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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

Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression

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Applied Mathematics and mechanics(English Edition) 2025年第1期46卷 1-24页

作者： Fan YANG Zhaoyang MA Xingming GUO Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and Mechanics School of Mechanics and Engineering ScienceShanghai University Shanghai institute of Aircraft mechanics and Control

A novel elastic metamaterial is proposed with the aim of achieving lowfrequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.

关键词： flexural wave bandgap graded design local resonance metamaterial O421+.5

Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 329-355页

作者： Yufeng Xing Ye Yuan Gen Li institute of Solid mechanics Beihang University(BUAA)Beijing100191China

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical *** taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue ***,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are *** is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

关键词： Separation-of-variable method Rayleigh quotient nodal line eigenvalue equation bisection method

Effects of bidirectional interaction on inelastic seismic response:When is its effect significant?

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Earthquake Engineering and Engineering Vibration 2025年第1期24卷 113-134页

作者： Atanu Santra Rana Roy Department of Aerospace Engineering and Applied mechanics Indian Institute of Engineering Science and TechnologyShibpur 711103India

Motivated by the early works on bidirectional interaction and the breakthrough to estimate seismic response to bidirectional shaking via unidirectional analysis,it is essential to answer the question:When is the interaction effect significant?Early works concluded that the effect of interaction is pronounced for stiff systems;consequently,the straightforward method for estimating seismic response to bidirectional excitation by using unidirectional analyses is verified primarily for short period ***,it is essential to identify the domain of significance for bidirectional interaction before adopting this simple methodology in *** parametrically defined systems with elastoplastic and degrading hysteresis models are studied under near-fault motions,assuming strength-independent and strength-dependent *** force-based and displacement-based analyses,conducted in parallel,reveal that the interaction effect is considerable for stiff systems,especially with degrading characteristics in a relatively low inelasticity ***,the bidirectional effect may be significant even for highly flexible systems,especially for residual deformation,which in earlier works was *** range of significance depends on the hysteresis model,system parameters,and response *** analysis is carried out with the results of the case studies,and the derived regression models may be used for a preliminary assessment of the impact of interaction in advance.

关键词： bidirectional residual forward-directive fling force-based displacement-based regression

RECENT PROGRESS IN CAVITATION RESEARCH IN THE institute OF HIGH SPEED mechanics TOHOKU UNIVERSITY

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Journal of Hydrodynamics 1989年第4期1卷 1-10页

作者： S.Kamiyama institute of High Speed mechanics Tohoku UniversitySendaiJapan

Recent activities on cavitation research in the institute of High Speed mechanics,Tohoku University,Japan are ***,our recent research project on cavitation occurrence in various liquids other than water is explained in relation to the thermodynamic and gas content ***,study on cavitation damage is *** this field,the mechanism of a single bubble collapse near solid wall and the related pit formation in soft test materials have been ***,the effects of fluid properties on the cavitation damage are ***,a special study on shock wave propagating through gas- liquid two-phase magnetic fluid is explained to extend further developments of cavitation research.

关键词： test RECENT PROGRESS IN CAVITATION RESEARCH IN THE institute OF HIGH SPEED mechanics TOHOKU UNIVERSITY

Some fundamental issues in buoyancy-driven flows with implications for geophysical and astrophysical systems

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Acta Mechanica Sinica 2025年第1期41卷 1-21页

作者： Ke-Qing Xia Kai Leong Chong Guang-Yu Ding Lu Zhang Center for Complex Flows and Soft Matter Research Southern University of Science and TechnologyShenzhen 518055China Department of mechanics and Aerospace Engineering Southern University of Science and TechnologyShenzhen 518055China Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China

Buoyancy-driven flows are prevalent in a wide range of geophysical and astrophysical systems. In this review, we focus on threepivotal effects that significantly influence the dynamics and transport properties of buoyancy-driven flows and may have impli-cations for natural systems. These effects pertain to the role of boundary conditions, the impact of rotation, and the effect offinite size. Boundary conditions represent how the fluid flow interacts with different kinds of surfaces. Rotation, as the Earth’srotation in geophysical systems or the whirling of astrophysical systems, introduces Coriolis and centrifugal forces, leading tothe profound vortical structure and distinct transport property. Finite size, representing geometrical constraints, influences thebehavior of buoyancy-driven flows across varying geometrical settings. This review aims to provide a holistic understanding ofthe intricate interplay of these factors, offering insights into the complex natural phenomena from the perspectives of the threeeffects.

