally, it was found that coupling a highly damped linear vibration absorber to the X− shape isolator not only eliminates the strong oscillations of the structure when subjected to high-frequency base excitations but also enhances the structure's low-frequency vibration isolation performance. Moreover, it was reported that integrating a nonlinear vibration absorber with either soft or hard spring characteristics instead of a linear one may degrade the vibration isolation performance of the structure rather than enhance it. Finally, numerical validation of all the analytical results was performed, which showed excellent correspondence with the analytical findings.

Nonoperative management of glenoid baseplate failure in reverse shoulder arthroplasty

BackgroundGlenoid baseplate failure in reverse total shoulder arthroplasty (RSA) remains a challenging problem. Nonoperative management may be an option in certain patients. The purpose of this study was to evaluate outcomes following nonoperative management of glenoid baseplate failure after RSA. MethodsUtilizing a single-institution database, a retrospective review was performed to identify patients from 2010 to 2019 who sustained glenoid baseplate failures after RSA and were treated nonoperatively. The exclusion criteria included revision surgery and presence of active infection. Included patients had a minimum 2-year clinical and radiographic follow-up. Chart review captured patient demographics, surgical indications, and techniques. Radiographs were reviewed to determine the etiology of baseplate failure and other implant complications. Glenosphere inclination angle was measured on true anteroposterior radiographs immediately postoperatively and after baseplate failure. ResultsEighteen patients had glenoid baseplate failures treated nonoperatively during the study period. Five patients were deceased, leaving 13 patients who were available for clinical follow-up. Twelve (92%) patients were successfully contacted. The mean age was 77 years, body mass index was 28, and 8 out of 12 were female. The mean Charlson Comorbidity Index score was 4.1. The mean preoperative American Shoulder and Elbow Surgeons (ASES) score was 43.0, and visual analog scale (VAS) pain was 6.3. At a mean 5.7-year follow-up, patients had an ASES score of 49.2, VAS pain of 4.3, single assessment numeric evaluation of 49%, and 50% of patients were satisfied with their outcome. The preoperative and final follow-up ASES and VAS scores were similar. The average time from index surgery to baseplate failure was 19 months. Of the eighteen identified patients, 16 (89%) failures resulted in increased baseplate superior tilt (7 with concomitant broken baseplate screws). For these 16 patients, the mean glenosphere inclination angle after failure (131°) was significantly greater than the initial inclination angle (100°), P = .03. The other 2 failures resulted in increased baseplate anteversion. 8 out of 18 (44%) patients had bone grafting at the time of surgery. When comparing dissatisfied and satisfied patients, there were no specific patient characteristics or radiographic parameters that were associated with satisfaction. ConclusionNonoperative management of glenoid baseplate failure yields modest patient-reported outcomes, with 50% patient satisfaction at mid-term follow-up. The mortality rate in this cohort of patients was almost 30%. Therefore, in select patients, nonoperative treatment of RSA baseplate failure may be a reasonable option.

An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

AbstractMicrocrack growth during progressive compressive failure in brittle rocks strongly influences the safety of deep underground engineering. The external shear stress τxy on brittle rocks greatly affects microcrack growth and progressive failure. However, the theoretical mechanism of the growth direction evolution of the newly generated wing crack during progressive failure has rarely been studied. A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. This model consists of the wing crack growth model under the principal compressive stresses, the direction correlation of the general stress, the principal stress and the initial microcrack inclination, and the relationship between the wing crack length and strain. The shear stress effect on the relationship between y‐direction stress and wing crack growth and the relationship between y‐direction stress and y‐direction strain are analyzed. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y‐direction peak stress and the wing crack growth direction during the progressive compressive failure considering shear stress is also discussed. A crucial conclusion is that the direction of wing crack growth has a U‐shaped variation with the growth of the wing crack. The rationality of the analytical results is verified by an experiment and from numerical results. The study results provide theoretical support for the evaluation of the safety and stability of surrounding rocks in deep underground engineering.

