应用数学和力学

Progresses in the Study on Vibration Damping Properties of Novel Lightweight Composite Sandwich Structures

MA Li, YANG Jin-shui

2017, 38(4): 369-398. doi: 10.21656/1000-0887.370328

Abstract(2316) PDF(1250)

Abstract:
As a new generation of advanced super-strong lightweight structural materials, composite grid and lattice sandwich structures have received extensive attention from domestic and foreign scholars. An abundant amount of research on such novel sandwich structures focused on the manufacturing techniques and mechanical properties was carried out. However, it needs to be pointed out that, the research on the vibration and damping characteristics of such sandwich structures has just started, which is a new topic. Here a comprehensive review of the state of the research on vibration damping models was made for fiber reinforced resin matrix composite laminates and sandwich structures. Firstly, the related damping mechanisms were elaborated, and then an overview of micro- and macro-damping models for simple composite laminates, viscoelastic damping and novel sandwich structures was given. Finally, the results and shortcomings of the existing research on the vibration damping characteristics of such structures were summarized and the possible development in the future was predicated.

Effects of Solar Radiation Pressure on Orbits of Space Solar Power Station

WEI Yi, DENG Zi-chen, LI Qing-jun, WANG Yan

2017, 38(4): 399-409. doi: 10.21656/1000-0887.370309

Abstract(1389) PDF(1321)

Abstract:
The orbital dynamic behaviors of 3 typical space solar power stations (SSPSs) under the gravity gradient stabilized flight strategy were investigated. In view of the earth shadow and the effective cross-sectional area, a solar radiation pressure model was established. Firstly, the energy method was used, through the Legendre transformation and with the generalized momenta introduced, the canonical equations for the orbits in the Hamiltonian system were derived; then, the symplectic Runge-Kutta method was adopted to solve the corresponding canonical equations. Finally, several numerical examples were given, and the effectiveness of the proposed model and the stability of the numerical scheme were verified, in comparison with the previously reported results. The effects of the earth shadow and the effective cross-sectional area variations on SSPSs are significant. Meanwhile, the curves of the semi-major axis, eccentricity and orbital inclination in the geosynchronous orbit were obtained. The results provide a theoretical reference for the design of SSPSs.

A Numerical Method for Dynamic Responses of Aviation Aluminum Alloy Plates Under Blast Loads

XIE Jiang, LI Han, ZHOU Shu-ting, ZHENG Jin-guo, FENG Zhen-yu

2017, 38(4): 410-420. doi: 10.21656/1000-0887.370252

Abstract(1023) PDF(729)

Abstract:
In order to explore the numerical analysis method suitable for dynamic responses of aviation aluminum alloy plates under explosive impact loads, numerical simulation of the aluminum alloy plate under explosion was carried out with the LSDYNA explicit dynamic analysis software. Influences of different advection steps of the arbitrary LagrangianEulerian method (ALE), the fluidstructure coupling mode, the number of coupling points, the mesh size and the finite element type on the numerical results were detailedly studied. Comparisons between the numerical results and the test results show that the dynamic responses of the aluminum alloy plate under explosive impact loading can be calculated accurately with the van Leer+HIS advection step, the penalty coupling method, 3 coupling points, a ratio of 2∶1 between the structure mesh size and the air mesh size, and the Shell163 element. Simultaneously, the calculation efficiency can be improved and computation time saved.

Characteristics of Elastic Waves Through Frictional Contact Interfaces Between 2 Anisotropic Piezoelectric Materials

LU Gui-hua, ZHAO Man, YUE Qiang

2017, 38(4): 421-431. doi: 10.21656/1000-0887.370068

Abstract(1067) PDF(859)

Abstract:
The Fourier analysis and the singular integral equation technique were used to investigate the propagation characteristics of elastic wave through frictional contact interface between 2 generally anisotropic piezoelectric materials. The method and procedure were developed to solve the question in the case of slipping but not separating in local interface areas, and the extents and locations of slipping and sticking regions varying with the external mechanical-electrical loads were given. Furthermore, with a polarized ceramic material and quartz, which belong to the hexagonal crystal system and the trigonal crystal system respectively, as the examples, different responses of the friction contact interface between different materials to incident elastic wave were analyzed, and the interface behaviors influenced by different incident angles and external mechanical-electrical loads were studied. High-frequency harmonics will occur because of non-linearity (boundary non-linearity) brought by separation or slip in local interface areas if the incident wave is strong enough. Finally, with quartz as an example, the amplitudes of the reflected and refracted high-frequency harmonics varying with mechanical-electrical loads were comparatively discussed.

Dynamics Research of Bistable Electromagnetic Energy Harvesters With Auxiliary Nonlinear Oscillators

LIU Rui, WU Zi-ying, YE Wen-teng

2017, 38(4): 432-446. doi: 10.21656/1000-0887.370167

Abstract(1285) PDF(1794)

Abstract:
With the progress of the micro-electromechanical technology, the systems self-powered by ambient vibration have become a focus in nonlinear dynamics. The concept of bistable electromagnetic vibration energy harvesters with auxiliary nonlinear oscillators was proposed through combination of a mass-spring-damper system with a bistable vibration energy harvester, and the mechanical model and control equations for this system were established, the dynamic responses of the bistable electromagnetic vibration energy harvester with a nonlinear oscillator under harmonic excitation were investigated with the parametrical changes of the mass ratio and the tuning ratio through numerical simulation. Then, in comparison with that on the bistable system with an auxiliary linear oscillator, the influence rule of the above changing parameters on the bistable electromagnetic vibration energy harvester with an auxiliary nonlinear oscillator, which would get into chaotic movement, was obtained, and the superiority of the one with an auxiliary nonlinear oscillator was demonstrated. Moreover, the optimal parameters for the bistable electromagnetic vibration energy harvester with an auxiliary nonlinear oscillator in continuous large-amplitude chaotic motion were given. These above results provide a theoretical basis for the research of bistable electromagnetic vibration energy harvesters.

