An Approach to Experimental Computation of an Anisotropic Viscoelastic Plate Stiffnesses
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An Approach to Experimental Computation of an Anisotropic Viscoelastic Plate Stiffnesses L. A. Kabanova* (Submitted by A. V. Lapin) Moscow State University, Moscow, 119991 Russia Received April 1, 2020; revised April 9, 2020; accepted April 15, 2020
Abstract—The viscoelastic behavior of anisotropic composite is studied in this paper. Constitutive relations and equilibrium equations are derived for a Kirchhoff plate using general linear viscoelasticity constitutive relations for the anisotropic case. The derived model parameters—plate stiffnesses— are experimental functions. An approach to these parameters identification is given for certain cases of material properties. DOI: 10.1134/S1995080220100091 Keywords and phrases: linear viscoelasticity, plates theory, identification problem, anisotropic materials, total least squares.
1. INTRODUCTION Viscoelastic properties study is one of the most dynamically developing branches of material science, as well as composite mechanics. For applications, some simplified models like rods, plates, and shells are significant. This paper comes to continue papers [1–6], dedicated to the construction of composite mechanics models of nonhomogeneous anisotropic rods and plates. Two results are presented there: following the approach stated in [5] a plate model is derived for time-dependent material properties, as a generalization of the elastic case; and an approach to the said model identification method. The method of model construction is based on classical for engineering mechanics approach of reducing three-dimensional continuum equilibrium equations into two-dimensional field equations. The considered reduction is based on kinematical and statical hypotheses, but there are also different methods like the power series expansion, asymptotic methods, etc, some of them are illustrated in [7–12]. Such approaches, first arising in linear elasticity tasks, were successfully generalized for an anisotropic, nonhomogeneous case, as well as for isotropic viscoelastic case. This paper presents a version of anisotropic viscoelastic plates theory—an isotropic one is enough for some thin structures like foams [16–18], but an increase of thickness leads to the significant influence of anisotropy. A noticeable difficulty of anisotropic viscoelasticity constitutive relations usage lies in asymmetric modulus tensor [19], which does not occur in the isotropic case, but still allows using Kirchhoff hypothesis [13]. In accordance with an approach [20] of reducing identification problem into a least-squares one a set of experimental tests, as well as a data processing method, were supplied by one of the authors for an elastic plate, this paper is conscripted to suggest a solution for a linear viscoelastic plate. A classical coordination of a plate is used; small Latin indexes i, j are supposed to ∈ [1..3], big Latin ∂a , a dot is derivative with indexes I, J ∈ [1..2], a comma represents partial spatial derivative a,j = ∂x j respect to time. *
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2010
AN APPROACH TO EXPERIMENTAL COMP
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