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    2023,21(5):1-15, DOI: 10.6052/1672-6553-2022-020
    This paper proposes a dielectric elastomer (DE) soft actuator with sensing function, which can achieve synchronous measurement and control of membrane structures surfaces. Firstly, the dynamic model of electric driven process of the DE actuator is established, which can describe its electro-mechanical coupling behavior. Then, the parameters of the dynamic model are identified by a series of experiments. Moreover, the influence of some model parameters on dynamic responses of the DE actuator are analyzed to understand its basic dynamic characteristics. Next, the simplified circuit model for self-sensing process of the DE actuator is established, and the relationship between the electrical parameters and displacement of the DE actuator was calibrated experimentally. Finally, experiments of adaptive control of membrane surface are carried out, and the corresponding control strategy is designed. Experimental results indicate that the DE actuator has high precision in both actuation and sensing. Therefore, the DE soft actuator is highly promising in construction of high-precision space membrane antennas.
    2023,21(5):16-26, DOI: 10.6052/1672-6553-2022-069
    Dynamic analysis of functionally graded material beams using meshless point interpolation method and radial basis point interpolation method. On the basis of considering the shear effect,the thermal strain is also included in the constitutive relationship of the beam. The deformation field of the beam is discretized by four discrete methods,the first order approximate rigid flexible coupling model of the functionally graded material beam with large overall motion is derived via Lagrange’s equations of the second kind,and the dynamic response of the beam under different temperature fields is studied. The simulation results show that the temperature field has little influence on the transverse deformation of the functionally graded material beam with transverse symmetry distribution,but has great influence on the longitudinal deformation. The influence of axial deformation should not be ignored in the temperature field.
    2023,21(5):27-34, DOI: 10.6052/1672-6553-2022-032
    A dynamic model of planetary gear system including random backlash, friction, time varying meshing stiffness and other factors affecting gear vibration is established. The nonlinear dynamics method is used to solve the equation, and the influence of excitation frequency on the system is analyzed. The active noise reduction measures of profile modification are proposed, the system is improved, and the dynamic equation of planetary gear system is recalculated. The influence of the excitation frequency on the improved system is solved and analyzed, and compared with the results obtained by the original system, it can be seen that the modification is effective for the vibration reduction of the gear system.
    2023,21(5):35-43, DOI: 10.6052/1672-6553-2022-044
    In this paper, a stochastic averaging method based on elliptic function is proposed to evaluate the probabilistic solution of ship roll motion excited by bounded noises. We carry out local sensitivity analysis on the rolling model to analyze the influence of main parameters, thus laying a foundation for the random analysis. By introducing the Jacobi elliptic functions (JEFs), we acquire the stochastic differential equation and the Ito equation regarding the amplitude and phase of the roll motion. Then, we obtain the probabilistic solutions of the rolling system by solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation. Then apply this method to investigate the probabilistic solution of ship’s nonlinear rolling motion under bounded noise excitation, which shows perfect agreement with the sensitivity quantification. Finally, the feasibility and accuracy of the proposed technique are verified by the Monte Carlo simulations.
    2023,21(5):44-52, DOI: 10.6052/1672-6553-2022-061
    In view of the contradiction that the traditional linear vibration isolator will sacrifice the vibration isolation performance while reducing the resonance peak, a vibration isolator with piecewise damping is designed. First of all, the variable damping device of moving cam is used. With the design of cam profile, the vertical damping coefficient of the system is controlled by the magnitude of vibration displacement and presents piecewise linear characteristics, and the damping characteristics of the device are analyzed. Then the piecewise damping device is applied to the vibration isolator, and the active vibration isolation system model with piecewise damping and its dynamic equation are established. The equivalent linear damping coefficient of the piecewise damping system is obtained through the energy equivalence principle, and the theoretical solution of the system response under simple harmonic force excitation is solved. The correctness of the theoretical solution is verified by the numerical simulation of the fourth-order Runge-Kutta method. Finally, the dynamic characteristics of the piecewise damping vibration isolation system are studied, and the effects of the main parameters on the amplitude frequency response characteristics and force transmissibility characteristics are analyzed. The results show that through reasonable parameter selection, the piecewise damping vibration isolator can take into account the advantages of undamped vibration isolator and linear damping vibration isolator, which can not only effectively reduce the resonance peak value of the system, but also ensure the excellent vibration isolation performance in the high frequency region. It provides a theoretical basis for the design of new nonlinear vibration isolators.
