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    2025,23(10):1-9, DOI: 10.6052/1672-6553-2025-040
    Abstract:
    Structural dynamics modeling is a key technological task in the development of launch vehicles, load design, mechanical environment prediction, control system design, and POGO vibration suppression. Combined with the development process of launch vehicles, the application of structural dynamics analysis technology in the field of launch vehicles is reviewed from four aspects: beam model, beam-shell hybrid model, 3D model based on direct modeling and 3D model based on model assembly. Combining the development of numerical computation technology and the iterative development path of launch vehicles, this analysis examines the trends in the engineering application of launch vehicles from several aspects, including efficient liquid-solid coupling computational technology, multidisciplinary dynamics analysis technology, dynamics analysis twin technology, and launch vehicle dynamics analysis technology based on artificial intelligence. These insights provide guidance and reference for the future design of rockets.
    2025,23(10):10-17, DOI: 10.6052/1672-6553-2025-059
    Abstract:
    Fluid-conveying pipes hold significant engineering value. In practical applications, pipes are often subjected to vibrations due to various factors. Excessive vibration amplitudes can cause damage to the pipe itself and its supporting structures, while even minor vibrations may lead to cumulative damage over time. Therefore, mitigating pipe vibrations has become a critical issue that needs to be addressed.In this study, a fluid-conveying pipe model is established based on the Timoshenko beam theory. The nonlinear energy sink (NES) cell, as a novel vibration suppression concept, is applied to reduce pipe vibrations. The governing equations of the system are derived using the generalized Hamilton’s principle, and the system’s natural frequencies are obtained through the complex modal method. The system’s response is solved using the harmonic balance method and numerical simulations. The influence of different NES cell quantities and installation configurations on vibration suppression efficiency is investigated. The study found that when external excitation is near specific frequencies, a single-point concentrated distribution exhibits superior vibration reduction performance, whereas multi-point concentrated and uniform distributions provide better vibration reduction efficiency for broadband excitation, providing theoretical guidance for vibration control in engineering pipes.
    2025,23(10):18-25, DOI: 10.6052/1672-6553-2025-042
    Abstract:
    To investigate the impact of geometric nonlinearity on human-induced vibrations of flexible suspension bridges, a nonlinear finite element model of a flexible pedestrian suspension bridge is established based on an engineering background and validated using measured results. Subsequently, nonlinear transient vibration analysis of the suspension bridge, considering geometric nonlinearity, is conducted. This analysis reveals the structural displacement response time histories and time-frequency characteristics under different main cable sag-to-span ratios and excitation amplitudes, as well as the response-excitation amplitude curves. The results indicate that single-frequency excitation at low-order vertical modes can induce high-order frequency vibrations at 1∶2 and 1∶3 ratios. When the ratio of vertical to horizontal natural frequencies is close to 2∶1, a certain level of vertical excitation on the main girder can cause lateral sway of the structure. Increasing the main cable sag-to-span ratio can effectively suppress vertical and lateral coupling vibrations. As the vertical excitation level increases, the sway amplitude exhibits a sudden jump and significant increase at a critical excitation level. Under pedestrian-induced excitation, the flexible suspension bridge exhibits significant geometric nonlinear vibration characteristics.
    2025,23(10):26-34, DOI: 10.6052/1672-6553-2025-037
    Abstract:
    For a new type of multi-segment pontoon bridge with alternately supported floats in the span range, a theoretical model of the dynamic response that can simultaneously consider the roles of connection hinge stiffness and float support stiffness is established.In the model, the pontoon segments are regarded as Euler-Bernoulli beams with hinges at both ends, and the action of the floating body and the hydrostatic water is equivalent to the elastic support distributed along the length of the beams, and the neighbouring segments are connected by hinges with rotational stiffness.The relationship between the structural self-resonance characteristics and the moving vehicle load response with the above two stiffness parameters is investigated.The results show that: the method can obtain the response sensitivity interval of the floating body support stiffness and the rotational stiffness of the connection hinges; with the increase of the rotational stiffness, the segment connection transitions from articulation to rigidity, and the relative angle of the two ends of the hinged joint in the modal state is changed from the “sharp angle” mutation form to the smooth form; when the rotational stiffness is smaller, there is the vertical direction of the connection.When the rotational stiffness is small, there are vertical displacement extremes and corner mutations in the connection, and the structural displacement and internal force envelope tends to be stable after increasing to a specific value.
