scholarly journals Mathematical modelling of thermoelasticity problems for thin biperiodic cylindrical shells

2021 ◽  
Author(s):  
B. Tomczyk ◽  
M. Gołąbczak ◽  
A. Litawska ◽  
A. Gołąbczak
Keyword(s):  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Asymptotic Model ◽  
Heat Sources ◽  
Asymptotic Models ◽  
Stationary Action ◽  
Constant Coefficients ◽  
A Cell ◽  
Fourier Heat Conduction ◽  
Tolerance Model

AbstractThe objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss two new averaged mathematical models for the analysis of selected dynamic thermoelasticity problems for the shells under consideration: the non-asymptotictolerance and the consistent asymptotic models. The starting equations are the well-known governing equations of linear Kirchhoff-Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation in which the heat sources are neglected. For the microperiodic shells under consideration, the starting equations mentioned above have highly oscillating, non-continuous and periodic coefficients. The tolerance model is derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. It has constant coefficients depending also on a cell size. Hence, this model makes it possible to study the effect of a microstructure size on the global shell thermoelasticity (the length-scale effect). The consistent asymptotic model is obtained using the consistent asymptotic approach. It has constant coefficients being independent of the period lengths. Moreover, the comparison between the tolerance model for biperiodic shells proposed here and the known tolerance model for cylindrical shells with a periodic structure in the circumferential direction only (uniperiodic shells) is presented.

scholarly journals Tolerance and asymptotic modelling of dynamic thermoelasticity problems for thin micro-periodic cylindrical shells

Meccanica ◽  
2020 ◽  
Vol 55 (12) ◽  
pp. 2391-2411 ◽  
Author(s):  
Barbara Tomczyk ◽  
Marcin Gołąbczak
Keyword(s):  
Cell Size ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Theory Of Elasticity ◽  
Asymptotic Model ◽  
Dynamic Thermoelasticity ◽  
Oscillating Coefficients ◽  
Stationary Action ◽  
A Cell ◽  
Model Equations

AbstractThe problem of linear dynamic thermoelasticity in Kirchhoff–Love-type circular cylindrical shells having properties periodically varying in circumferential direction (uniperiodic shells) is considered. In order to describe thermoelastic behaviour of such shells, two mathematical averaged models are proposed—the non-asymptotic tolerance and the consistent asymptotic models. Considerations are based on the known Kirchhoff–Love theory of elasticity combined with Duhamel-Neumann thermoelastic constitutive relations and on Fourier’s theory of heat conduction. The non-asymptotic tolerance model equations depending on a cell size are derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. The consistent asymptotic model equations being independent on a microstructure size are obtained by means of the consistent asymptotic approach. Governing equations of both the models have constant coefficients, contrary to starting shell equations with periodic, non-continuous and oscillating coefficients. As examples, two special length-scale problems will be analysed in the framework of the proposed models. The first of them deals with investigation of the effect of a cell size on the shape of initial distributions of temperature micro-fluctuations. The second one deals with study of the effect of a microstructure size on the distribution of total temperature field approximated by sum of an averaged temperature and temperature fluctuations.

scholarly journals Micro-Vibrations and Wave Propagation in Biperiodic Cylindrical Shells

2020 ◽  
Vol 22 (3) ◽  
pp. 789-808
Author(s):  
Barbara Tomczyk ◽  
Anna Litawska
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Combined Model ◽  
Asymptotic Models ◽  
Wave Propagation Problem ◽  
Modelling Procedure ◽  
Constant Coefficients ◽  
A Cell ◽  
Averaged Model

AbstractThe objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

scholarly journals Length-scale effect in stability problems for thin biperiodic cylindrical shells: extended tolerance modelling

2020 ◽  
Author(s):  
B. Tomczyk ◽  
M. Gołąbczak ◽  
A. Litawska ◽  
A. Gołąbczak
Keyword(s):  
Scale Effect ◽  
Cylindrical Shells ◽  
Length Scale ◽  
Stability Problems ◽  
Constant Coefficients ◽  
A Cell ◽  
Circular Cylindrical Shells ◽  
Tolerance Modelling ◽  
Tolerance Model ◽  
Shell Equations

Abstract Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells of periodically micro-inhomogeneous structure in circumferential and axial directions (biperiodic shells) are investigated. The aim of this contribution is to formulate and discuss a new averaged nonasymptotic model for the analysis of selected stability problems for these shells. This, so-called, general nonasymptotic tolerance model is derived by applying a certain extended version of the known tolerance modelling procedure. Contrary to the starting exact shell equations with highly oscillating, noncontinuous and periodic coefficients, governing equations of the tolerance model have constant coefficients depending also on a cell size. Hence, the model makes it possible to investigate the effect of a microstructure size on the global shell stability (the length-scale effect).

