The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The ef...The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.展开更多
The propagation of thermoelastic waves in a homogeneous,isotropic elastic semi-infinite space is subjected to rotation and initial stress,which is at temperature T_(0)-initially,and whose boundary surface is subjected...The propagation of thermoelastic waves in a homogeneous,isotropic elastic semi-infinite space is subjected to rotation and initial stress,which is at temperature T_(0)-initially,and whose boundary surface is subjected to heat source and load moving with finite velocity.Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions.Numerical results have been given and illustrated graphically in each case considered.Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress.The results indicate that the effect of the rotation and initial stress is very pronounced.展开更多
In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and ...In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.展开更多
This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initial...This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.展开更多
The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the prob...The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.展开更多
A theoretical analysis of the lateral resonances in 1-3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that i...A theoretical analysis of the lateral resonances in 1-3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that include initial stress for the propagation of acoustic plane waves are made. Numerical calculations are performed to study the effects of the initial stress on the lateral mode frequencies and the stop band. It is found that lateral mode frequencies increase with the piezoelectricity of the piezocomposites, but decrease with the poling initial stress. The influence of the initial shear stress on the lateral mode frequencies is minimal, and can thus be neglected.展开更多
Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a comp...Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.展开更多
The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initia...The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.展开更多
By using GDS dynamic hollow cylinder torsional apparatus, a series of cyclic torsional triaxial tests under complex initial consolidation condition are performed on Nanjing saturated fine sand. The effects of the init...By using GDS dynamic hollow cylinder torsional apparatus, a series of cyclic torsional triaxial tests under complex initial consolidation condition are performed on Nanjing saturated fine sand. The effects of the initial principal stress direction αo, the initial ratio of deviatoric stress η0, the initial average effective principal stress Po and the initial intermediate principal stress parameter b0 on the threshold shear strain γt of Nanjing saturated fine sand are then systematically investigated. The results show that γt increases as η0,p0 and b0 increase respectively, while the other three parameters remain constant. ao has a great influence on γt, which is reduced when ao increases from 0° to 45°and increased when α0 increases from 45° to 90°. The effect of α0 on γt, plays a leading role and the effect of η0 will weaken when ao is approximately 45°.展开更多
Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation i...Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.展开更多
The dispersion relation of torsional wave in a dissipative,incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated.The governing equation and closed form solutions ar...The dispersion relation of torsional wave in a dissipative,incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated.The governing equation and closed form solutions are derived with the aid of Biot’s principle.Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details.We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form.Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs.The analytical and numerical solutions reveal that,the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell.The numerical results reveal that,the initial stresses and dissipation,considerably,effect the phase velocity of the torsional wave.It has been observed that,any change in dissipation parameter(δ)produces a substantial change in damping velocity of torsional wave.In addition,it can be seen that,the phase velocity increases as the initial stress parameter increases.Finally,the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation.The conclusion made shown the consistency with the Biot’s incremental deformation theory,and the effective on model such as engineering mechanics and displacement of particles.展开更多
This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of...This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder.It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system.After appearance of the initial stresses,the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load.This influence is studied with utilizing the so-called threedimensional linearized theory of elastic waves in elastic bodies with initial stresses.For solution of the corresponding mathematical problems,the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved.Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed.In particular,it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.展开更多
In this paper,we present our report on the forced vibration of a bi-layered plate-strip with initial stress resting on a rigid foundation induced by a time-harmonic force.The investigation is carried out according to ...In this paper,we present our report on the forced vibration of a bi-layered plate-strip with initial stress resting on a rigid foundation induced by a time-harmonic force.The investigation is carried out according to the piecewise homogeneous body model with utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies(TLTEWISB).The materials of the body are chosen to be linearly elastic,homogeneous,and isotropic.The interface between the layers is assumed to be imperfect,and is simulated by the spring-layer model.A similar degree of imperfection on the interface is realized in the normal and tangential directions.The mathematical model for the problem under consideration is designed,and the system of the equations of motion is approximately solved by employing the finite element method(FEM).The numerical results explaining the influence of the parameter that characterizes the degree of corresponding imperfectness on the dynamic response of the plate-strip are presented.In particular,we demonstrate that the distributions of the normal stress become flat,as the normal-spring parameter increases.展开更多
