The Biot Model and Its Application in Viscoelastic Composite Structures

2007 ◽  
Vol 129 (5) ◽  
pp. 533-540 ◽  
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.

scholarly journals Dissipative properties of composite structures. 1. Statement of problem

2021 ◽  
Vol 4 (398) ◽  
pp. 24-34
Author(s):  
Boris Yartsev ◽  
◽  
Viktor Ryabov ◽  
Lyudmila Parshina ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Composite Structures ◽  
Sandwich Plate ◽  
Complex Modulus ◽  
Viscoelastic Composite ◽  
Hamilton Variational Principle ◽  
Viscoelastic Polymer ◽  
Rigid Layer ◽  
Anisotropic Layers ◽  
Generalized Curves

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.

Elastic–Viscoelastic Composite Structures Analysis With an Improved Burgers Model

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Shanhong Ren ◽  
Guozhong Zhao ◽  
Shunqi Zhang
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Composite Structures ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Refined Model ◽  
Viscoelastic Materials ◽  
Viscoelastic Composite ◽  
Burgers Model

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.

Kinematic Optimization of a Modified Helical Gear Train

1997 ◽  
Vol 119 (2) ◽  
pp. 307-314 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay ◽  
Ching-Huan Tseng
Keyword(s):  
Mathematical Model ◽  
Gear Tooth ◽  
Optimization Method ◽  
Helical Gear ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Numerical Examples ◽  
Kinematic Optimization ◽  
Kinematic Errors ◽  
Center Distance

A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.

THE INFLUENCE OF FLEXIBILITY OF THE SUPPORT ON DYNAMIC BEHAVIOR OF A CRANE

2011 ◽  
Vol 21 (10) ◽  
pp. 2963-2974 ◽  
Author(s):  
ANDRZEJ URBAŚ ◽  
MAREK SZCZOTKA ◽  
STANISŁAW WOJCIECH
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Dynamic Behavior ◽  
Dynamic Optimization ◽  
Optimization Method ◽  
Numerical Calculations ◽  
Final Position ◽  
Joint Coordinates ◽  
The Mathematical Model

The problem of control of the motion of a crane is considered in the paper. The mathematical model of the system is formulated using joint coordinates and homogenous transformations. The dynamic optimization method is applied in order to find drive functions realizing the desired trajectory and stabilizing the final position of the load at the end of motion in spite of the flexibility of the support. The results of numerical calculations and possible applications of models developed using artificial neural networks are also presented.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

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

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.

scholarly journals Stability of Membrane Elastodynamics with Applications to Cylindrical Aneurysms

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
A. Samuelson ◽  
P. Seshaiyer
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Arterial Wall ◽  
Abdominal Aortic Aneurysms ◽  
Medical Problem ◽  
Aortic Aneurysms ◽  
Numerical Techniques ◽  
Abdominal Aortic ◽  
Complex Fluid ◽  
Fluid Solid Interaction

The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

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