    2025,23(10):35-44, DOI: 10.6052/1672-6553-2025-050
    Abstract:
    This study presents a reinforcement-learning-based intelligent configuration method for optimizing the actuation of multi-segment earthworm-like robots. First, a dynamic model of the multi-segment robotic system is established, and the actuator arrangement problem is formulated as a Markov decision process. By designing a multi-discrete action space, computational costs are significantly reduced. A reward function integrating locomotion speed and energy consumption constraints is proposed to effectively balance exploration and exploitation. For actuator-limited conditions, an action masking mechanism enables efficient policy search under hard constraints. Key findings include: (1) Midline-symmetric actuation yields optimal performance under full-drive conditions; (2) A “posterior-priority, centripetal-clustering” distribution pattern emerges under constrained actuation.
    2025,23(10):45-52, DOI: 10.6052/1672-6553-2025-039
    Abstract:
    The inverse kinematics of redundant manipulators require avoiding joint limits to ensure that the solutions are subject to the actual physical constraints. Current methods based on differential kinematics typically consider only local instantaneous states and cannot guarantee that the joints remain within the physical limits throughout the continuous motion. To address this issue, this paper proposes an inverse kinematics method for redundant manipulators based on model predictive control. By combining the null space parameterization of the Jacobian matrix, the proposed method effectively accounts for the future evolution of the system's kinematic states and constraints. The constraints and optimization objective functions are designed to handle joint limits, and the inverse kinematics problem is transformed into a constrained optimization problem, where redundancy is fully exploited to avoid joint limits. Furthermore, to ensure the feasibility of the optimization problem, a task scaling method is introduced to handle violations of constraints by the end-effector velocity. Simulation experiments with a 7-DOF redundant manipulator demonstrate that, compared with benchmark methods, the proposed method can predict and avoid potential joint limit violations while accurately tracking the target trajectory of the end-effector.
    2025,23(10):53-60, DOI: 10.6052/1672-6553-2025-043
    Abstract:
    Blade tip clearance is one of the most critical factors affecting the flight safety of coaxial rigid rotor helicopters. To achieve high-precision calculations of blade tip clearance in forward flight, this study establishes a rotor/body coupling aeroelastic model based on 15-degree-of-freedom (15-DOF) medium-deformable beam and free wake model. Validation against the rotor natural frequency of XH-59A demonstrates a computational error that less than 5%, confirmed the accuracy of the forward-flight blade tip clearance prediction method. This study analyzes the influence of lateral differential control, pitch angle, and sideslip angle on blade tip clearance during forward flight. The results indicate that lateral differential control can effectively control rotor rolling moment, and lateral differential control serve as a reliable means to ensure safe blade tip clearance during forward flight. Additionally, a decrease in fuselage pitch angle during forward flight leads to more critical blade tip clearance conditions. An increase in sideslip angle affects the rotor lift offset and reduce blade tip clearance.
    2025,23(10):61-67, DOI: 10.6052/1672-6553-2025-053
    Abstract:
    Low- and medium-frequency noise transmits vibrations to the cabin structure, which subsequently radiates noise into the interior. In order to solve the vibration and noise optimization problem of stiffened thin plates, topology optimization is utilized to improve the vibration and noise reduction effects by optimizing the layout of stiffeners. This study focuses on four-edge clamped stiffened thin plates and employs density-based topology optimization method to maximize its first-order modal frequency. Under the constraint of constant mass, the optimal distribution of stiffeners on the plate is designed. Modal, stiffness, and sound transmission loss analyses are conducted for the stiffened thin plate before and after optimization. The results show that the optimized stiffened plate achieves an increase in its first-order modal frequency and improves sound transmission loss within a certain frequency range, without significantly reducing the overall stiffness. The study provides a reference for vibration and noise reduction optimization in the structural design of stiffened plates.
    2025,23(10):68-76, DOI: 10.6052/1672-6553-2025-074
    Abstract:
    Based on the Shanxi Linyi Yellow River Bridge, an experimental study was conducted to investigate the wind-induced vibrations and control measures of an ultra-long steel launching nose during the incremental launching construction of a steel-concrete composite girder bridge. First, the dynamic characteristics of the bridge structure were analyzed using the finite element method. Then, aeroelastic models of the bridge with the launching nose were designed and fabricated. Wind tunnel tests under turbulent flow conditions were carried out to examine the buffeting responses of the launching nose under different yaw angles. Finally, considering the actual characteristics of the bridge, an inclined stay cable system anchored at the center of the pier was proposed to suppress the wind-induced vibrations of the launching nose. The results show that under the design reference wind speed, the standard deviations of vertical and lateral displacements at the cantilever tip of the launching nose are 0.10 m and 0.04 m, respectively. Within a yaw angle of 30°, the vibration responses remain relatively constant, while a significant reduction is observed when the yaw angle exceeds 30°. The proposed inclined wind-resistance cables can reduce the vertical vibration magnitude at the cantilever tip by approximately 50%.