Less fuel strategies for space debris removal in Low Earth Orbit

This paper proposes less fuel strategies for space debris removal. To mitigate the risk of space debris cost-efficiently, multi-rendezvous missions are under development. On the other hand, multi-rendezvous missions often require changing orbital planes of removal satellites, which requires a huge amount of ΔV. Therefore, this study focuses on exploiting the J2 perturbation force as an auxiliary force and aims to establish maneuver rules that minimize ΔV consumption while maximizing the benefit of the J2 perturbation. The J2 perturbation equation is explored analytically, which clarifies whether the change in the semi-major axis or the inclination dominates the efficiency of the exploitation. A straightforward criterion is extracted which determines the efficient maneuver based on the initial inclination of the satellite.

Black hole outflows initiated by a large-scale magnetic field

Context. Accreting black hole sources show variable outflows at different mass scales. For instance, in the case of galactic nuclei, our own Galactic center Sgr A* exhibits flares and outbursts in the X-ray and infrared bands. Recent studies suggest that the inner magnetospheres of these sources have a pronounced effect on these emissions. Aims. Accreting plasma carries the frozen-in magnetic flux along with it down to the black hole horizon. During the infall, the magnetic field intensifies, and this can lead to a magnetically arrested state. We investigate the competing effects of inflows at the black hole horizon and the outflows that develop in the accreting plasma through the action of the magnetic field in the inner magnetosphere, and we determine the implications of these effects. Methods. We started with a spherically symmetric Bondi-type inflow and introduced a magnetic field. In order to understand the influence of the initial configuration, we started the computations with an aligned magnetic field with respect to the rotation axis of the black hole. Then we proceeded to the case of magnetic fields that are inclined to the rotation axis of the black hole. We employed the 2D and 3D versions of the code HARM for the aligned field models and used the 3D version for the inclined field. We compared the results of computations with each other. Results. We observe that the magnetic lines of force start to accrete with the plasma while an equatorial intermittent outflow develops. This outflow continues to push some material away from the black hole in the equatorial plane, while some other material is ejected in the vertical direction from the plane. In consequence, the accretion rate fluctuates as well. The direction of the black hole spin prevails at later stages. It determines the flow geometry near the event horizon. On larger scales, however, the flow geometry remains influenced by the initial inclination of the field.

Development and validation of a hysteretic model for a novel self-centering friction damper

This study aimed to develop a novel self-centering friction damper (SC-FD) consisting of the winding rope, the friction shaft and the self-centering spring. The theoretical model and equations for the mechanical properties of the SC-FD were derived. Then, the dynamic performance test of the SC-FD and finite element simulation were done to validate the theoretical mechanical model of the SC-FD. Finally, the influence of the main parameters on the dynamic performance of SC-FD was analyzed and design recommendations were made. The study showed that the SC-FD exhibited stable flag-type hysteretic behavior, with good energy dissipation capability and self-centering performance. The theoretical model and equations derived in this study can be used to predicate the behavior of the SC-FD accurately. The parameters, such as the initial inclination angle of the winding rope, winding turns of the winding rope and the stiffness of the self-centering spring and so on, had significant influences on the mechanical performance of SC-FD, which should be optimized in the designing of the SC-FD in order to get excellent mechanical performance.

Inclination instability of circumbinary planets

ABSTRACT We analyse a tilt instability of the orbit of an outer planet in a two-planet circumbinary system that we recently reported. The binary is on an eccentric orbit and the inner circumbinary planet is on a circular polar orbit that causes the binary to undergo apsidal precession. The outer circumbinary planet is initially on a circular or eccentric orbit that is coplanar with respect to the binary. We apply a Hamiltonian in quadrupole order of the binary potential to show that the tilt instability is the result of a secular resonance in which the apsidal precession rate of the binary matches the nodal precession rate of the outer planet. A resonance is possible because the polar inner planet causes the apsidal precession of the binary to be retrograde. The outer planet periodically undergoes large tilt oscillations for which we analytically determine the initial evolution and maximum inclination. Following a typically relatively short adjustment phase, the tilt grows exponentially in time at a characteristic rate that is of order the absolute value of the binary apsidal precession rate. The analytic results agree well with numerical simulations. This instability is analogous to the Kozai–Lidov instability, but applied to a circumbinary object. The instability fails to operate if the binary mass ratio is too extreme. The instability occurs even if the outer planet is instead an object of stellar mass and involves tilt oscillations of the inner binary.