关键词： Buoyancy-driven flows Geophysical turbulence Rayleigh-B´enard convection

Rock fracture mechanism of buffer blasting with cushion layer at the borehole bottom

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 325-334页

作者： Xinguang Zhu Chenxi Ding Zhe Sui Hong Su Xu Guo School of Civil and Resources Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory for mechanics in Fluid Solid Coupling Systems Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of mechanics and Civil Engineering China University of Mining and Technology(Beijing)Beijing 100083China School of Chemical and Blasting Engineering Anhui University of Science and TechnologyHuainan 232001China

This study primarily investigates the rock fracture mechanism of bottom cushion layer blasting and explores the effects of the bottom cushion layer on rock *** involves analyses of the evolution patterns of blasting stress,characteristics of crack distribution,and rock fracture features in the ***,blasting model experiments were carried out using the dynamic caustics principle to investigate the influence of bottom cushion layers and initiation methods on the integrity of the bottom rock *** experimental results indicate that the combined use of bottom cushion layers and inverse initiation effectively protects the integrity of the bottom rock ***,the process of stress wave propagation and dynamic crack propagation in rocks was simulated using the continuum-discontinuum element method(CDEM)and the Landau explosion source model,with varying thicknesses of bottom cushion *** numerical simulation results indicate that with increasing cushion thickness,the absorption of energy generated by the explosion becomes more pronounced,resulting in fewer cracks in the bottom rock *** illustrates the positive role of the cushion layer in protecting the integrity of the bottom rock mass.

关键词： bottom cushion layer blasting crack propagation continuum-discontinuum element method dynamic stress intensity factor

Targets capture by distributed active swarms via bio-inspired reinforcement learning

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Science China(Physics,mechanics & Astronomy) 2025年第1期68卷 206-217页

作者： Kun Xu Yue Li Jun Sun Shuyuan Du Xinpeng Di Yuguang Yang Bo Li institute of Biomechanics and Medical Engineering Applied Mechanics LaboratoryDepartment of Engineering MechanicsTsinghua UniversityBeijing 100084China institute of Nuclear and New Energy Technology Tsinghua UniversityBeijing 100084China Shanghai Aerospace Control Technology institute Shanghai 201109China Shanghai Key Laboratory of Aerospace Intelligent Control Technology Shanghai 201109China College of Automation Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Natural swarms arranged from cells to herds are usually decentralized but display intriguing collective intelligence in coordinating individuals across large scales to efficiently achieve their common *** from nature may provide new strategies for controlling collective dynamics of synthetic swarms to accomplish specific ***,we present a bioinspired computational framework that steers distributed active swarms to collectively capture and merge targets via reinforcement *** exploit collective milling structures of natural herds to cage the targets,and adopt a switching control policy inspired by sperms’chiral dynamics to optimize the trajectories of individuals,through which the active swarms can selforganize to enclose single or multiple distant targets in a dynamical,adaptive and scalable *** exists a critical swarm size,beyond which the excessive competition between agents would generate large mechanical forces,leading to capture instability but enabling the transition from short-distance to long-distance merging capture of multiple *** work provides physical insights into distributed active swarms and could offer a multilevel,decentralized strategy toward controlling swarm robotics in wide applications such as bio-medical devices,machine immunity,and target clearance.

关键词： swarm intelligence robotics multi-tasks artificial intelligence bionics

Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers

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Applied Mathematics and mechanics(English Edition) 2025年第3期46卷 423-446页

作者： Mengru ZHANG Mingzhu XU Weiting CHEN Yapu ZHAO State Key Laboratory of Nonlinear mechanics Institute of MechanicsChinese Academy of Sciences School of Engineering Science University of Chinese Academy of Sciences

The initial stresses widely exist in elastic materials. While achieving a continuum stress-free configuration through compatible unloading is desirable, mechanical unloading alone frequently proves insufficient, posing challenges in avoiding virtual stress-free configurations. In this paper, we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain. Our focus is on initially stressed cylindrical and spherical elastomers, where we first derive the Saint-Venant, Beltrami-Michell, and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory. It is shown that for any given axially or spherically distributed initial stress, an equivalent temperature variation always exists. Furthermore,we propose two innovative initial stress forms based on the steady-state heat *** introducing an equivalent temperature variation, the initial stress can be released through a compatible thermo-mechanical unloading process, offering valuable insights into the constitutive theory of initially stressed elastic materials.

关键词： Cesàro-Volterra path integral compatibility condition initial stress O343.6 orthogonal curvilinear coordinate thermal effect