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    2025,23(12):1-12, DOI: 10.6052/1672-6553-2025-054
    Abstract:
    This paper proposes a combined dynamic vibration absorber and establishes a coupled dynamic model of an elastic simply-supported beam equipped with a dynamic vibration absorber. Using the modal superposition method, analytical expressions for the amplitude-frequency response of different vibration modes are derived. Focusing on the first-order mode of the elastic beam, analytical solutions for the optimal tuning ratio, optimal stiffness ratio, and optimal damping ratio are obtained based on the H∞ optimization criterion and fixed-point theory, along with the corresponding optimal operating range of the inerter . The validity of the derived design formulas is further verified through the finite difference method. The results indicate that connecting the inerter between the primary and secondary systems does not enhance the vibration reduction performance. In addition, the proposed dynamic vibration absorber demonstrates exhibits excellent vibration suppression capability for the first-order mode of the elastic beam and effectively broadens the vibration absorption frequency band.
    2025,23(12):13-23, DOI: 10.6052/1672-6553-2025-047
    Abstract:
    Quasi-zero stiffness (QZS) isolators have been widely studied owing to their superior low-frequency vibration isolation performance. However, the heavy damping in prototypes will lead to no relative motions between the isolated mass and the excitation at low frequencies, thus the vibration isolation is of failure at low frequencies. To address this limitation, compression springs are replaced with tension springs to reduce system damping in the prototype. These tension springs are configured to form both positive and negative stiffness structures arranged in parallel, thereby enabling the design of a QZS isolator utilizing exclusively tension springs. The QZS condition is derived from the static analysis, and the influence of key parameters on QZS features is analyzed. Wide QZS ranges around the static equilibrium position can be achieved. For dynamic analysis, the harmonic balance method is employed to validate the displacement transmissibility results calculated by the incremental harmonic balance method combined with a continuation algorithm. Theoretical predictions calculated by both methods demonstrate close agreement within the effective isolation frequency band. Finally, a prototype had been designed, fabricated and dynamically tested. Meanwhile, a corresponding simulation model was analyzed using ADAMS. Both the tested and simulated displacement transmissibilityexhibit strong consistency with theoretical predictions. The findings demonstrate that the proposed QZS isolator achieves the initial frequency of 1.5 Hz for vibration isolation and the corresponding linear isolator without negative stiffness is 6 Hz. The results verify the superior performance of the vibration isolation of the QZS isolator based on the parallel mechanism of the positive and negative stiffness structures constructed by tension springs.
    2025,23(12):24-35, DOI: 10.6052/1672-6553-2025-049
    Abstract:
    This paper investigates the problem of adaptive fuzzy periodic event-triggered control for output-feedback interconnected switched nonlinear systems under arbitrary switching. Fuzzy logic systems are employed to approximate the unknown nonlinear terms. A state observer and fuzzy adaptive laws are constructed by using only the sampled output information. To reduce the waste of communication results, a novel controller is developed that only uses the information at the event-triggered instants. Furthermore, the proposed discrete-time event-triggering mechanism performs intermittent monitoring at the sampling instants. It is finally proven that all states of the closed-loop system remain bounded under arbitrary switching, and the effectiveness of the proposed scheme is verified through simulation results.
