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Register a new userNonlinear viscoelastic wave propagation: an extension of Nearly Constant Attenuation (NCQ) models
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Added by
Jean-Francois Semblat
Publication date
2009
fields
Physics
and research's language is
English
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Hysteretic damping is often modeled by means of linear viscoelastic approaches such as nearly constant Attenuation (NCQ) models. These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. The aim of this paper is to propose a mechanical model involving nonlinear viscoelastic behavior for isotropic materials. This model simultaneously takes into account nonlinear elasticity and nonlinear damping. On the one hand, the shear modulus is a function of the excitation level; on the other, the description of viscosity is based on a generalized Maxwell body involving non-linearity. This formulation is implemented into a 1D finite element approach for a dry soil. The validation of the model shows its ability to retrieve low amplitude ground motion response. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content).
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The quality factor (Q) links seismic wave energy dissipation to physical properties of the Earths interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common assumption in practice for seismic Q
Time-domain seismic forward and inverse modeling for a dissipative medium is a vital research topic to investigate the attenuation structure of the Earth. Constant Q, also called frequency independence of the quality factor, is a common assumption for seismic Q inversion. We propose the first- and second-order nearly constant Q dissipative models of the generalized standard linear solid type, using a novel Q-independent weighting function approach. The two new models, which originate from the Kolsky model (a nearly constant Q model) and the Kjartansson model (an exactly constant Q model), result in the corresponding wave equations in differential form. Even for extremely strong attenuation (e.g., Q = 5), the quality factor and phase velocity for the two new models are close to those for the Kolsky and Kjartansson models, in a frequency range of interest. The wave equations for the two new models involve explicitly a specified Q parameter and have compact and simple forms. We provide a novel perspective on how to build a nearly constant Q dissipative model which is beneficial for time-domain large scale wavefield forward and inverse modeling. This perspective could also help obtain other dissipative models with similar advantages. We also discuss the extension beyond viscoacousticity and other related issues, for example, extending the two new models to viscoelastic anisotropy.
We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe, analytically and numerically, the effects of nonlinear interaction force and energy loss on the dispersion of Rayleigh waves. We develop closed-form expressions to predict the dispersive characteristics of nonlinear Rayleigh waves by adopting a leading-order effective medium description. In particular, we demonstrate how hardening nonlinearity reduces and eventually eliminates the linear filtering bandwidth of the metasurface. Softening nonlinearity, in contrast, induces lower and broader spectral gaps for weak to moderate strengths of nonlinearity, and narrows and eventually closes the gaps at high strengths of nonlinearity. We also observe the emergence of a spatial gap (in wavenumber) in the in-phase branch of the dispersion curves for softening nonlinearity. Finally, we investigate the interplay between nonlinearity and energy loss and discuss their combined effects on the dispersive properties of the metasurface. Our analytical results, supported by finite element simulations, demonstrate the mechanisms for achieving tunable dispersion characteristics in nonlinear metasurfaces.
In this paper, we show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced by a corresponding generalised continuum of the relaxed micromorphic type. Specifically, we compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties: (i) the relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic continuum. We show that, while the Cauchy theory is able to describe the overall behaviour of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency band-gap and at frequencies intersecting the optical branches. In addition, we observe a computational time reduction associated with the use of the relaxed micromorphic continuum, compared to the sensible computational time needed to perform a transient computation in a micro-structured domain.
We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin-Voigt model. Simple analytical expressions for the radiation force and torque are obtained considering the low- and high-frequency approximation in the viscoelastic model. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) with a low- and high-density polyethylene particle chosen as examples. Negative axial radiation force and torque are predicted when the ratio of the longitudinal to shear relaxation times is smaller than a constant that depends on the speed of sound in the particle. In addition, a full 3D tractor Bessel vortex beam acting on the high-density polyethylene is depicted. These predictions may enable new possibilities of particle handling in acoustophoretic techniques.
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