    2023,21(5):53-59, DOI: 10.6052/1672-6553-2023-008
    For rotor components in a rotating machinery, if there occurs a fault, the rotor’s vibration will increase rapidly and even result in serious damage. So the rotor needs a type of vibration energy absorption structure that has the feature of light weight and high energy absorption ratio. In this study, based on the negative Poisson ratio (auxetic) metamaterial, we propose an asymmetric star unit cell with negative Poisson ratio, and then design an arc shaped vibration attenuation structure suited for the rotor system. First, the unit cell of negative Poisson ratio is proposed and the metamaterial vibration attenuation structure is designed. Then, the collision model is established and corresponding simulation is carried out. The influences of some key parameters are investigated, e.g., the impact velocity and impact angle. It is found that for the low impact speed, the large impact angle will lead to a good energy absorption ratio; for the medium impact speed, the small impact angle will give a good energy absorption. Especially, for the high impact speed, the structure experiences plastic deformation and can reach a high energy absorption ratio. Finally, corresponding validation experiment was carried out on a rotor setup. For a rotor with two disks, the imbalance fault is produced. The experimental results show that the proposed negative- Poisson-ratio structure can attenuate the rotor vibration significantly, and absorb the vibration kinetic energy effectively.
    2023,21(5):60-68, DOI: 10.6052/1672-6553-2022-037
    In this paper, a quarter vehicle model and a uniform cross section simply supported beam model are used to establish a vehicle bridge coupling system. The global maximum values and its location on the bridge of dynamic deflection, dynamic bending moment and dynamic shear force are analyzed when the vehicle travelling through the bridge at a constant speed. The effects of vehicle speed, distance between front and rear vehicles, and bridge modal truncation order on the global maximum value are further analyzed and calculated. The results show that the vehicle speed has a greater impact on the global maximum value of dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge. Both the global maximum dynamic deflection and the global maximum dynamic bending moment appear in the mid-span range, the locations are different with different vehicle speeds. The global maximum dynamic shear force appears at the beam end of the vehicle exiting the bridge. when two vehicles are on the bridge at the same time, the greater the distance between the front and rear vehicles, the smaller the global maximum value of dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge. When a certain distance is reached, the global maximum values are no longer reduced and are the same as the case of a single vehicle. In order to improve the calculation accuracy of the dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge, the bridge modal truncation order should be greater than 3 orders, 6 orders and 7 orders, respectively.
    2023,21(5):69-75, DOI: 10.6052/1672-6553-2023-029
    The wind induced vibration performance of super long parallel cables was investigated through a series of systematic aeroelastic model wind tunnel tests. The twin cables with different attack angles and spacing ratios were tested, and the characteristics of the motion track and the suppression measures were researched. Studies have shown that the downstream cable motion is elliptical and the vibratory direction is inclined to the wind axis. The direction of the elliptical orbit is such that the cable moves downstream near the outer edges of the wake and upstream nearer the center of the wake during the process of wake galloping. When the wake galloping occurs, the downstream cable absorbs energy from the wind flow at constant velocity and the amplitude changes slowly, while with the increase of wind velocity, the amplitude is growing quickly until an apparent limit cycle is reached. However, this motion consists of large oscillations in an elliptical orbit with the long ellipse axis oriented approximately along the main flow direction rather than inclined to that. Finally, the separator measures are carried out to suppress the wake galloping, and the study results can direct both the wind-resistant design and the vibration control of the parallel cables in cable-stayed bridges.
    2023,21(5):76-85, DOI: 10.6052/1672-6553-2023-053
    In light of the changeable primary mode interval of ultra-long stay cable vibration, the inertial damper of magnetic particle clutch has greater advantages as a semi-active inertial damper than as a passive inertial damper. Existing research, however, indicates that simply injecting direct current into the magnetic particle clutch's inertial damper would not be sufficient to realize the Constant value regulated function of the damper's inertial coefficient. This function will be accomplished in this study by inputting harmonic current.. First, the fundamental operation and mechanical features of the magnetic particle clutch's inertial damper are described. From the relative motion state of the two magnetic particle clutch axes, the mechanical characteristics are evaluated, and the control method for the input current to realize the adjustable function of the inertial coefficient of the damper of the damper is explored. The equivalent inertial coefficient of the damper under steady-state excitation is then expressed, and the mechanical model of the damper is developed based on the damper's fundamental structure. The equivalent inertial coefficient of the damper under input control current and the amplitude of the control current are eventually shown to have a quadratic linear relationship.Lastly, the inertial coefficient of the damper's adjustability was verified experimentally.