In this paper we introduce the effect of initial stress on a magneto-thermoe- lastic functionally graded material (FGM) with Green Naghdi theory with energy dissipation. A system of PDE was obtained. The normal mode a...In this paper we introduce the effect of initial stress on a magneto-thermoe- lastic functionally graded material (FGM) with Green Naghdi theory with energy dissipation. A system of PDE was obtained. The normal mode analysis method is used to convert these equations into ODE and get the analytical solution to write expressions for displacements, temperatures, stresses. Some comparisons carried out to view the initial stress influence on the field variables. Numerical results are graphed to view the influence of initial stress. Some particular cases are deduced in this study.展开更多
Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial...Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.展开更多
The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing c...The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.展开更多
Evaluation of hydromechanical shear behavior of unsaturated soils is still a challenging issue. The time and cost needed for conducting precise experimental investigation on shear behavior of unsaturated soils have en...Evaluation of hydromechanical shear behavior of unsaturated soils is still a challenging issue. The time and cost needed for conducting precise experimental investigation on shear behavior of unsaturated soils have encouraged several investigators to develop analytical, empirical, or semi-empirical models for predicting the shear behavior of unsaturated soils. However, most of the previously proposed models are for specimens subjected to the isotropic state of stress, without considering the effect of initial shear stress. In this study, a hydromechanical constitutive model is proposed for unsaturated collapsible soils during shearing, with consideration of the effect of the initial shear stress. The model implements an effective stress-based disturbed state concept (DSC) to predict the stress-strain behavior of the soil. Accordingly, material/state variables were defined for both the start of the shearing stage and the critical state of the soil. A series of laboratory tests was performed using a fully automated unsaturated triaxial device to verify the proposed model. The experimental program included 23 suction-controlled unsaturated triaxial shear tests on reconstituted specimens of Gorgan clayey loess wetted to different levels of suctions under both isotropic and anisotropic stress states. The results show excellent agreement between the prediction by the proposed model and the experimental results.展开更多
The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introdu...The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.展开更多
A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-s...A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10672017 and 10632020)the China Postdoctoral Science Foundation,Heilongjiang Province Postdoctoral Science Foundation Japan Society for the Promotion of Science(JSPS) to perform research work at Tokyo Institute of Technology,Japan.
文摘The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.
基金Dr.Fatima Bayones is thankful for the support of Deanship of Scientific Research at Taif University for funding the Future researcher Program,project No.(1-439-6094).
文摘The propagation of thermoelastic waves in a homogeneous,isotropic elastic semi-infinite space is subjected to rotation and initial stress,which is at temperature T_(0)-initially,and whose boundary surface is subjected to heat source and load moving with finite velocity.Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions.Numerical results have been given and illustrated graphically in each case considered.Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress.The results indicate that the effect of the rotation and initial stress is very pronounced.
基金Project supported by the National Natural Science Foundation of China(Nos.11922209,11991031 and 12021002)。
文摘In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.
文摘This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.
文摘The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.
基金Project supported by the National Natural Science Foundation of China(Nos.90205030 and 10472088)
文摘A theoretical analysis of the lateral resonances in 1-3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that include initial stress for the propagation of acoustic plane waves are made. Numerical calculations are performed to study the effects of the initial stress on the lateral mode frequencies and the stop band. It is found that lateral mode frequencies increase with the piezoelectricity of the piezocomposites, but decrease with the poling initial stress. The influence of the initial shear stress on the lateral mode frequencies is minimal, and can thus be neglected.
基金the National Natural Science Foundation of China(10562004,10662004)the Natural Science Foundation of Jiangxi of China(0512021)+1 种基金the Science Foundation of Jiangxi Educational Department of China([2006]3)the Foundation of Train
文摘Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.
基金the Western Transport Construction Science and Technology Project of the Ministry of Transport of the People's Republic of China(No.2009318000046)
文摘The back analysis of initial stress is usually based on measured stress values, but the measuring of initial stress demands substantial investment. Therefore, amounts of underground engineering have no measured initial stress data, such as tunneling engineering. Focusing on this problem, a new back analysis method which does not need measured initial stress data is developed. The fault is assumed to be caused by initial load, the displacement discontinuity method (DDM) which considered non-linear fault is adopted to establish a numerical model of the engineering site, and the multivariable regression analysis of the initial stress field around the faults is carried out based on the fault throw. The result shows that the initial stress field around the faults is disturbed significantly, stress concentration appears in the tip zone, the regressive fault throw matches the measured values well, and the regressive initial stress field is reliable.
