Hysteretic damping and causality

Bobrovnitskiĭ, Yu. I.

doi:10.1134/s1063771013030032

Cited by 10 publications

(15 citation statements)

References 6 publications

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“…Primarily, we find the total energy of one period icity cell for propagation of a normal wave of type (2) over the lattice. For this, we use method [14]. According to this method, the time averaged total energy of the cell is equal to where Z is the matrix of its input impedances (1), v is the 4 vector of velocity amplitudes at the cell terminals, and the prime means the frequency derivative.…”

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

“…We emphasize that formula (14) contains the frequency derivatives from the effective parameters. If the effec tive parameters are independent of frequency, the right hand side of (14) reduces to the classic expres sion for energy.…”

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

“…This means that the time averaged kinetic and potential energies of a cell are identical and equal to half the total energy (14). Further dividing the total energy by the area of the periodicity cell, thus determining the energy density in the lattice, and then multiplying it by the group velocity vector, which is calculated by Eq.…”

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

“…However, not every function of frequency can be an effective param eter of any AMM. The necessary positivity of mechan ical energy (14) imposes quite rigorous restrictions on the allowable frequency dependences of the effective parameters of two dimensional AMMs. We note the most important restrictions.…”

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

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Models and general wave properties of two-dimensional acoustic metamaterials and media

Bobrovnitskiĭ

2015

Acoust. Phys.

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For two dimensional linear acoustic metamaterials and media represented in the form of periodic structures made of complex cells, a general model is proposed, formulas are derived for the effective param eters and energy characteristics, and the restrictions imposed on such media are formulated. They are divided into four main types, differing in general wave properties; the differentiating features of each type are shown. Several new schemes of negative and hyperbolic types of discrete and continuous metamaterials are pre sented, for which the dispersion dependences are constructed and the corresponding "wave" equations are written.

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Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

Section: Energy Characteristics and Restrictions On Ammsmentioning

confidence: 99%

See 2 more Smart Citations

Models and general wave properties of two-dimensional acoustic metamaterials and media

Bobrovnitskiĭ

2015

Acoust. Phys.

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“…Then, the composite becomes a metamaterial with unique acoustic properties [8][9][10][11][12][13][14] analogous to those of an electrodynamic medium with a negative permittivity and a negative permeability [15,16].…”

Section: Introductionmentioning

confidence: 99%

Transverse waves in a dispersive metamaterial with spherical inclusions

Fedotovskii

2015

Acoust. Phys.

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The propagation of transverse waves in a dispersive composite with solid inclusions is considered as propagation in a pseudoinhomogeneous medium whose effective properties, namely, the dynamic density and the shear rotational elasticity, depend in a resonance way on the wave frequency and the parameters of translatory and rotary oscillations of inclusions. Estimates are obtained for the natural oscillation frequencies of spherical inclusions in an incompressible elastic medium and for other internal dynamic parameters of the composite that determine the frequency bands corresponding to negative values of the dynamic density and the shear rotational elasticity. When the dynamic properties are simultaneously negative, the dispersive com posite is an acoustic metamaterial, which, from the viewpoint of certain specific effects, is analogous to left handed electrodynamic media much discussed in the literature. The parameters of the composite and the transverse wave frequencies at which the metamaterial properties can be achieved in practice are estimated.

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Seismic optimal design of hysteretic damping tuned mass damper (HD-TMD) for acceleration response control

Xiang,

Tan,

et al. 2023

Acta Mech

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Hysteretic damping and causality

Cited by 10 publications

References 6 publications

Models and general wave properties of two-dimensional acoustic metamaterials and media

Models and general wave properties of two-dimensional acoustic metamaterials and media

Transverse waves in a dispersive metamaterial with spherical inclusions

Seismic optimal design of hysteretic damping tuned mass damper (HD-TMD) for acceleration response control

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