Dissipative properties of composite structures. 1. Statement of problem

Object and purpose of research. The object under study is a sandwich plate with two rigid anisotropic layers and a filler of soft isotropic viscoelastic polymer. Each rigid layer is an anisotropic structure formed by a finite number of orthotropic viscoelastic composite plies of arbitrary orientation. The purpose is to develop a mathematical model of sandwich plate. Materials and methods. The mathematical model of sandwich plate decaying oscillations is based on Hamilton variational principle, Bolotin’s theory of multilayer structures, improved theory of the first order plates (Reissner-Mindlin theory), complex modulus model and principle of elastic-viscoelastic correspondence in the linear theory of viscoelasticity. In description of physical relations for rigid layers the effects of oscillation frequencies and ambient temperature are considered as negligible, while for the soft viscoelastic polymer layer the temperaturefrequency relation of elastic-dissipative characteristics are taken into account based on experimentally obtained generalized curves. Main results. Minimization of the Hamilton functional makes it possible to reduce the problem of decaying oscillations of anisotropic sandwich plate to the algebraic problem of complex eigenvalues. As a specific case of the general problem, the equations of decaying longitudinal and transversal oscillations are obtained for the globally orthotropic sandwich rod by neglecting deformations of middle surfaces of rigid layers in one of the sandwich plate rigid layer axes directions. Conclusions. The paper will be followed by description of a numerical method used to solve the problem of decaying oscillations of anisotropic sandwich plate, estimations of its convergence and reliability are given, as well as the results of numerical experiments are presented.

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The Biot Model and Its Application in Viscoelastic Composite Structures

Journal of Vibration and Acoustics ◽

10.1115/1.2731408 ◽

2007 ◽

Vol 129 (5) ◽

pp. 533-540 ◽

Cited By ~ 21

Author(s):

J. Zhang ◽

G. T. Zheng

Keyword(s):

Mathematical Model ◽

Dynamic Behavior ◽

Composite Structures ◽

Optimization Method ◽

Noise Attenuation ◽

Viscoelastic Materials ◽

Numerical Techniques ◽

Viscoelastic Composite ◽

Biot Model ◽

Numerical Examples

Application of viscoelastic materials in vibration and noise attenuation of complicated machines and structures is becoming more and more popular. As a result, analytical and numerical techniques for viscoelastic composite structures have received a great deal of attention among researchers in recent years. Development of a mathematical model that can accurately describe the dynamic behavior of viscoelastic materials is an important topic of the research. This paper investigates the procedure of applying the Biot model to describe the dynamic behavior of viscoelastic materials. As a minioscillator model, the Biot model not only possesses the capability of its counterpart, the GHM (Golla-Hughes-McTavish) model, but also has a simpler form. Furthermore, by removing zero eigenvalues, the Biot model can provide a smaller-scale mathematical model than the GHM model. This procedure of dimension reduction is studied in detail here. An optimization method for determining the parameters of the Biot model is also investigated. With numerical examples, these merits, the computational efficiency, and the accuracy of the Biot model are illustrated and proved.

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Finite Element Martensite Ratio Derivation on NiTi via Measurable Criteria of Strain Rate

Volume 1: Active Materials, Mechanics and Behavior; Modeling, Simulation and Control ◽

10.1115/smasis2009-1452 ◽

2009 ◽

Author(s):

Abbas Amini ◽

Hamid Mehdigholi ◽

Mohammad Elahinia

Keyword(s):

Mathematical Model ◽

Strain Rate ◽

Composite Structures ◽

High Sensitivity ◽

Smart Composite ◽

Rate Dependency ◽

Smart Composites ◽

Measurable Amount ◽

Macro Scale ◽

Smart Composite Structures

The shape memory alloys (SMAs) and smart composites have a large use in high and low level industry, while a lot of research is being done in this field. The existence of smart composite structures is because of the advance mechanical benefits of the above materials. This work refers to dynamic and quasi static nonlinear explanation of these materials. After mathematical model consideration on the rate of strain, a model which is about martensite ratio of NiTi has been presented. This work has been done because of the high sensitivity of these materials to strain rate and use of visual and measurable engineering criteria to access other variables. As the martensite ratio is not engineering measurable amount, it needs to have macro scale property to measure this important nano scale criteria. Relative experiments are done to show the rate dependency of NiTi.

