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Science China Mathematics 2012年第2期55卷 337-352页

作者： HE Cheng HUANG FeiMin YONG Yan National Natural Science Foundation of China Beijing 100085China institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China College of Science University of Shanghai for Science and TechnologyShanghai 200093China

It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u）〉 0, u（±∞, t）： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.

关键词： stability planar diffusion wave nonlinear evolution equation

Strong shock propagation for the finite-source circular blast in a confined domain

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Applied Mathematics and mechanics(English Edition) 2024年第6期45卷 1071-1084页

作者： Qihang MA Kaileong CHONG Bofu WANG Quan ZHOU Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shanghai institute of Aircraft mechanics and Control Shanghai 200092China

The circular explosion wave produced by the abrupt discharge of gas from a high-temperature heat source serves as a crucial model for addressing explosion phenomena in compressible *** reflection of the primary shock and its propagation within a confined domain are studied both theoretically and numerically in this *** the assumption of strong shock,the scaling law governing propagation of the main shock is *** dimensionless frequency of reflected shock propagation is associated with the confined *** numerical simulation for the circular explosion problem in a confined domain is performed for *** the influence of confinement,the principal shock wave systematically undergoes reflection within the domain until it weakens,leading to the non-monotonic attenuation of kinetic energy in the explosion fireball and periodic oscillations of the fireball volume with a certain *** simulation results indicate that the frequency of kinetic energy attenuation and the volume oscillation of the explosive fireball align consistently with the scaling law.

关键词： explosion confinement main shock frequency

Receptivity of Mack modes to localized unsteady blowing and suction in a chemical non-equilibrium hypersonic boundary layer

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Acta Mechanica Sinica 2024年第7期40卷 1-18页

作者： Qingjiang Yuan Runjie Song Ming Dong State Key laboratory of Nonlinear mechanics Institute of MechanicsChinese Academy of SciencesBeijing 100190China

This paper studies the local receptivity of the Mack-mode instability to localized unsteady blowing and suction(UBS)in a chem-ical non-equilibrium(CNE)hypersonic boundary *** five-species CNE model is employed,and the receptivity efficiency is formulated by use of the residual *** with the results for the calorically perfect gas(CPG)model,we find that the real-gas effect enhances the receptivity efficiency remarkably in the majority of the second-mode frequency band,and the enhancement is mainly attributed to the modification of the base flow due to the CNE effect,which is akin to the cold-wall effect in hypersonic boundary *** with the destabilizing role of the CNE effect on the Mack second mode,it is concluded that the CNE effect would lead to a greater linearly accumulated perturbation amplitude,implying premature of transition to turbulence in a high-enthalpy hypersonic boundary layer subject to localized perturbations.

关键词： Chemical non-equilibrium flow Boundary-layer instability Hypersonic Receptivity Transition to turbulence

An improved interval model updating method via adaptive Kriging models

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Applied Mathematics and mechanics(English Edition) 2024年第3期45卷 497-514页

作者： Sha WEI Yifeng CHEN Hu DING Liqun CHEN Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shanghai institute of Aircraft mechanics and Control Shanghai 200092China

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample ***,the surrogate model in IMU methods mostly adopts the one-time construction *** makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU ***,an improved IMU method via the adaptive Kriging models is *** method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey *** optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is *** the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity *** sampling is then performed in key subspaces based on the maximum mean square error(MMSE)*** interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy *** effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical *** results show that the updated results of the interval model are in good agreement with the experimental results.

关键词： interval model updating(IMU) non-probabilistic uncertainty adaptive Kriging model surrogate model grey number

Dirac method for nonlinear and non-homogenous boundary value problems of plates

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Applied Mathematics and mechanics(English Edition) 2024年第1期45卷 15-38页

作者： Xiaoye MAO Jiabin WU Junning ZHANG Hu DING Liqun CHEN Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Shanghai institute of Aircraft mechanics and Control Shanghai 200092China

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

关键词： rectangular plate Dirac operator nonlinear boundary time-dependent boundary boundary value problem

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

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Applied Mathematics and mechanics(English Edition) 2024年第2期45卷 239-260页

作者： Jie JING Xiaoye MAO Hu DING Liqun CHEN Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Shanghai institute of Aircraft mechanics and Control Shanghai 200092China

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is *** non-trivial equilibrium configuration is superposed by the modal functions of a simply supported *** the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical *** general,the pipe in the supercritical region is more sensitive to the pulsating *** nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the ***,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the *** addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response *** work further complements the theoretical analysis of pipes conveying pulsating fluid.