Unveiling the journey of a highly inclined CME

Context. A fast (∼2000 km s−1) and wide (> 110°) coronal mass ejection (CME) erupted from the Sun on March 13, 2012. Its interplanetary counterpart was detected in situ two days later by STEREO-A and near-Earth spacecraft, such as ACE, Wind, and Cluster. We suggest that at 1 au the CME extended at least 110° in longitude, with Earth crossing its east flank and STEREO-A crossing its west flank. Despite their separation, measurements from both positions showed very similar in situ CME signatures. The solar source region where the CME erupted was surrounded by three coronal holes (CHs). Their locations with respect to the CME launch site were east (negative polarity), southwest (positive polarity) and west (positive polarity). The solar magnetic field polarity of the area covered by each CH matches that observed at 1 au in situ. Suprathermal electrons at each location showed mixed signatures with only some intervals presenting clear counterstreaming flows as the CME transits both locations. The strahl population coming from the shortest magnetic connection of the structure to the Sun showed more intensity. Aims. The aim of this work is to understand the propagation and evolution of the CME and its interaction with the surrounding CHs, to explain the similarities and differences between the observations at each spacecraft, and report what one of the most longitudinal expanded CME structures measured in situ would be. Methods. Known properties of the large-scale structures from a variety of catalogues and previous studies were used to have a better overview of this particular event. In addition, multipoint observations were used to reconstruct the 3D geometry of the CME and determine the context of the solar and heliospheric conditions before the CME eruption and during its propagation. The graduated cylindrical shell model (GCS) was used to reproduce the orientation, size and speed of the structure with a simple geometry. Also, the Drag-Based Model (DBM) was utilised to understand the conditions of the interplanetary medium better in terms of the drag undergone by the structure while propagating in different directions. Finally, a comparative analysis of the different regions of the structure through the different observatories was carried out in order to directly compare the in situ plasma and magnetic field properties at each location. Results. The study presents important findings regarding the in situ measured CME on March 15, 2012, detected at a longitudinal separation of 110° in the ecliptic plane despite its initial inclination being around 45° when erupted (March 13). This suggests that the CME may have deformed and/or rotated, allowing it to be observed near its legs with spacecraft at a separation angle greater than 100°. The CME structure interacted with high-speed streams generated by the surrounding CHs. The piled-up plasma in the sheath region exhibited an unexpected correlation in magnetic field strength despite the large separation in longitude. In situ observations reveal that at both locations there was a flank encounter – where the spacecraft crossed the first part of the CME – then encountered ambient solar wind, and finally passed near the legs of the structure. Conclusions. A scenario covering all evidence is proposed for both locations with a general view of the whole structure and solar wind conditions. Also, the study shows the necessity of having multipoint observations of large-scale structures in the heliosphere.

The eccentricity growth phenomenon for MEO navigation satellites

Lunisolar resonances shape the dynamics in the MEO region and have the effect of increasing an object’s eccentricity possibly up to a value so high that the orbit’s perigee reaches the atmosphere and friction determines the re-entry. The focus of this paper is the eccentricity growth phenomenon observed for navigation satellites. In particular, starting from a secular Hamiltonian model, analytical estimates for the maximum eccentricity reachable along an inclination-only dependent lunisolar resonance are derived as a function of the initial inclination. Also, trajectories that minimize an object’s lifetime are studied, and analytical estimates for such a minimum lifetime are provided as a function of the initial eccentricity of the object. In addition, lifetime cartography maps are presented in the plane of the argument of perigee and the longitude of the ascending node.