    2025,23(10):77-86, DOI: 10.6052/1672-6553-2025-056
    Abstract:
    With the continuous development of intelligent driving technology, the demand for high-precision vehicle status information is becoming increasingly urgent. Road gradient is a key parameter for vehicle operation, having a significant impact on the vehicle's dynamics control. High-precision and low-latency road gradient estimation is a prerequisite for precise control, which can effectively enhance the intelligence level of the vehicle. Adaptive extended Kalman filter (AEKF) is a commonly used algorithm for road gradient estimation, but it has certain limitations in complex operating conditions with different noise levels. This paper proposes an improved adaptive Kalman filter algorithm, which enhances the estimation accuracy of road gradients in complex conditions by setting dynamic noise scaling factors. Through simulation tests under double lane change conditions and steady-state circular motion conditions, the effectiveness of the proposed method is verified, achieving a road gradient estimation accuracy with a root mean square error (RMSE) of less than 2°.
    2025,23(10):87-96, DOI: 10.6052/1672-6553-2025-083
    Abstract:
    During the process of the end effector of an industrial robot arm accurately tracking the welding path, there exist joint friction (disturbance) and communication time delay. To address such issues, this study investigates the performance output tracking problem of a one-dimensional unstable heat equation, where the model involves unknown external disturbances and the input end exhibits time delay.Based on the properties of the first-order transport equation, the control system can be modeled as a cascaded system consisting of a heat equation and a transport equation, with the transport equation serving as the actuator dynamic of the heat equation system. The system features a non-collocated structure; the difficulties arising from this structure are resolved by constructing an appropriate auxiliary system, and the control problem of the cascaded system is solved via the actuator dynamics compensation method.An error-based observer is constructed to simultaneously estimate external disturbances and system states, and a full-state feedback law is successfully designed to achieve the performance output tracking of the system. Finally, it is proven that the designed observer is well-posed and the resulting closed-loop system possesses exponential stability.
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    2014,12(3):269-273, DOI: 10.6052/1672-6553-2014-043
    [Abstract] (3704) [HTML] (0) [PDF 336.30 K] (21955)
    Abstract:
    Aiming at the problem that the longitudinal modes of structural system of rocket need to be identified from its integral modes in engineering, a method that automatically identifies the longitudinal modes of structural system of rocket was proposed according to the theory of modal effective mass. Taking the vibration characteristics of system with lumped mass as a computing example, applying the finite element software, the beam model of system with lumped mass was established, and the longitudinal modes of the system were automatically identified based on the method. Compared with the system modal information calculated by the method of modal analysis, this automatic identification method not only can accurately identify the longitudinal modes of vibrating system, but also has automatic and high efficiency identification feature. It provides a theoretical basis for the dynamic model of POGO vibrating system in liquid rockets and other model of engineering systems to be accurately and promptly established.
    2014,12(3):193-200, DOI: 10.6052/1672-6553-2014-046
    [Abstract] (3520) [HTML] (0) [PDF 748.46 K] (19456)
    Abstract:
    The spacecraft's ability to adapt to the harsh dynamics environment is critical for the whole space mission. Vibration test control technology is the key part of the dynamic environment test. The current progress, fundamental principles and key techniques development level of the spacecraft and vibration control algorithms overseas were analyzed. The basic ideas, effective ways and suggestions were given to domestic following research.
    2017,15(5):385-405, DOI: 10.6052/1672-6553-2017-039
    [Abstract] (2276) [HTML] (0) [PDF 1.91 M] (19242)
    Abstract:
    In this review article, the growth and related academic communications in the dynamics of multibody systems are firstly surveyed. Then, the recent advances in the numerical algorithms for solving the dynamic equations of flexible multibody systems, the contact/impact dynamics of flexible multibody systems and the deployment of flexible space structures are systematically reviewed, together with several open problems of concern. Finally, some suggestions are made for the prospective researches on the dynamics of flexible multibody systems.
