Damping studies in fiber-reinforced composites : a review

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

https://iopscience.iop.org/article/10.1088/0034-4885/76/12/126501/pdf

Metamaterials beyond electromagnetism

Preface. 1. SINGLE DEGREE OF FREEDOM SYSTEMS. Introduction. Spring-Mass System. Spring-Mass-Damper System. Forced Response. Transfer Functions and Frequency Methods. Measurement and Testing. Stability. Design and Control of Vibrations. Nonlinear Vibrations. Computing and Simulation in Matlab. Chapter Notes. References. Problems. 2. LUMPED PARAMETER MODELS. Introduction. Classifications of Systems. Feedback Control Systems. Examples. Experimental Models. Influence Methods. Nonlinear Models and Equilibrium. Chapter Notes. References. Problems. 3. MATRICES AND THE FREE RESPONSE. Introduction. Eigenvalues and Eigenvectors. Natural Frequencies and Mode Shapes. Canonical Forms. Lambda Matrices. Oscillation Results. Eigenvalue Estimates. Computational Eigenvalue Problems in Matlab. Numerical Simulation of the Time Response in Matlab. Chapter Notes. References. Problems. 4. STABILITY. Introduction. Lyapunov Stability. Conservative Systems. Systems with Damping. Semidefinite Damping . Gyroscopic Systems. Damped Gyroscopic Systems. Circulatory Systems. Asymmetric Systems. Feedback Systems. Stability in the State Space. Stability Boundaries. Chapter Notes. References. Problems. 5. FORCED RESPONSE OF LUMPED PARAMETER SYSTEMS. Introduction. Response via State Space Methods. Decoupling Conditions and Modal Analysis. Response of Systems with Damping. Bounded-Input, Bounded-Output Stability. Response Bounds. Frequency Response Methods. Numerical Simulations in Matlab. Chapter Notes. References. Problems. 6. DESIGN CONSIDERATIONS. Introduction. Isolators and Absorbers. Optimization Methods. Damping Design. Design Sensitivity and Redesign. Passive and Active Control. Design Specifications. Model Reduction. Chapter Notes. References. Problems. 7. CONTROL OF VIBRATIONS. Introduction. Controllability and Observability. Eigenstructure Assignment. Optimal Control. Observers (Estimators). Realization. Reduced-Order Modeling. Modal Control in State Space. Modal Control in Physical Space. Robustness. Positive Position Feedback Control. Matlab Commands for Control Calculations. Chapter Notes. References. Problems. 8. VIBRATION MEASUREMENT. Introduction. Measurement Hardware. Digital Signal Processing. Random Signal Analysis. Modal Data Extraction (Frequency Domain). Modal Data Extraction (Time Domain). Model Identification. Model Updating. Chapter Notes. References. Problems. 9. DISTRIBUTED PARAMETER MODELS. Introduction. Vibrations of Strings. Rods and Bars. Vibration of Beams. Membranes and Plates. Layered Materials. Viscous Damping. Chapter Notes. References. Problems. 10. FORMAL METHODS OF SOLUTION. Introduction. Boundary Value Problems and Eigenfunctions. Modal Analysis of the Free Response. Modal Analysis in Damped Systems. Transform Methods. Green's Functions. Chapter Notes. References. Problems. 11. OPERATORS AND THE FREE RESPONSE. Introduction. Hilbert Spaces. Expansion Theorems. Linear Operators. Compact Operators. Theoretical Modal Analysis. Eigenvalue Estimates. Enclosure Theorems. Oscillation Theory. Chapter Notes. References. Problems. 12. FORCED RESPONSE AND CONTROL. Introduction. Response by Modal Analysis. Modal Design Criteria. Combined Dynamical Systems. Passive Control and Design. Distribution Modal Control. Nonmodal Distributed Control. State Space Control Analysis. Chapter Notes. References. Problems. 13. APPROXIMATIONS OF DISTRIBUTED PARAMETER MODELS. Introduction. Modal Truncation. Rayleigh- Ritz-Galerkin Approximations. Finite Element Method. Substructure Analysis. Truncation in the Presence of Control. Impedance Method of Truncation and Control. Chapter Notes. References. Problems. APPENDIX A: COMMENTS ON UNITS. APPENDIX B: SUPPLEMENTARY MATHEMATICS. Index.

Vibration With Control

In this paper, research on transverse vibrations of axially moving strings and their control is thoroughly reviewed. In the last few decades, there have been extensive studies on analysis and control of transverse vibrations of axially moving strings because of the wide applications of many engineering devices that axially moving strings represent. In the investigations adopting linear models of moving strings, the paper summarizes recent studies on modal analysis, complicatedly constrained strings, coupled vibrations, and parametric vibration, as well as some early results. In the investigations adopting nonlinear models of moving strings, the paper presents the governing equations with large amplitude, and reviews progress on discretized or direct approximate analytical analyses and numerical approaches based on the Galerkin method or the finite difference method. Furthermore, investigations are reported on modeling of damping mechanisms as viscoelastic materials, coupled vibration of power transmission systems, and bifurcation and chaos. The state of the art of active control of moving strings is surveyed on controllability and observability, the Laplace transform domain analysis and the energy analysis, nonlinear vibration control and adaptive vibration control. Finally, future research directions are suggested such as nonlinear vibration of moving strings under complex constraints and couplings, energetics of nonlinear and time-varying strings, bifurcation and chaos in transverse motion of moving strings, control of hybrid systems containing moving strings, robust and adaptive controls of nonlinear moving strings, and experimental investigations. In this review article there are 242 references cited. @DOI: 10.1115/1.1849169#

Analysis and Control of Transverse Vibrations of Axially Moving Strings

Research and applications of viscoelastic vibration damping materials: A review

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

On introduit l'idee de gyricite distribuee selon laquelle chaque element de volume d'un milieu continu possede une quantite infinitesimale de moment angulaire stocke. Le milieu continu est suppose elastique. On etablit une equation aux derivees partielles regissant les petits deplacements de ce milieu continu gyroelastique. On deduit les modes de vibration gyroelastique

Dynamics of Gyroelastic Continua

This paper builds on the theory of gyroelastic dynamics presented in a recent paper by the authors. An elastic continuum with a continuous distribution of stored angular momentum ( called gyricity) is considered. We introduce the modal parameters (coefficients) thereof, including integrals of the mode shapes, and show they must satisfy a number of useful identities. In addition to the coefficients (p α and h α ) associated with momentum and angular momentum which also arise in the dynamics of a purely elastic body, there is a third coefficient (g α ) wholly attributable to the gyricity distribution. The modal parameter analysis presented here is an extension of that for purely elastic continua. The analysis concludes with a simple demonstration of the theoretical results using a spatially discretized model of a cantilevered rod.

P. C. Hughes

Papers

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

Dynamics of Gyroelastic Continua

Modal Parameter Analysis of Gyroelastic Continua

Asymptotic Stability of Linear Stationary Mechanical Systems

Influence of Stored Angular Momentum on the Modal Characteristics of Spacecraft With Flexible Appendages