Wave impact pressure and pressure impulse on a square column with an overhanging deck in regular waves

As the main component of semi-submersible platforms, the deck-column structure is inevitably subjected to severe wave impacts in extreme ocean environments. The wave impact pressure and its time integral, impact pressure impulse, play an important role in the structural design, especially for the analysis of dynamic response. To investigate the characteristics of impact pressure and pressure impulse, wave impact tests on a square column with overhanging deck were carried out under a series of regular waves. Wavelet denoising technique and empirical mode decomposition (EMD) method were employed to remove the noise interference and the dynamic amplification effect from raw data. Considering the stochastic feature, statistical analysis of pressure impulse was performed based on generalized extreme value (GEV) and two-parameter Weibull distribution models. The results show the strong variability of the wave pressure impulse and the necessity of statistical analysis even in regular waves. The peak impact pressure is more sensitive to the variation of initial air gap and column incline angle than the pressure impulse. The probability distribution of extreme pressure impulse agrees well with the GEV distribution and is mainly distinguished by the shape parameter. Furthermore, the probability distribution of extreme pressure impulse is significantly affected by the initial air gap, and the effect is also related to wave parameters. The present research reveals the probability distribution of wave pressure impulse in regular waves and lays a foundation for the statistical analysis of pressure impulse in irregular waves.

Strategies selection for building e-commerce platforms for agricultural wholesale markets: A tripartite evolutionary game perspective.

The rapid advancement and widespread implementation of digital technology have created opportunities for the e-commerce transformation of agricultural wholesale markets. The building of e-commerce platforms in this process is of utmost importance and should be approached methodically. This article analyzes the interests and behavioral choices of the agricultural wholesale markets, local government, and wholesalers by establishing a tripartite evolutionary game model. It applies replicator dynamics equations to describe the evolutionary strategies of each party. The findings of the study indicate that the behavioral choices of agricultural wholesale markets, local government, and wholesalers are influenced by their initial intentions. Furthermore, there exists a degree of alignment between the choices made by agricultural wholesale markets and wholesalers. The building of e-commerce platforms by agricultural wholesale markets can be facilitated through direct and indirect government subsidies; this also motivates wholesalers to adopt and utilize these platforms. Agricultural wholesale markets may further incentivize wholesalers to utilize their own e-commerce platforms by offering additional benefits. On the other hand, if the agricultural wholesale markets demonstrate strong initial inclinations toward using third-party e-commerce platforms. In this scenario, the local government has the potential to promote the widespread use of these platforms by providing both direct and indirect financial incentives to these markets, as well as actively encouraging wholesalers to participate in them. This study presents policy recommendations for agricultural wholesale markets and local government to support the effective implementation of e-commerce platforms in the agricultural wholesaler markets and facilitate a smooth transition to e-commerce in agricultural wholesale markets.

The Effect of Radial Inclination on the Stage of Kienbock Disease at the Time of Initial Diagnosis.

Negative ulnar variance is a widely accepted risk factor for the development of Kienbock disease (KD). Variation in radial inclination has been proposed as a risk factor, but evidence thus far has been inconclusive. We aim to clarify the relationship between radial inclination and KD. A retrospective analysis of all KD patients from a single institution from 2007 to 2021 was conducted. Radiographs were reviewed to measure anatomic parameters and stage of disease. An exploratory multinomial regression model was created to examine the association of patient age, radial height, ulnar variance, radial inclination, volar tilt, scapholunate angle, duration of symptoms prior to evaluation, history of wrist trauma, and diagnosis of diabetes with stage of disease. Fifty-seven cases of KD were identified, with a mean duration of disease of 33.3 months. A history of trauma to the wrist was common (53%) and significantly associated with stage of disease at initial presentation. Twenty-seven cases (47%) were stage IIIB or greater. The average initial radial inclination, radial height, and ulnar variance was 21.9°, 10.7 mm, and -1.23 mm, respectively. A multinominal logistic regression model revealed decreased initial radial inclination is associated with Lichtman stage IIIB or greater at the time of initial patient presentation. A correlation exists between decreased radial inclination and more advanced KD at presentation, suggesting this may be a risk factor for disease progression. This correlation is strengthened by our finding of decreased ulnar variance being associated with later stage at presentation, which is one of the most widely accepted proposed risk factors for development and progression of disease. IV.

