2018 Vol. 39, No. 3

Display Method:
Dual Pulse Wave Structure of Elastic Stress Waves and Plate Impact Verification
LIU Zhanfang, GUO Yuan, TANG Shaoqiang, HUANG Xinjia, ZHUANG Zhuo
2018, 39(3): 249-265. doi: 10.21656/1000-0887.380324
Abstract(1031) PDF(1034)
A revised elastic stress wave theory was proposed. The existent theory of elastic stress waves has some deficiencies in aspects of rotational deformation as well as its corresponding internal force, and wave equations, etc. It was revealed that there exist both volumetric waves and deviatoric waves in elastic solids, the volumetric wave travels independently but the deviatoric wave is influenced by the volumetric wave, and them 2 form a weakly coupled wave system. An impacted plate should be treated as a 3D strain system other than a 1D one. In plate impact tests, the 2 wave variables remained 2ndorder tensors but the independent variable was simplified as a volumetric strain plus a principal deviatoric strain, consequently the wave equations were simplified as 2 weakly coupled wave equations. The interface effects of stress waves involved generation of stress waves on the impact surface and reflection of stress waves on the free surface. Relationships between the boundary conditions and the wave variables on the impact surface and the free surface were established. In the numerical tests, the volumetric and deviatoric waves were simultaneously generated on the impact surface, but the volumetric wave and a part of the deviatoric wave constituted a composite pulse propagating at a faster speed, and the rest of the deviatoric wave made a deviatoric pulse traveling at a slower speed. Both the 2 incident pulses on the free surface were reflected respectively to produce a composite pulse and a deviatoric pulse again, which meant 4 reflected pulses were generated. The dual pulse structure of stress waves may explain very well the recompressive phenomenon of the free surface velocity curves of plate specimens under plate impact. Recompressive signals measured on 10 alumina plate specimens of different thicknesses verify the theoretical prediction of the deviatoric pulse.
Combined Parametric and Forced Resonance of Axially Moving and Current-Carrying Beams Under Moving Loads
RONG Yantian, HU Yuda
2018, 39(3): 266-277. doi: 10.21656/1000-0887.380128
Abstract(614) PDF(599)
The combined parametric and forced resonance of axially moving beams subjected to moving loads in magnetic field environment was investigated. For an axially moving and current-carrying beam, the mechanical model under moving load in the magnetic field was established. The Hamiltonian variational principle was applied to formulate the nonlinear magnetoelastic vibration equations. By means of the Galerkin integral method and the multiscale method, the nonlinear primary parametric amplitude-frequency response equations were achieved with the moving load as a variable. The curves of the amplitude changing with the tuning parameters, the tension disturbance, the moving load, the magnetic induction intensity and the moving load length were drawn. The influences of the axial tension, the moving load and other parameters on the dynamic behaviors of the parametric system were analyzed through numerical calculation. The results show that the system presents typical nonlinear vibration characteristics; moreover, the moving load and the magnetic field control the occurrence of the multi-value amplitude phenomenon.
Vibration Characteristics Analysis of Periodic Cylindrical Shells-Based on the Transfer Matrix Method
JU Haiyan, FU Mingfu, XU Bin
2018, 39(3): 278-285. doi: 10.21656/1000-0887.380090
Abstract(715) PDF(560)
Based on the phononic crystal theory and the Love shell theory, the radial axisymmetric vibration equations for cylindrical shells were established. The dynamic stiffness matrix of each cell in the periodic cylindrical shell was obtained, and the transfer matrix between adjacent cells was derived with the transfer matrix method. The effects of the elastic modulus and geometric sizes on the wave propagation characteristics were analyzed according to the numerical examples. Numerical results show that there exist band gaps and pass gaps during the process of wave propagation in periodic cylindrical shells; the change of the length ratio has a significant effect on the amplitude, the width and the number of the band gaps. Therefore, it is possible to regulate the wave propagation characteristics of the structure through adjustment of the structural dimensions, which provides a new way for the design and vibration control of the structure.
Comprehensive Simulation of Shape Memory Alloys Based on a Finite Elastoplastic Model
WANG Xiaoming, XIAO Heng
2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067
Abstract(728) PDF(854)
A new elastoplastic J2 flow model was proposed for shape memory alloys to comprehensively simulate the pseudo-elastic stage with perfect strain recovery, the plastic stage with partial strain recovery and the softening stage up to failure. To this end, a new explicit method based on any given uniaxial data was introduced to obtain the multi-axial expression for the constitutive quantities incorporated in this model. The advantage of this model lies in avoiding the usual complicated numerical procedures in treating nonlinear rate constitutive equations with a number of phase transition conditions and micro-macro averaging methods. Numerical examples give results in good accordance with experiment data.
