Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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Convolution-based time-domain simulation for fluidelastic instability in tube arrays

Nonlinear Dynamics ◽

10.1007/s11071-021-06475-3 ◽

2021 ◽

Author(s):

Mingjie Zhang ◽

Ole Øiseth

Keyword(s):

Impulse Response ◽

Response Function ◽

Time Domain ◽

Impulse Response Function ◽

Time Domain Simulation ◽

Unit Step ◽

Tube Arrays ◽

Unit Impulse ◽

The Time Domain ◽

Unit Impulse Response

AbstractA convolution-based numerical algorithm is presented for the time-domain analysis of fluidelastic instability in tube arrays, emphasizing in detail some key numerical issues involved in the time-domain simulation. The unit-step and unit-impulse response functions, as two elementary building blocks for the time-domain analysis, are interpreted systematically. An amplitude-dependent unit-step or unit-impulse response function is introduced to capture the main features of the nonlinear fluidelastic (FE) forces. Connections of these elementary functions with conventional frequency-domain unsteady FE force coefficients are discussed to facilitate the identification of model parameters. Due to the lack of a reliable method to directly identify the unit-step or unit-impulse response function, the response function is indirectly identified based on the unsteady FE force coefficients. However, the transient feature captured by the indirectly identified response function may not be consistent with the physical fluid-memory effects. A recursive function is derived for FE force simulation to reduce the computational cost of the convolution operation. Numerical examples of two tube arrays, containing both a single flexible tube and multiple flexible tubes, are provided to validate the fidelity of the time-domain simulation. It is proven that the present time-domain simulation can achieve the same level of accuracy as the frequency-domain simulation based on the unsteady FE force coefficients. The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions. However, the indirectly identified unit-step or unit-impulse response function may fail to capture the underlying discontinuity in the stability curve due to the prespecified expression for fluid-memory effects.

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