ЕНЕРГЕТИКА БРАННЯ СТЕБЕЛ ЛЬОНУ ДИСКОВО-ПАСОВИМ ЛЬОНОБРАЛЬНИМ АПАРАТОМ

The article describes a new design of the disc-belt flax-pulling apparatus, which will increase the durability of the pulling belts and reduce the material consumption of the flax gleaning machine. The geometrical parameters of the pulling section of the disc-belt flax-pulling apparatus have been established. The energetics of the process of picking flax stalks, which are clamped in the curved longitudinal pulling stream of the disc-belt flax-pulling apparatus, have been theoretically investigated. The dynamics of changes in the components of pulling power when moving the flax stalk along the pulling stream were studied, depending on: the initial inclination of the flax stalk; from the forward speed of the flax harvester; from the angle of inclination of the pulling apparatus to the horizon. The energy per second of pulling and the value of its components are determined.

Scaling behavior of granular columns collapse on erodible-inclined surfaces

This paper explores the effects of slope angle, initial column aspect ratio, and interparticle friction coefficient on the mobility and erodibility of granular columns collapsing on an erodible-inclined layer before spreading and depositing on a nonerodable-horizontal surface using Discrete Element Method. The numerical results showed that the column collapse with higher aspect ratio or smaller friction coefficient induces larger normalized kinetic energy, leading to larger granular masses out the inclined region and longer runout distance. The slope angle, on the other hand, shows trivial impacts on the kinetic energy and apparent friction coefficient. Remarkably, these physical quantities are nontrivially behaved by a new dimensionless number that incorporates the initial column aspect ratio, inclination angle, and interparticle friction coefficient. These findings may significantly complement the better understanding of the behavior of natural disaster events such as landslides, rock and snow avalanches, or pyroclastic flows on complex surfaces.

Coupled vibration characteristics of marine shafting with complex change of inclination under ice loads

With the intensifying exploitation of the resources and the waterway of the Arctic region in worldwide, the variable inclination propulsion system are gradually used in the ice-sailing ship, its design and strength study are of great engineering significance and application value. A variable inclination propulsion shafting with universal joint is introduced and its mechanical model is established in this paper. By combine torsional stress and inclination angle calculation, a decoupling algorithm based on Newmark is designed, and then the analysis of ice loads response in both frequency domain and time domain are completed. The results show that due to the complex triangle function relation among the various components of the shafting, there is an interaction between the propeller and the transmission shafting. In particular, when considering the dynamic change of inclination, nonlinear bending-torsional coupling vibration may occur and further lead to the enhancement effect of torsional vibration. Among the three working conditions defined by DNV, the bending-torsional coupling effect vary with rotation speed and inclination angle, and is mainly concentrated in high frequency bands. In the ice loads condition 2, with the largest time domain excitation amplitude and the smallest high order component, it’s vibration response is the strongest, and the change law of dangerous phase angle is similar to the bending moment. With the increase of initial inclination angle, the amplitude of low frequency vibration decreases, yet the amplitude of high frequency vibration increase. This trend is more obvious with the increase of rotation speed, and more high frequency resonance points appear in the condition 1 and condition 3.

Large Deflection Model and Optimal Design for a Morphing Wing Leading-Edge Skin

Morphing leading edge has great potential to enhance the flight efficiency of a vehicle due to its smooth and seamless surface. To improve the computational efficiency of leading-edge bending deformation, this paper developed a parametric method for modeling the large planar deflection of the flexible skins. Based on the chain beam constrained model, the curvature of the skin is approximated by introducing the parameter of the initial inclination angle. The correctness of the model is verified through tests and finite element analysis. Based on this model, the number and position of driving points, the magnitude of driving force, and the thickness of the skin were optimized with the accuracy of leading-edge bending deformation as the optimization target. The results show that the accuracy of leading-edge bending deformation gradually improves as the number of drive points increases and the driving force range expands. The solution’s accuracy with the driving point’s target position as the driving variable is significantly higher than that of the solution with the driving force magnitude as the variable. The change in skin thickness can provide a local improvement in accuracy for the part of the curvature that has a large variation.