应用数学和力学

Model Updating for Large Structures Based on the Modal Synthesis Method

PIAO Siyang, QI Feng, ZHANG Yahui

2018, 39(9): 989-998. doi: 10.21656/1000-0887.390065

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Abstract:
A synthetic technology for substructure test modeling was developed based on the finite element model updating theory and the modal synthesis method. During the substructure model updating, the fixed interface component modal synthesis method was adopted to reduce the substructure model, improve the computational efficiency and thereby promote the overall efficiency of the substructure test modeling. The steps of the design parameter method in model updating and the corresponding formulas based on the reduced model were given. With a launch vehicle model as the example, and by means of the secondary development of ANSYS, the present method gets verification of effectiveness.

Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity

SHEN Anming, CHEN Rui, DU Qiumei

2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301

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Abstract:
Classical elasticity has been widely applied in engineering technologies. But the length scale parameter is not included in the classical elasticity, which leads to the scale effects on mechanical characteristics and no longer satisfies the micro scale. Generalized elasticity is especially applicable to microstructures with scale effects, where both the rotational deformation and the couple stress are taken into account, and the measurement of deformation is improved. By means of Hamilton’s variation principle and generalized elasticity, the vibration differential equations for the micro cantilever beam in different motion states were derived. Then natural frequencies and vibration modes of the micro cantilever beam were analyzed. The results show that, with the decreasing of the micro beam height, the scale effect on the natural frequency is closely related to the mode. The corresponding natural frequencies of torsional and bending modes have significant increment and scale effect compared with those according to the classical elasticity, for the rotational deformation is considered. However, little variation of the natural frequency of the tensile mode is found because there is no rotational deformation involved.

Mechanical Model Research on Point Contact Between the Sleeve and the Inner Core With Over-Hang Lengths for Sleeved Columns

ZHAO Xiaofeng, SHEN Bo, MA Kejian, LIU Panpan, WANG Hui, WU Junyang, YANG Lei

2018, 39(9): 1009-1020. doi: 10.21656/1000-0887.380288

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Abstract:
To study the sleeved column with inner core over-hang lengths under axial compression, the deformation process of point contact between the initially bending inner core and the flexible sleeve was studied theoretically. The 2nd-order differential equilibrium equations of small deflection were used to deduce the formulas for the physical quantities including the deflection, the moment, the shear force and the contact reaction of the inner core and the sleeve, etc. The comparison of the theoretical results shows: 1) for the inner core with over-hang lengths, the contact process significantly increases the bending axial displacement of the sleeved column under axial compression, and reduces its nonlinear axial stiffness; 2) the contact process dramatically raises the reaction forces between the inner core and the sleeve ends, even more sharply with the increase of the axial compression; 3) the contact process remarkably magnifies the shear force and the bending moment of the inner core, and the moment increases faster especially in the case of a larger flexural rigidity ratio of the inner core to the sleeve. This research provides a basis for the design of sleeved columns and the end connection between the inner core and the sleeve.

A Connection Cloud-Evidence Theory Coupling Model for Prediction of Rockburst Intensity

WANG Mingwu, DONG Hao, YE Hui, ZHOU Tianlong, JIN Juliang

2018, 39(9): 1021-1029. doi: 10.21656/1000-0887.380286

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Abstract:
Rockburst mechanism is a complex problem involving various uncertain factors. Although the cloud model can deal with the randomness and fuzziness of indicators for prediction of rockburst intensity, it cannot simulate the state of evaluation indicators in a finite distribution interval and address the distortion of data fusion. Herein, a connection cloud-evidence theory coupling model was built to remedy these defects. In this model, evaluation indicators were firstly expressed quantitatively by connection numbers. Then the evaluation matrix was constructed with the connection cloud model and the basic probability assignment based on the evidence theory was obtained. Finally, with the combination weight obtained from a distance function, classification of the rockburst intensity was determined according to the mean evidence value. The case study and comparison with other methods show that, the proposed model is effective and feasible for the prediction of rockburst intensity. It can overcome the shortcomings of the normal cloud model and the evidence theory, making a novel method for comprehensive prediction of rockburst intensity.

Stability Analysis of Binary Gas Mixing Layers

GAO Jun, LI Jia, LIU Fengjun, SHI Xiaotian, YUAN Xiangjiang

2018, 39(9): 1030-1042. doi: 10.21656/1000-0887.390064

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Abstract:
For the mixing layer flow composed of oxygen and nitrogen, the linear stability analysis was utilized to investigate the stability characteristics. The basic flow profile of the binary gas mixing layers was obtained from the similar solution. The effects of the convective Mach number on the similar solution were firstly investigated. Then, the influences of the convective Mach number, 2D and 3D waves on the stability were studied. The results of linear stability indicate that, the maximum growth rate of the 1st mode is always larger than that of the 2nd mode, and the maximum growth rates of the 1st and 2nd modes are suppressed with the increasing convective Mach number.