关键词： pipe conveying fluid axially functionally graded supercritical resonance multi-scale method parametric resonance

Numerical investigation on compressible flow around a cylinder in proximity to the heated wall

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Journal of Hydrodynamics 2024年第3期36卷 519-533页

作者： Yu-lu Liu Jun-wang Qu Yi-zhou Tao Yong-guang Lyu Xiang Qiu Shanghai institute of Technology School of ScienceShanghai201418China Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai200072China

In this study,direct numerical simulations were conducted to investigate the compressible flow around a circular cylinder near a heated wall at a Reynolds number(Re)of 500 and a Mach number(Ma)of *** heating ratio T^(*)ranging from 1.0 to 1.6 represents the different situations of a heated wall,whereas the gap ratio ranges from 0.3 to *** study analyzed the impact of heating effect and wall proximity on flow characteristics and aerodynamic *** results indicated that the stability of the flow was enhanced as the gap ratio decreased or the heating ratio *** the calculation of enstrophy,it was found that the strength of shedding vortices weakens with a decrease in gap ratio or an increase in heating ***,the mean drag coefficient decreases as the heating ratio increases or the gap ratio *** contrast,the mean lift coefficient initially decreases and then increases as the gap ratio ***,the drag reduction mechanism was analyzed by examining the pressure distribution on the surface of the cylinder.

关键词： Compressible flow wall proximity heating effect stability enstrophy

Analysis of the discrete contact characteristics based on the Greenwood-Williamson model and the localization principle

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Friction 2024年第5期12卷 1042-1056页

作者： Anastasiya A.YAKOVENKO Irina G.GORYACHEVA Ishlinsky institute for Problems in mechanics RAS Moscow119526Russia

The contact of a rigid body with nominally flat rough surface and an elastic half-space is *** solve the contact problem,the Greenwood-Williamson statistical model and the localization principle are *** developed contact model allows us to investigate the surface approach and the real contact area with taking into account the asperities *** is shown that the mutual influence of asperities changes not only contact characteristics at the macroscale,but also the contact pressure distribution at the *** follows from the results,the inclusion in the contact model of the effect of the mutual influence of asperities is especially significant for studying the real contact area,as well as the contact characteristics at high applied *** results calculated according to the proposed approach are in a good agreement with the experimentally observed effects,i.e.,the real contact area saturation and the additional compliance exhaustion.

关键词： surface roughness elasticity Greenwood-Williamson model localization principle asperity interaction

Discontinuous phase diagram of amorphous carbons

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National Science Review 2024年第4期11卷 164-171页

作者： YinBo Zhu ZhouYu Fang ZhongTing Zhang HengAn Wu CAS Key Laboratory of Mechanical Behavior and Design of Materials Department of Modern MechanicsUniversity of Science and Technology of China State Key Laboratory of Nonlinear mechanics Institute of Mechanics Chinese Academy of Sciences

The short-range order and medium-range order of amorphous carbons demonstrated in experiments allow us to rethink whether there exist intrinsic properties hidden by atomic disordering. Here we presented six representative phases of amorphous carbons（0.1–3.4 g/cm3）, namely, disordered graphene network（DGN）, high-density amorphous carbon（HDAC）, amorphous diaphite（a-DG）, amorphous diamond（a-D）, paracrystalline diamond（p-D）, and nano-polycrystalline diamond（NPD）, respectively, classified by their topological features and microstructural characterizations that are comparable with experiments. To achieve a comprehensive physical landscape for amorphous carbons, a phase diagram was plotted in the sp3/sp2versus density plane, in which the counterintuitive discontinuity originates from the inherent difference in topological microstructures, further guiding us to discover a variety of phase transitions among different amorphous carbons. Intriguingly, the power law, log（sp3/sp2） ∝ ρn, hints at intrinsic topology and hidden order in amorphous carbons, providing an insightful perspective to reacquaint atomic disorder in non-crystalline carbons.

关键词： amorphous carbons disordered carbons phase diagram microstructural topology phase transition