scholarly journals On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

2019 ◽  
Vol 32 (4) ◽  
pp. 1197-1216 ◽  
Author(s):  
Barbara Tomczyk ◽  
Marcin Gołąbczak ◽  
Anna Litawska ◽  
Andrzej Gołąbczak
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Heterogeneous Structure ◽  
Combined Model ◽  
Asymptotic Models ◽  
Constant Coefficients ◽  
A Cell ◽  
Circular Cylindrical Shells ◽  
Averaged Model

Abstract The objects of consideration are thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having a periodically micro-heterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to study certain problems of micro-vibrations and of wave propagation related to micro-fluctuations of displacement field caused by a periodic structure of the shells. These micro-dynamic problems will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling includes both the asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the combined model have constant coefficients depending also on a cell size. Hence, this model takes into account the effect of a microstructure size on the dynamic behaviour of the shells (the length-scale effect). It will be shown that the micro-periodic heterogeneity of the shells leads to cell-depending micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

Light-Induced Non-Contact Actuation and Control With Photostrictive Actuators

1997 ◽  
Author(s):  
H. S. Tzou ◽  
B. J. Liu
Keyword(s):  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Time History ◽  
Ultra Violet ◽  
High Energy ◽  
Electromechanical Actuators ◽  
Modeling And Analysis ◽  
Control Effectiveness ◽  
Control Forces ◽  
And Control

Abstract Non-contact light activated distributed opto-electromechanical actuators represent a new class of precision distributed actuator which are based on the photodeformation process and controlled by high energy lights, e.g., lasers and ultra-violet lights. Fundamental opto-thermo-electromechancial constitutive relations are discussed and formulations of optically induced control forces and moments introduced. Mathematical modeling and analysis of distributed opto-electromechanical shell actuators are presented. A generic distributed photo-actuation theory is proposed and the closed-loop opto-thermo-electromechancial equations of circular cylindrical shells are derived. The systems equations reveal the couplings among elasticity, photodeformation, pyroelectricity, and thermoelasticity. Active distributed control of flexible cylindrical shells using segmented distributed opto-electromechanical shell actuators are investigated and the control effectiveness is evaluated. Membrane and bending control effects are evaluated. Time history analyses of independent modal control reveal that the Lyapunov control is more effective than the proportional feedback control.

Thermoelastic state of cylindrical shells heated with moving normal-circular heat sources

1988 ◽  
Vol 20 (4) ◽  
pp. 539-546
Author(s):  
V. N. Maksimovich ◽  
L. V. Khomlyak ◽  
E. N. Novosad
Keyword(s):  
Cylindrical Shells ◽  
Thermoelastic State ◽  
Heat Sources ◽  
Circular Heat

Transient response of cylindrical shells to localized heat sources

1979 ◽  
Vol 54 (3) ◽  
pp. 337-347 ◽  
Author(s):  
Kaoru Shirakawa ◽  
Yoshihiro Ochiai
Keyword(s):  
Transient Response ◽  
Cylindrical Shells ◽  
Heat Sources

Heat Conduction in Composites: Homogenization and Macroscopic Behavior

1997 ◽  
Vol 50 (6) ◽  
pp. 327-356 ◽  
Author(s):  
Piotr Furman˜ski
Keyword(s):  
Heat Conduction ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Local Heat ◽  
Temperature Fields ◽  
Heat Sources ◽  
Ensemble Averaging ◽  
Macroscopic Behavior ◽  
Classical Behavior ◽  
Homogeneous Media

The review article discusses methods of macroscopic averaging of heat conduction in composite materials that lead to models of homogenized, macroscopic behavior of these media. It is shown that essentially two continuum models are in use: 1) the effective medium and 2) the mixture. The ensemble averaging technique allows one to derive the constitutive relations for both models assuming Fourier-like conduction on the microstructure level of a composite. These constitutive relations contain effective, macroscopic properties of the composite material which can be forecast when properties of individual constituents, the form of thermal interaction at constituent interfaces, amount of each material and its distribution are known. For weakly varying mean temperature fields, thermal behavior of the composite is essentially the same as homogeneous media but, for stronger variation, a non-classical behavior is observed. This non-classical behavior can be associated either with space nonlocality and memory phenomena or with wall effects and, in some cases, with influence of local heat sources on the effective properties. Most of these effects are not well known and need further detailed studies. The article includes 158 references.

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