    2014,12(1):18-23, DOI: 10.6052/1672-6553-2013-068
    [Abstract] (3337) [HTML] (0) [PDF 1.13 M] (18930)
    Abstract:
    The electromechanical coupling model of cantilevered piezoelectric harvester was developed by considering the nonlinearities of piezoelectric material, based on Hamilton theory, Rayleigh-Ritz method, Euler-Bernoulli beam theory and constant electrical field across the piezoelectric element. The response characteristics of the system were investigated numerically, and the influences of piezoelectric material nonlinear coefficient on the system response were analyzed. By exploring the nonlinear characteristics of the piezoelectric vibrator near the resonant frequency, the nature of the multi-solutions and jump phenomena in the resonance region was revealed. The results were verified experimentally. which provides a theoretical basis for the study of nonlinear mechanism of piezoelectric power generation system.
    2014,12(3):243-247, DOI: 10.6052/1672-6553-2014-054
    [Abstract] (2753) [HTML] (0) [PDF 1.07 M] (18513)
    Abstract:
    Random vibration test is very important to the aerospace equipment. The windage of ASD outside the frequency bandwidth was analyzed. The reason, premonition, affection and effective way were given. And the commonly used random vibration test and vibration test metrology standard for the ASD outside the frequency bandwidth were analyzed.
    2016,14(2):97-108, DOI: 10.6052/1672-6553-2015-009
    [Abstract] (2769) [HTML] (0) [PDF 1.87 M] (18357)
    Abstract:
    Based on the current research status of multi agents system control theory and technology, the paper makes a detailed overview for unmanned ground systems. From two aspects of behaviour and task cooperative control for multi agents, the relevant theory and application problem is discussed. Moreover, some existed open problems are presented and a possible future development is proposed. For unmanned ground systems, cooperative control will be of great importance in promoting social and military benefits and maximizing the executive function of ground mission.
    2015,13(5):361-366, DOI: 10.6052/1672-6553-2014-064
    [Abstract] (1484) [HTML] (0) [PDF 826.19 K] (18182)
    Abstract:
    Dynamic and control systems often contain uncertain parameters that may result in uncertain predictions. In the interest of quantifying the effects of parameter uncertainties on response variability, this paper develops a stochastic response surface based method for the sensitivity analysis of uncertain parameters. Stochastic response surfaces were firstly constructed to describe the explicit relationships between uncertain parameters and responses. Then partial derivations were performed on the mathematical expressions of stochastic response surfaces in order to obtain sensitivity indices that simultaneously embody the effects of parameter means and standard deviations. Lastly, the developed method has been verified against a numerical cantilever beam containing uncertain geometric and material parameters. The sensitivity analysis results were compared with those given by the analysis of variance method.
    2014,12(3):225-229, DOI: 10.6052/1672-6553-2014-051
    [Abstract] (2716) [HTML] (0) [PDF 1.38 M] (18093)
    Abstract:
    Based on the staggered solution procedure of ANSYS and CFX software, the fluid structure coupling response of projectile during tail slapping has been researched. Structural response was simulated by using FEM and flow field was simulated by using inhomogeneous model and SST turbulence model. Finally, the influences of fluid structure coupling effect have been analyzed and the change law of body stress has been given.
    2013,11(1):12-19, DOI: 10.6052/1672-6553-2013-003
    [Abstract] (2713) [HTML] (0) [PDF 530.95 K] (17969)
    Abstract:
    The dynamics of the whole aero-engine system has always been the important part that cannot be neglected in the research and design of the engine, as the framework of the engine, the vibration of the casing directly reflects the level of the whole aero engine vibration. In this paper, an analysis was made on the research of the problems and fault classification of aero-engine casing dynamics, and an overview was made on the research of present situation, development trend, problems and solutions of the domestic and foreign of casing dynamics, which expanded the present situation of the Inclusiveness problems of aero-engine casing dynamics. Finally, some proposals were put forward for the development of the casing dynamics suitable for our country aero-engine technology level.
    2012,10(1):21-26, DOI:
    [Abstract] (1055) [HTML] (0) [PDF 567.09 K] (17632)
    Abstract:
    A discrete finite dimensional dynamical model was built to describe the space large overall motion of tethered satellite system with an infinite dimensional viscoelastic tether in a long time. The tethered satellite system is a complex nolinear dynamic system. Considering the tether’s viscoelasticity, distributed mass and space form, the established improved bead model can meticulously describe the tether’s vertical and horizontal vibration. According to tether’s characteristic of tensile and not compressive, the slack tether unit model was set up to accurately reflect real stress of tether. The determination of the number of degrees of freedom of the system was studied. Based on numerical integral calculation, the dynamic response was obtained via numerical simulation of the deployment, retrievement and retainment process of tethered satellite system in a long time. The result is convergent. The simulation proves the important role of the stable equilibrium position in the dynamics of tethered space system.