A Strain-Based Criterion for General

LI Yi-fan, DONG Shi-ming, LI Nian-bin, HUA Wen

2017, 38(4): 447-456. doi: 10.21656/1000-0887.370212

Abstract(1167) PDF(743)

Abstract:
The maximum tangential strain (MTSN) criterion proposed in the past under mixed mode Ⅰ/Ⅱ loading was extended to spatial cracks. The effects of the Poisson’s ratio on the in-plane and out-of-plane fracture angles and on the fracture envelopes were detailedly discussed for mixed mode cracks. It is shown that the Poisson’s ratio has little effect on the out-of-plane fracture angles for mixed mode Ⅰ/Ⅲ cracks. For mixed modes Ⅱ/Ⅲ and Ⅰ/Ⅱ/Ⅲ cracks, a higher value of the Poisson’s ratio would bring a smaller value of in-plane fracture angle θ_f but a bigger value of out-of-plane fracture angle φ_f. It is also shown that the fracture envelope decreases with the Poisson’s ratio for mixed mode cracks. The influence of the Poisson’s ratio on the fracture envelope is greater than that on the in-plane fracture angle and is the least on the out-of-plane fracture angle. The theoretical results fit the experimental data well, so the extended MTSN criterion can predict spatial fracture satisfactorily.

Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

LONG Pu-jun, YANG Xin-min, WANG Bing-wu

2017, 38(4): 457-468. doi: 10.21656/1000-0887.370238

Abstract(1261) PDF(498)

Abstract:
The directional Mordukhovich normal cones of sets, directional Mordukhovich coderivatives of set-valued mapping, and directional sequential normal compactness of sets and set-valued mapping in the framework of generalized differentiation were studied. Based on the intersection rule for directional Mordukhovich normal cones of sets, the calculus rules on directional Mordukhovich normal cones of sets and directional Mordukhovich coderivatives of set-valued mapping were established under some directional inner semicompactness assumptions. Furthermore, in virtue of the intersection rule for directional sequential normal compactness of sets, the sum rule, inverse mapping rule, and composition rule for directional (partial) sequential normal compactness of sets and set-valued mapping were presented under some directional inner semicompactness assumptions and suitable qualification conditions.

Positive Periodic Solutions to the Nonlinear Disturbed Model for Sea-Air Coupling Climate Systems

CHEN Li-juan, LU Shi-ping, XU Jing

2017, 38(4): 469-476. doi: 10.21656/1000-0887.370188

Abstract(1137) PDF(626)

Abstract:
The focus was given on the tropical large-scale ocean-atmosphere interaction associated with ENSO, which was considered as one of the most important mechanisms for the global inter-annual climate variability. From a group of sea-air coupling equations, a nonlinear disturbed model was built for sea-air coupling climate systems. Based on the continuation theorem of Mawhin’s coincidence degree, the existence of positive periodic solutions to a class of nonlinear problems was discussed. A strict proof of the existence of positive periodic solutions to the model was obtained, and the potential application value of the result was expected. The study of air-sea interaction, which helps to understand the process of climate variability, provides a theoretical basis for climate simulation and prediction.

Study on Path Curves of a Class of Fermi Gases in Optical Lattices With Nonlinear Mechanism

SHI Juan-rong, ZHU Min, MO Jia-qi

2017, 38(4): 477-485. doi: 10.21656/1000-0887.370046

Abstract(1033) PDF(399)

Abstract:
A nonlinear disturbed model for a class of Fermi gases in optical lattices was investigated. Firstly, in the nondisturbed case, the exact solution of the model path curves of Fermi gases in optical lattices was given. Secondly, the generalized functional analysis homotopic mapping was introduced and an iterative system was constructed, the arbitrary order asymptotic solution to the nonlinear disturbed model for the path curves of Fermi gases in optical lattices was obtained. Finally, a nonlinear small disturbance system was studied. With the proposed method, the asymptotic expressions of the path curves can be conveniently formulated and further extended.

Stability of an SIR Epidemic Model With 2 Patches and Population Movement

FU Jin-bo, CHEN Lan-sun

2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087

Abstract(1556) PDF(638)

Abstract:
Based on the epidemic dynamics, in view of the population movement between 2 patches and the nonlinear infection rate, a class of SIR epidemic model with 2 patches and population movement was established. With the qualitative method and the stability method for ordinary differential equations, the permanence of the model and the existence of nonnegative equilibrium points were analyzed. Through construction of proper Lyapunov functions and according to the limit system theory, the sufficient conditions for the global asymptotic stability of the diseasefree equilibrium points and the endemic equilibrium points were obtained. The results show that, the basic reproduction number makes a threshold to determine wether the disease spreads or not. When the basic reproduction number is less than or equal to 1, the infection will gradually disappear, the virus will tend to be extinct; when the dominant regeneration number of the virus is greater than 1 and satisfies the permanence conditions, the infection will persist, and the virus will continue to prevail and become an endemic disease.

2017 Vol. 38, No. 4