    2025,23(12):36-45, DOI: 10.6052/1672-6553-2025-071
    Abstract:
    Based on the Linyi Yellow River Bridge in Shanxi Province, experiments and computational fluid dynamics (CFD) numerical simulations were conducted to study the mechanism of vortex induced vibration (VIV) and aerodynamic countermeasures (AC) for a steel box- concrete composite girder with sound barriers. Firstly, wind tunnel tests were conducted on the original design scheme of the girder section using a segment model with a geometric scale ratio of 1:60. Then, experimental studies were conducted to investigate the influence of the installation position of horizontal guide plates on the VIV control performance, including installing 2.0 m-wide horizontal guide plates on both webs of the steel box–concrete composite girder at a height of 2.6 m above the bottom plate (AC-1), as well as installing 2.0 m-wide horizontal guide plates at the ends of the flange plates (AC-2) . Finally, CFD simulations were performed to analyze the vortex-induced vibration and control mechanism of the original design scheme of the steel box-concrete composite girder section with/without AC-1 and AC-2, respectively, based on flow field characteristics. The results show that the original design scheme of the steel box-concrete girder section exhibits both vertical and torsional VIV at 0 ° and+3 ° angles of attack, and the maximum amplitude exceeds code-specified limits. After adopting the aerodynamic control measure AC-1 on both sides of the steel box-concrete composite girder at a height of 2.6 m above the bottom plate, the torsional VIV response of the girder section is eliminated, while the vertical VIV amplitude slightly increases. Furthermore, after adopting the aerodynamic control measure AC-2, the VIV amplitude of the girder section was effectively suppressed, and the torsional VIV of the girder disappeared. Moreover, the mechanism of VIV and aerodynamic control of the steel box-concrete girder section with sound barriers can be summarized as follows: the airflow passing over the girder section induces alternately shedding vortices on the downstream side, which leads to vortex-induced vibration. The vortex intensity shows no significant reduction after adopting the aerodynamic control measure AC-1, while the vortex intensity is weakened to to a certain extent after adopting the aerodynamic control measure AC-2, whichc ontributes to the effective suppression of the VIV response of the girder section.
    2025,23(12):46-53, DOI: 10.6052/1672-6553-2025-048
    Abstract:
    To solve the problem of large volume and storage difficulty of bridge health monitoring data, the deep convolutional autoencoder is proposed to compress data. By designing a damage indicator, structural damage location is identified from the compressed data, thereby ensuring the effectiveness of the data compression. Firstly, an appropriate deep convolutional autoencoder model is designed, and the autocorrelation functions of acceleration responses under the healthy state of the bridge are used as training data to obtain appropriate model parameters. Secondly, the real-time monitored acceleration autocorrelation functions are input into the trained deep convolutional autoencoder model to obtain compressed data. Then, the Euclidean distance between the compressed data under both healthy and real-time states is calculated as a damage indicator, with each damage indicator corresponding to a specific structural location. Next, the damage condition at the corresponding location is determined according to whether the indicator changes. Finally, numerical models of a simply supported beam and a continuous beam, as well as a simply supported beam test in laboratory, are adopted to verify the effectiveness and noise robustnessof the proposed method.
    2025,23(12):54-65, DOI: 10.6052/1672-6553-2025-069
    Abstract:
    Spacecraft micro-vibrations, characterized by multiple excitation sources, broadband frequency, and complex transmission, challenge conventional suppression methods and threaten mission reliability. To address the trade-off between lightweight design and vibration mitigation in passive damping structures, this paper proposes a topology optimization design methodology for maximizing the modal damping ratio of a free-layer damping structure. Utilizing the variable density method, the optimization model is established with sensitivity and density filtering techniques to achieve optimal material distribution under multi-modal targets. Case studies on two-end fixed and cantilever plates demonstrate that the optimized layouts enhance target modal damping ratios and reduce vibration transmissibility peaks.
    2025,23(12):66-73, DOI: 10.6052/1672-6553-2025-072
    Abstract:
    The Z-Tilt-Torsion (ZTT) precision motion platform is a core component of semiconductor inspection equipment, and its control performance directly affects the yield of semiconductor inspection. Due to the fact that the ZTT precision motion platform is a multi-axis motion platform composed of flexible hinge guides, the nonlinearity and disturbance problems inherent in the system pose challenges to the design of controllers. Therefore, the research on the controller for the ZTT precision motion platform is very important. Currently, the existing controllers mainly include Proportional-Integral-Derivative (PID) control, sliding mode control, and H∞ controller. Among them, when the system is subject to strong external disturbances, the performance of the PID controller will decline, which may even lead to system instability. Although the sliding mode controller can solve the problem of external disturbances, its switching characteristics make it very sensitive to high-frequency noise and measurement errors, which may amplify these disturbances and make it difficult to implement in practical applications. To solve the above problems, this paper adopts the H∞ control method and designs an H∞ controller to make the closed-loop function of the system meet certain H∞ norm constraints, thereby ensuring the stability and performance of the system. Through experimental methods, the effects of PID control and H∞ control were compared. The results show a good suppression effect on external disturbances and could effectively suppress the fluctuations of the motion platform caused by disturbances.