Solution of the Transient Stream-Groundwater Model With Linearly Varying Stream Water Levels

WU Dan, TAO Yuezan, LIN Fei

2018, 39(9): 1043-1050. doi: 10.21656/1000-0887.380250

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Abstract:
Based on the first linearized Boussinesq equation, the analytical solution of the transient groundwater model for description of phreatic flow in a semi-infinite aquifer bordered by a linear stream with linearly varying stream water levels, was derived through the Laplace transform and in view of the integral property of the Laplace transform. The solution is composed of some common functions and its expression form is relatively simple. According to the mathematical characteristics of the solution, its corresponding physical meaning was discussed. The variation rule of the phreatic level revealed by the solution shows that the temporal variation curve of the aquifer at any point is fixed and has nothing to do with the change rate of the water level of the river channel. The time of the maximum speed change of the phreatic aquifer nonlinearly varies with λ. Based on the variation rule of the phreatic level, the method determining the aquifer parameters with the changing velocity of the phreatic level was established, and the process of obtaining the parameter with the inflection point method was demonstrated through an example.

Stability of Traveling Wave Fronts for Delayed Lotka-Volterra Competition Systems With Stage Structures

GUO Zhihua, CAO Huarong

2018, 39(9): 1051-1067. doi: 10.21656/1000-0887.380293

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Abstract:
The stability of traveling wave solutions to a class of Lotka-Volterra competitive systems with age structures was studied. In the case of quasi-monotonicity, the existence and comparison theorems for the solutions to the initial value problems of the systems were first established on R with the analytic semigroup theory and the abstract functional differential equations. Then based on the weighted energy method, the comparison theorem as well as the embedding theorem, the global exponential stability of the monostable large-speed traveling wave solutions under the so-called large initial perturbation (i.e. the initial perturbation around the traveling wave decaying exponentially as x→-∞,but being arbitrarily large at other locations) was obtained for the systems in the weighted Sobolev space. The results show that, as the steady state solution of the system, the traveling wave solution usually determines the long-term asymptotic behavior of the solution to the initial value problem. Its stability reveals that the phenomena and results of inter-species competition systems can be clearly observed without interference by external factors.

Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions

YANG Mo, FU Na

2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254

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Abstract:
A class of wave equations with dynamic boundary conditions were studied. Through suitable decomposition, the existence of the stochastic attractor was proved. The decomposition shows that the point (or solution) of the attractor satisfies some stationary boundary condition. Finally, the attractor also exists in the stochastic dynamic system determined by the stochastic wave equation with the static boundary condition developed in decomposition.

Reliability Analysis of Asphalt Pavement Structure Based on the Fuzzy Mathematics Theory

LIU Junqing, HAN Jing

2018, 39(9): 1081-1090. doi: 10.21656/1000-0887.380278

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Abstract:
The fuzzy mathematics theory was introduced into the analysis of asphalt pavement structure reliability, to better fit the actual condition of pavement. The failure membership function was first given for asphalt pavement structure, then with the road surface deflection value as the control index, the asphalt pavement structure fuzzy reliability calculation model was built and verified with 2 asphalt roads in the Xixian New Area. The results show that, in a fuzzy event, the fuzzy reliability is always lower than the traditional reliability. Based on this, the reliability design of the pavement structure with the fuzzy reliability can strengthen the pavement performance and prolong the service life of pavement. In service, under the fuzzy reliability the pavement damage degree due to environmental factors is less than that under the traditional reliability, thus reducing the amount of pavement maintenance and saving manpower and maintenance cost. The values of k and fuzzy critical intervals of the selected membership functions play a direct role in the magnitude of the fuzzy reliability. Through the calculation of different road combinations and different k values, it is found that the reasonable value of k is within 800σ^-2_Z~1 800σ^-2_Z.In the real engineering practice, the critical interval shall be determined according to the actual situation, so as to ensure the safety of the structure.

Global Attractivity of Pseudo Almost Periodic Solutions to a Class of Lasota-Wazewska Models

WANG Li, LIANG Boqiang, LIU Jin

2018, 39(9): 1091-1098. doi: 10.21656/1000-0887.380256

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Abstract:
The Lasota-Wazewska model is often used to describe the regeneration of red blood cells in animals. Based on the Banach contraction mapping principle and through construction of the Lyapunov function, the existence, uniqueness and global attractivity of pseudo almost periodic solutions to a class of Lasota-Wazewska models were studied. The results have some advantages, and can enrich the characterization of the dynamic behavior of the Lasota-Wazewska model.

2018 Vol. 39, No. 9