    2008,6(4):301-306, DOI:
    [Abstract] (1479) [HTML] (0) [PDF 0.00 Byte] (17623)
    Abstract:
    The problem of P and PI feedback control to a time delay system was investigated,with the emphasis on the determination of the feedback gains that ensured the asymptotical stability of the delayed system. By means of Lambert W function,the feedback gain of P control can be expressed explicitly,so that the optimal feedback gain can be easily obtained. For the system under a PI control,the stable region of the feedback gains was determined on the basis of stability switches and D subdivision,and the optimal feedback gains that enabled the system to admit maximal stable margin were figured out numerically by using Lambert W function. From the viewpoint of computation,the present method is much simpler than the available methods.
    2014,12(2):183-187, DOI: 10.6052/1672-6553-2014-025
    [Abstract] (1583) [HTML] (0) [PDF 811.52 K] (17351)
    Abstract:
    PMSM due to little harmonic, high precision torque, commonly is used in the servo system and the high performance speed control system. In this paper,the physical model of PMSM is simplified and the mathematical model of the motor is established in order to facilitate research.Thispaper uses id=0 control manner which is the simplest manner is vector control methods,motor electromagnetic torque equation is established based on rotor field oriented vector control.The system model, speed and current control block are build and simulated with MATLAB/Simulink.Simulation results shows that the waveform is consistent with thoretical analysis,the model has fast response and small overshoot.The system runs stably with good dynamic and static characteristics. The simulation makes full use of modularization design. All the parameters and their influence on the system can be changed and observed.It also can easily validate the control strategies and select the most suitable one. So this kind of simulation is good for system design and adjusting and validating.
    2014,12(3):205-209, DOI: 10.6052/1672-6553-2014-059
    [Abstract] (2325) [HTML] (0) [PDF 467.15 K] (14846)
    Abstract:
    This paper investigated the passive nonlinear vibration control method used for energy absorbing in structures of spacecrafts. The structure and the dynamic model of the nonlinear energy sink which could adapt to the space environment were proposed. As nonlinear spring could not be acquired easily in reality, we proposed a new design for the NES based on employing an asymmetric NES force which was generated by two pairs of aligned permanent magnets. Then, the dynamic model for a cantilever beam structure coupled with nonlinear energy sink had been built theoretically. In addition, the passive vibration suppression effect of the nonlinear energy sink on the cantilever beam structure under transient excitation had been analyzed through Galerkin method and numerical analysis method. The results showed that the NES acquired up to 92% dissipation of the system energy imposed by shock excitation, hence the NES could adapt to the space environment and improve the reliability of space system.
    2014,12(3):283-288, DOI: 10.6052/1672-6553-2014-061
    [Abstract] (3374) [HTML] (0) [PDF 479.50 K] (14148)
    Abstract:
    A method was presented to analyze the nonlinear flutter. Based on this method, the flutter characteristics of the high aspect wing were illustrated. The numerical results show that the flutter speed is decreased when the first horizontal bending mode involved. Secondly, this study discussed how the main direction of the composite influenced the character of the nonlinear vibration and flutter, and established the method of the flutter clipping to the high aspect wing. And the result shows that the stiffness of structure can be changed by changing the main direction of the composite. It mainly changes the horizontal bending mode, makes the main direction tend to the trailing edge, and then makes the section line move to the leading edge. Further analyzing the nonlinear flutter reveals that it is the changing of the horizontal bending mode that causes the flutter speed change obviously. And by the section line of this mode moves ahead, the flutter speed will become larger. In the study, two examples were illustrated to validate its truthiness.
    2013,11(4):357-362, DOI: 10.6052/1672-6553-2013-041
    [Abstract] (1638) [HTML] (0) [PDF 350.50 K] (12232)
    Abstract:
    At present, the main task of designing a mounting system of automotive engine powertrain is to select appropriate stiffness, position and angle of mounting components so that free-vibration modal frequency of the mounting system can avert from the exciting-force frequency at the idle speed of the engine and the natural frequency of vibration of the vehicle body and that the decoupling degree of each mode shape is increased as far as possible, so as to improve the vibration-isolation effect of the mounting system. The design of a mounting system based on strict decoupling at predetermined frequencies is to make the modal frequencies of the designed mounting system completely equal to the frequencies predetermined in accordance with the frequency planning of automotive design, and to enable strict decoupling of each mode shape of each mode, i.e., the decoupling degree of vibration energy in every direction equals to 1. Based on a free-vibration equation for a mounting system, this paper presents an equation system for designing a mounting system with strict decoupling at predetermined frequencies, provides a solving method for this equation system by using the theory of generalized inverse matrix or method of constructing function, so as to provide an optimal design method more efficient and simpler than the current modal optimization method of mounting system. Relevant example has validated the correctness of equations and solving method of the strict-decoupling design at predetermined frequencies.