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Filling of a complex-shaped mold with a viscoelastic polymer. Part I: The mathematical model

Polymer Engineering & Science ◽

10.1002/pen.760330705 ◽

1993 ◽

Vol 33 (7) ◽

pp. 400-409 ◽

Cited By ~ 16

Author(s):

Thanasis D. Papathanasiou ◽

M. R. Kamal

Keyword(s):

Mathematical Model ◽

Viscoelastic Polymer ◽

Polymer Part ◽

The Mathematical Model

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The Scheffe’s method in the study of mathematical model of the polymeric hydrogels composite structures optimization

Mathematical Modeling and Computing ◽

10.23939/mmc2019.02.258 ◽

2019 ◽

Vol 6 (2) ◽

pp. 258-267

Author(s):

О. M. Grytsenko ◽

◽

P. Ya. Pukach ◽

O. V. Suberlyak ◽

V. S. Moravskyi ◽

...

Keyword(s):

Mathematical Model ◽

Composite Structures ◽

Polymeric Hydrogels

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Numerical method for nonlinear complex eigenvalues problems depending on two parameters: Application to three-layered viscoelastic composite structures

Mechanics of Advanced Materials and Structures ◽

10.1080/15376494.2017.1286418 ◽

2017 ◽

Vol 25 (15-16) ◽

pp. 1361-1373 ◽

Cited By ~ 4

Author(s):

Komlan Akoussan ◽

Hakim Boudaoud ◽

El Mostafa Daya ◽

Yao Koutsawa ◽

Erasmo Carrera

Keyword(s):

Numerical Method ◽

Composite Structures ◽

Viscoelastic Composite ◽

Complex Eigenvalues ◽

Two Parameters

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Improved layer-wise optimization algorithm for the design of viscoelastic composite structures

Composite Structures ◽

10.1016/j.compstruct.2017.05.047 ◽

2017 ◽

Vol 176 ◽

pp. 342-358 ◽

Cited By ~ 5

Author(s):

Komlan Akoussan ◽

Mohamed Hamdaoui ◽

El Mostafa Daya

Keyword(s):

Optimization Algorithm ◽

Composite Structures ◽

Viscoelastic Composite

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Finite Element Modelling of Frequency-Dependent Dynamic Behaviour of Viscoelastic Composite Structures

Advanced Composites Letters ◽

10.1177/096369350401300101 ◽

2004 ◽

Vol 13 (1) ◽

pp. 096369350401300 ◽

Cited By ~ 2

Author(s):

Evgeny Barkanov ◽

Andris Chate

Keyword(s):

Finite Element ◽

Composite Structures ◽

Laminated Composite ◽

Element Analysis ◽

Viscoelastic Composite ◽

Fitting Procedure ◽

Damping Characteristics ◽

Storage And Loss Moduli ◽

Free Vibration Frequency ◽

Viscoelastic Layers

Finite element analysis of sandwich and laminated composite structures with viscoelastic layers is performed. The present implementation gives the possibility to preserve the frequency dependence for the storage and loss moduli of viscoelastic materials exactly. Moreover, the storage and loss moduli in this case are defined directly in the frequency domain by an experimental technique for each material and can be used after curve fitting procedure in the numerical analysis. Damping characteristics of viscoelastic composite structures are evaluated by the energy method, the method of complex eigenvalues, from the resonant peaks of the frequency response function and using the steady state vibrations. Numerical examples are given to demonstrate the validity and application of the approaches developed for the free vibration, frequency and transient response analyses.

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