Study on Stress Intensity Factors of Concrete Beams With Sharp V Notches
TONG Gusheng, HU Zongqi, XU Penghua
2018, 39(3): 300-310. doi: 10.21656/1000-0887.380159
Abstract(675) PDF(707)
The failure behavior of the concrete beams with V notches is usually predicted by the notch stress intensity factor (NSIF), which quantify the intensities of the asymptotic linear elastic stress distributions around the notches. For a V-notched beam, the NSIF is determined by the notch angle. The strain energy density fracture criterion is used to judge the fracture failure of a member according to whether the strain energy density in a certain volume reaches the critical value. If the volume is small enough to neglect the higher-order solutions of the Williams equation, the strain energy density criterion can be used to calculate the NSIF. In view of the type-Ⅰ load condition, the theoretical NSIFs of the V notches obtained with the mean strain energy density fracture criterion and Carpinteri’s finite fracture mechanics method respectively, agree well with each other. Moreover, both the theoretical NSIFs given by the 2 criteria are fairly consistent with the experimental results from various V-notched concrete beam specimens.
Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method
2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092
Abstract(981) PDF(515)
The orthotropic rectangular thin plate equations were transformed into the Hamiltonian system, and the corresponding infinite dimensional Hamiltonian operator was obtained with the method of separation of variables. Then the eigenvalues and corresponding eigenfunctions of the Hamiltonian operator were calculated, and the eigenfunction system was proved to be of symplectic orthogonality and completeness. Finally, with the symplectic superposition method, the analytical bending solutions of fully clamped orthotropic rectangular thin plates were presented. The comparison between the analytical solutions and the numerical examples shows the correctness of the proposed method.
Bifurcation Evolution of Duffing Systems on 2-Parameter Planes
ZHANG Yanlong, WANG Li, SHI Jianfei
2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089
Abstract(856) PDF(494)
The calculation method for the top Lyapunov exponents in the parameter space was given. The top Lyapunov exponents of Dufffing systems on 2-parameter planes were calculated with the numerical method. Combined with the single-parameter top Lyapunov exponents, the bifurcation diagrams, the phase diagrams and the time response diagrams, the bifurcation and the bifurcation evolution process of Duffing systems on the 2-parameter planes were discussed in view of the change of system parameters. The results show that 2 different regions with the phenomena of missing edges appear when the pitchfork bifurcation occurs. The system has strong sensitivity to initial values in the regions where 2 attractors coexist. The system vibration amplitude decreases suddenly when the system moves through the period jump curve. The system flutter motion often occurs when the excitation frequency is relatively small. In addition, when the stiffness coefficient increases, the period-doubling bifurcation curve cycles constantly exist and nest each other in the 2 regions with the phenomena of missing edges, which makes the system finally evolve into a chaotic state via the period-doubling bifurcation sequences. The dynamic properties of the system are very complex on 2-parameter planes with the change of control parameters.
Dynamic Cycle Analysis of a Solow Model With Time Delays
LI Jiaorui, ZHANG Yanxia
2018, 39(3): 334-342. doi: 10.21656/1000-0887.380184
Abstract(777) PDF(595)
Based on the classical Solow model, a dual delay Solow model was proposed for the first time in view of the capital production investment time delay, the pollution treatment investment time delay and the environment purification parameters, to analyze the dynamic evolution mechanism of the economyenvironment system. Then the dynamic periodic fluctuation behavior of the model was discussed. The results show that the economic cycle will be triggered by any individual investment time delay or both 2 delays; with the increasing of the time delay, the economic cyclic fluctuation will become more intense; the appropriate adjustment of the investment policy will help achieve the expected equilibrium objective, and the stable cyclic operation of the economyenvironment system can be realized.
Modified Projective Synchronization of a Class of Fractional-Order Neural Networks Based on Active Sliding Mode Control
ZHANG Pingkui, YANG Xujun
2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098
Abstract(596) PDF(1449)
The modified projective synchronization of a class of fractionalorder neural networks was studied. An appropriate active controller was firstly selected to facilitate the design of the sliding mode controller. Afterwards, a suitable switching plane and 2 effective reaching laws were defined and several criteria were established to ensure the synchronization of the driveresponse systems based on the sliding mode control theory and the theory of fractional differential equations. Numerical examples verify the validity and feasibility of the theoretical results.
Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems
FENG Yihu, CHEN Huaijun, MO Jiaqi
2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110
Abstract(758) PDF(477)
A class of generalized Lienard singular perturbation systems were considered. Firstly, the reduced solution to the system was obtained. Next, the outer solution was constructed by means of the singular perturbation method. Then, a stretch variable was introduced and the initial layer corrective term was found. Finally, the arbitrary-order asymptotic analytic expansion of the system solution was given and the uniform validity of the solution was proved. The proposed method with the basic theory has wide application values.
Characterizations of D-Properly Semi-Prequasi-Invex Mappings
HUANG Yingquan
2018, 39(3): 364-370. doi: 10.21656/1000-0887.380269
Abstract(825) PDF(451)
The properties of D-properly semi-prequasi-invex mappings were studied. Firstly, it was verified that the η values satisfying condition E exist massively. Secondly, the level set of theD-properly semi-prequasi-invex mapping was proved to be a semi-invex set, and two equivalent propositions of the D-properly semi-prequasi-invex mapping were given with D-upper semi-continuity, *-upper semi-continuity and intermediate-point D-properly semi-prequasi-invexity. Finally, the equivalent relation between the D-properly semi-strict semi-prequasi-invex mapping and the D-properly strict semi-prequasi-invex mapping was established under the condition of the intermediate-point D-properly strict semi-prequasi-invexity.