    2025,23(12):74-83, DOI: 10.6052/1672-6553-2025-061
    Abstract:
    Inertial devices can convert linear motion into high-speed rotation to amplify the physical mass of the system. Combining a conventional tuned mass damper (TMD) with an inertial device results in a tuned inertial mass damper (TMDI). Previous studies by many scholars have shown that the TMDI system has certain advantages in controlling the vibration response of structures. In order to make the TMDI system fully exploit its vibration reduction potential, this paper proposes an accurate optimal parameter design formula for the single-degree-of-freedom TMDI system under harmonic load excitation. In order to verify the effectiveness of the optimal parameter design formula, a comparative study with the traditional tuned mass damper (TMD) was also carried out. The results show that when a single-degree-of-freedom structure is subjected to random seismic excitation, the parameters obtained by the TMDI optimal parameter design method proposed in this paper can effectively realize the vibration reduction potential of TMDI. When the traditional tuned mass damper (TMD) is used to control the vibration response of structures under non-stationary random seismic excitation, its vibration reduction effect is not ideal, but after the TMDI system is set with the optimal parameters, it can achieve the expected vibration reduction performance.
    2025,23(12):84-94, DOI: 10.6052/1672-6553-2025-066
    Abstract:
    Permanent Magnet Synchronous Motor (PMSM), owing to their high energy efficiency and structural advantages, has been widely adopted in high-performance motion control applications such as rail transit systems. However, chaotic behaviors inherent in PMSM systems can lead to operational instability, necessitating highly effective control strategies. This paper proposes a dual-parameter cooperative control strategy—referred to as GWO-Volterra—based on the integration of Grey Wolf Optimization (GWO) and the Volterra series, aiming to achieve precise control of chaotic motions in PMSMs. In this strategy, the distance between two adjacent projection points on the Poincaré section is selected as the control input. Furthermore, the complex coupling effects of system parameters on dynamic behavior are thoroughly considered by constructing a dual-parameter controller within the Volterra series framework. To enhance control performance, the GWO algorithm is introduced to optimize and adaptively adjust key parameters. Simulation results demonstrate that, compared with single-parameter control strategies, the proposed GWO-Volterra approach exhibits superior performance in terms of faster response, reduced overshoot, and enhanced control stability, thereby validating its effectiveness and practical applicability.
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    2014,12(3):269-273, DOI: 10.6052/1672-6553-2014-043
    [Abstract] (3759) [HTML] (0) [PDF 336.30 K] (22001)
    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] (3567) [HTML] (0) [PDF 748.46 K] (19506)
    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] (2320) [HTML] (0) [PDF 1.91 M] (19336)
    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] (3390) [HTML] (0) [PDF 1.13 M] (18957)
    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] (2810) [HTML] (0) [PDF 1.07 M] (18548)
    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] (2826) [HTML] (0) [PDF 1.87 M] (18387)
    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] (1523) [HTML] (0) [PDF 826.19 K] (18214)
    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] (2760) [HTML] (0) [PDF 1.38 M] (18136)
    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] (2776) [HTML] (0) [PDF 530.95 K] (18006)
    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.
    2008,6(4):301-306, DOI:
    [Abstract] (1540) [HTML] (0) [PDF 0.00 Byte] (17685)
    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.
    2012,10(1):21-26, DOI:
    [Abstract] (1094) [HTML] (0) [PDF 567.09 K] (17653)
    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.
    2014,12(2):183-187, DOI: 10.6052/1672-6553-2014-025
    [Abstract] (1618) [HTML] (0) [PDF 811.52 K] (17381)
    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] (2379) [HTML] (0) [PDF 467.15 K] (14881)
    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] (3435) [HTML] (0) [PDF 479.50 K] (14214)
    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] (1691) [HTML] (0) [PDF 350.50 K] (12261)
    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] (2164) [HTML] (0) [PDF 2.18 M] (9509)
    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] (2477) [HTML] (0) [PDF 2.22 M] (7947)
    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] (2353) [HTML] (0) [PDF 1.00 M] (6351)
    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] (2462) [HTML] (0) [PDF 296.79 K] (6054)
    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] (1908) [HTML] (0) [PDF 832.87 K] (5492)
    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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