    2016,14(3):247-252, DOI: 10.6052/1672-6553-2015-052
    [Abstract] (2126) [HTML] (0) [PDF 2.18 M] (9447)
    Abstract:
    Tires are the only carrier of the contact between the vehicle and road surface. Their mechanical property is important for analysis and control on the vehicle dynamic response. At present, the tire simulation mostly focuses on the steady state model. But it can not describe the dynamic characteristic of the tire accurately. Therefore, it plays a significant role to add the dynamic tire model in the vehicle dynamics simulation. The tire friction model in the multi body dynamical software ADAMS is static, where the friction is regarded as a static value. However, in actual, the friction between the tire and road surface is dynamic, and it should be a dynamic function of the relative velocity and displacement. To this end, in this paper, the dynamic tire LuGre model using the Matlab/Simulink software is constructed. Through connecting the interface with Adams/Car, co simulation between the vehicle model and the simulink tire model is carried out in order to achieve the dynamic contact between tire and road and improve the accuracy of vehicle system analysis.
    2014,12(1):36-43, DOI: 10.6052/1672-6553-2013-110
    [Abstract] (2429) [HTML] (0) [PDF 2.22 M] (7914)
    Abstract:
    The coupling nonlinear dynamic model of dual rotor system was established by using finite element method, and then the critical speed of revolution and mode shape were calculated by using the software MATLAB. In addition, the unbalance responses of dual rotor system were studied, and the vibration performances in different speeds of dual rotor casing systems were obtained. The research provides a theoretical basis for the design of the dual rotors system in engineering.
    2014,12(3):253-258, DOI: 10.6052/1672-6553-2014-056
    [Abstract] (2306) [HTML] (0) [PDF 1.00 M] (6328)
    Abstract:
    Taking account of the structural stiffness and the low order vibration frequencies, two schemes of multi-objective topology optimization were proposed to obtain the best aircraft lifting-surface structural design. Based on penalized density theory, the scheme one (named as constrain method) is to convert the multi-objective optimization to single-objective optimization by considering the minimum structural mass as the objective with constraints of reference points displacements and the low order vibration frequencies. The scheme two (named as the combination of constrain method and criterion function method) settles the multi-objective optimization by defining combined compliance index (CCI) as the objective, with the constraints of volume fraction and the low order vibration frequencies. The CCI is the function of structural compliance and low order vibration frequencies. Numerical results demonstrate the proposed schemes not only realize reducing the structural mass but also raise the first and second order frequencies.
    2014,12(3):201-204, DOI: 10.6052/1672-6553-2014-048
    [Abstract] (2408) [HTML] (0) [PDF 296.79 K] (6025)
    Abstract:
    Non-linear factors cannot be avoided in the design of aircraft structures. In this paper, a two-degree-of-freedom airfoil and cubic stiffness nonlinearities in pitching degree-of-freedom operating in supersonic flight speed regimes has been analyzed. The averaging method and the theory of flutter were used to analyze the nonlinear dynamic system of the dualistic airfoil in the supersonic flow. Then the correctness of the theoretical calculation was verified by numerical calculation, and the analysis result was given.
    2014,12(1):62-66, DOI: 10.6052/1672-6553-2013-097
    [Abstract] (1860) [HTML] (0) [PDF 832.87 K] (5460)
    Abstract:
    A spline finite point method was presented to study the natural frequency of arch. The displacement mode shape function of the arch free vibration was simulated with a linear combination of cubic B spline. The free vibration frequency equation of arch structures was derived according to Hamilton principle, in which the effect of the dead load was considered. Meanwhile, the effect of the dead load on the natural frequency of arch structures was analyzed. The results show that the natural frequency of arch is reduced. The effect of influence depends on the stiffness of the arch itself. When the arch stiffness is certain, the bigger the rise span ration and the radius to thickness ration, the higher the effect of the dead load on the natural frequency of arch structures.

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