Abstract: Periodic structures are an important form of constructing structures in natural and human engineering. The Bloch modulation caused by translational symmetry gives them unique band structures and rich time/frequency domain dynamic characteristics, providing new avenues for elastic/acoustic wave propagation regulation, novel wave-based functional device design, vibration and noise control, etc. Nonlinear effects can break through the constraints of linear theoretical frameworks and can enhance or even expand the functions of artificial periodic structures. However, nonlinear periodic systems have many difficulties in unit cell design and modeling analysis. They also face key scientific problems such as the broken of space-time invariance, the complexity of nonlinear response characteristics and mechanisms, which brings challenge to the dynamic design and practical application of nonlinear periodic structures. In response to the above problems, scholars have carried out some fruitful research by integrating multidisciplinary research methods in fileds such as mechanics, acoustics, materials science and band physics. This article aims to timely summarize the important research progress concerning about wave dynamics and control in nonlinear periodic structures, sort out the shortcomings and key problems, gather strength and promote the in-depth development of this field. First, the sources of nonlinear effects of periodic structures, unit cell structure design methods, and nonlinear dynamics modeling and analysis methods are summarized. Then, the main characteristics of nonlinear periodic structures in terms of passband, bandgap, and local energy confinement are reviewed, and the rich dynamic phenomena such as amplitude-induced band shift, wave mode coupling, low-frequency broadband bandgap, and spatial confinement of wave modes in the bandgap caused by nonlinearity are introduced. Some application explorations of nonlinear periodic structures in wave control devices, vibration and noise reduction are sorted out. Finally, in view of some shortcomings and key problems in existing research, several development directions that need special attention in future theoretical research and application exploration are prospected.
Gao P L, Gong L Y, Wang G X, Luo Y, Zhu J Z, Gao H, Ma H B, Qu Y G. Review on the dynamics and wave control in nonlinear periodic structures. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-24-047.
Abstract: Dynamics and control is a discipline that studies the dynamic mechanisms of systems and their control strategies, and plays an important role in modern engineering and scientific research. The complexity caused by geometric nonlinearity, the non-smoothness of contact forces, and the uncertainty of environmental interferences and multi-physics problems poses significant challenges to dynamic modeling, prediction and intelligent control. The rapid development of data-driven methods has provided new ideas and new research paradigms for addressing these challenges. Recent researches have shown that data-driven methods can not only solve some problems that traditional dynamics methods cannot address but also significantly enhance the ability to predict dynamical behavior and design advanced structures. These methods lay the foundation for intelligent research in dynamics and control and demonstrate great potential and scientific value in the modeling, analysis, and regulation and control of complex systems. This paper briefly reviews the research progress of data-driven methods in areas such as robot motion control, transonic aeroelastic modeling and analysis, dynamics design, stochastic dynamics, neurodynamics, fault diagnosis and remaining useful life prediction of machinery. It also discusses the challenges and trends in these fields.
DING Q, ZHANG S, HUANG R, HE M X, XU Y, HAN F, LI X, CUI L Y, WANG Q Y, XU J. Recent Advances on Data-Driven Dynamics and Control. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-25-005.
Abstract: This paper is intended to reconcile the stress-based and strain-based formulations for material failure criteria, where a longstanding and deep division is present. The two approaches do not naturally agree with each other, and they not genuinely complement each other, either. Most popular criteria are stress-based when originally proposed, including the maximum stress, Tresca, von Mises, Raghava-Caddell-Yeh and the Mohr criteria. Their formulations are unique and self-consistent, i.e. capable of reproducing the input data. Their strain-based counterparts, with the maximum strain criterion being considered as the strain-based counterpart of the maximum stress criterion, are neither unique nor necessarily self-consistent. It has been proven that the self-consistent ones reproduce their respective stress-based counterparts identically in effect with a disadvantage of requiring an additional material property to apply, without a single benefit. For the Mohr criterion as a special case, a strain-based counterpart is simply infeasible in general. All undesirable features of strain-based criteria are rooted in a single source: the failure strains can only be measured under a uniaxial stress state, which corresponds to a combined strain state in general, not a uniaxial strain state! Given the arguments presented, the reconciliation proves to be biased completely towards the stress-based side if mathematics, logic and common sense prevail over perception and prejudice.
Li S G. Stress or Strain?. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-24-035.
Abstract
HTML
PDF
Cited by
Email Alert
RSS