    2023,21(5):86-92, DOI: 10.6052/1672-6553-2023-053
    The study on dynamic characteristics and wind resistance performance of concrete encasement stage of arch bridge with stiff skeleton has great guidance for its construction. Tian'e Longtan Bridge serves as the research model here. With the aid of FEM software MIDAS/Civil, three dimensional finite element models of Tian'e Longtan Bridge are set up. Then, the change laws of natural frequency and wind resistance performance of the bridge in different construction stages under three different working platform conditions is investigated. The results show that the lateral frequency of the bridge shows a monotonically upward trend in the process of encasing concrete, while the vertical frequency is decreased first and then increased, and the phenomenon of veering will occur. the wind resistance performance is increased first, then decreased and finally increased again. The wind resistance is also affected by the number of working platforms. The more working platform there are, the weaker the lateral wind resistance of the structure.
    2023,21(5):93, DOI: 10.6052/1672-6553-2023-055
    When the self-centering structure is subjected to earthquake or strong wind load, significant nonlinear random vibration will occur, which may lead to the structural performance greatly reduced or even complete failure.In this paper, the first-passage failure problem of a self-centering structure with two-degrees-of-freedom under random excitation is studied.The generalized harmonic balance technique is used to decompose the self-centering restoring force and obtain the equivalent random system.The average Ito stochastic differential equation with respect to amplitude is derived by means of stochastic average method.The backward Kolmogorov (BK) equation is solved to obtain the conditional reliability function (CRF) and conditional probability density function of the first pass time (PDF).As an example, Kanai-Tajimi filtered white noise model is used to analyze the influence of the change of excitation strength D and soil damping ratio ξg on conditional reliability function and conditional probability density function.The validity of the analytical solution is verified by comparing with Monte Carlo simulation results.
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    2014,12(3):193-200, DOI: 10.6052/1672-6553-2014-046
    [Abstract] (2296) [HTML] (0) [PDF 748.46 K] (4930)
    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.
    2014,12(1):18-23, DOI: 10.6052/1672-6553-2013-068
    [Abstract] (2381) [HTML] (0) [PDF 1.13 M] (4663)
    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.
    2017,15(5):385-405, DOI: 10.6052/1672-6553-2017-039
    [Abstract] (1477) [HTML] (0) [PDF 1.91 M] (4457)
    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.
    2015,13(5):361-366, DOI: 10.6052/1672-6553-2014-064
    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):243-247, DOI: 10.6052/1672-6553-2014-054
    [Abstract] (2170) [HTML] (0) [PDF 1.07 M] (4397)
    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.
    2014,12(3):225-229, DOI: 10.6052/1672-6553-2014-051
    [Abstract] (1766) [HTML] (0) [PDF 1.38 M] (4005)
    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.
    2014,12(3):269-273, DOI: 10.6052/1672-6553-2014-043
    [Abstract] (2609) [HTML] (0) [PDF 336.30 K] (3982)
    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.
    2016,14(2):97-108, DOI: 10.6052/1672-6553-2015-009
    [Abstract] (1708) [HTML] (0) [PDF 1.87 M] (3899)
    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.
    2012,10(1):21-26, DOI:
    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:
    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] (1075) [HTML] (0) [PDF 811.52 K] (3589)
    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.
    2013,11(1):12-19, DOI: 10.6052/1672-6553-2013-003
    [Abstract] (1673) [HTML] (0) [PDF 530.95 K] (3546)
    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.
    2013,11(4):357-362, DOI: 10.6052/1672-6553-2013-041
    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.
    2014,12(3):283-288, DOI: 10.6052/1672-6553-2014-061
    [Abstract] (2283) [HTML] (0) [PDF 479.50 K] (3360)
    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.
    2014,12(3):205-209, DOI: 10.6052/1672-6553-2014-059
    [Abstract] (1810) [HTML] (0) [PDF 467.15 K] (3354)
    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):253-258, DOI: 10.6052/1672-6553-2014-056
    [Abstract] (1570) [HTML] (0) [PDF 1.00 M] (3254)
    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.
    2016,14(3):247-252, DOI: 10.6052/1672-6553-2015-052
    [Abstract] (1437) [HTML] (0) [PDF 2.18 M] (3251)
    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] (1460) [HTML] (0) [PDF 2.22 M] (3189)
    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):201-204, DOI: 10.6052/1672-6553-2014-048
    [Abstract] (1907) [HTML] (0) [PDF 296.79 K] (3091)
    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] (1064) [HTML] (0) [PDF 832.87 K] (3016)
    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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