基金supported by the Key Research Project of National Natural Science Foundation of China under grant No. 90715018the Special Fund for the Commonweal Industry of China under grant No. 200808022the Key Basic Research Program of Natural Science of University in Jiangsu Province under grant No. 08KJA560001
文摘By using GDS dynamic hollow cylinder torsional apparatus, a series of cyclic torsional triaxial tests under complex initial consolidation condition are performed on Nanjing saturated fine sand. The effects of the initial principal stress direction αo, the initial ratio of deviatoric stress η0, the initial average effective principal stress Po and the initial intermediate principal stress parameter b0 on the threshold shear strain γt of Nanjing saturated fine sand are then systematically investigated. The results show that γt increases as η0,p0 and b0 increase respectively, while the other three parameters remain constant. ao has a great influence on γt, which is reduced when ao increases from 0° to 45°and increased when α0 increases from 45° to 90°. The effect of α0 on γt, plays a leading role and the effect of η0 will weaken when ao is approximately 45°.
基金Indian Institute of Technology (Indian School of Mines),Dhanbad,India for providing Junior Research Fellowship
文摘Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.
基金The authors thank Taif university researchers for supporting project number(TURSP-2020/16),Taif University,Taif,Saudi Arabia.The first author would like to acknowledge the supports provided by the Deanship of Scientific Research of Prince Sattam bin Abdulaziz University during this research work.
文摘The dispersion relation of torsional wave in a dissipative,incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated.The governing equation and closed form solutions are derived with the aid of Biot’s principle.Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details.We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form.Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs.The analytical and numerical solutions reveal that,the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell.The numerical results reveal that,the initial stresses and dissipation,considerably,effect the phase velocity of the torsional wave.It has been observed that,any change in dissipation parameter(δ)produces a substantial change in damping velocity of torsional wave.In addition,it can be seen that,the phase velocity increases as the initial stress parameter increases.Finally,the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation.The conclusion made shown the consistency with the Biot’s incremental deformation theory,and the effective on model such as engineering mechanics and displacement of particles.
文摘This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder.It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system.After appearance of the initial stresses,the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load.This influence is studied with utilizing the so-called threedimensional linearized theory of elastic waves in elastic bodies with initial stresses.For solution of the corresponding mathematical problems,the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved.Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed.In particular,it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.
基金supported by Research Fund of Kastamonu University under project number KUBAP-01/2016-4.
文摘In this paper,we present our report on the forced vibration of a bi-layered plate-strip with initial stress resting on a rigid foundation induced by a time-harmonic force.The investigation is carried out according to the piecewise homogeneous body model with utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies(TLTEWISB).The materials of the body are chosen to be linearly elastic,homogeneous,and isotropic.The interface between the layers is assumed to be imperfect,and is simulated by the spring-layer model.A similar degree of imperfection on the interface is realized in the normal and tangential directions.The mathematical model for the problem under consideration is designed,and the system of the equations of motion is approximately solved by employing the finite element method(FEM).The numerical results explaining the influence of the parameter that characterizes the degree of corresponding imperfectness on the dynamic response of the plate-strip are presented.In particular,we demonstrate that the distributions of the normal stress become flat,as the normal-spring parameter increases.
文摘In this paper we introduce the effect of initial stress on a magneto-thermoe- lastic functionally graded material (FGM) with Green Naghdi theory with energy dissipation. A system of PDE was obtained. The normal mode analysis method is used to convert these equations into ODE and get the analytical solution to write expressions for displacements, temperatures, stresses. Some comparisons carried out to view the initial stress influence on the field variables. Numerical results are graphed to view the influence of initial stress. Some particular cases are deduced in this study.
文摘Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.
基金Project supported by the National Natural Science Foundation of China(Nos.12241205 and 12032019)the National Key Research and Development Program of China(No.2022YFA1203200)the Strategic Priority Research Program of Chinese Academy of Sciences(Nos.XDB0620101 and XDB0620103)。
文摘The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.
文摘Evaluation of hydromechanical shear behavior of unsaturated soils is still a challenging issue. The time and cost needed for conducting precise experimental investigation on shear behavior of unsaturated soils have encouraged several investigators to develop analytical, empirical, or semi-empirical models for predicting the shear behavior of unsaturated soils. However, most of the previously proposed models are for specimens subjected to the isotropic state of stress, without considering the effect of initial shear stress. In this study, a hydromechanical constitutive model is proposed for unsaturated collapsible soils during shearing, with consideration of the effect of the initial shear stress. The model implements an effective stress-based disturbed state concept (DSC) to predict the stress-strain behavior of the soil. Accordingly, material/state variables were defined for both the start of the shearing stage and the critical state of the soil. A series of laboratory tests was performed using a fully automated unsaturated triaxial device to verify the proposed model. The experimental program included 23 suction-controlled unsaturated triaxial shear tests on reconstituted specimens of Gorgan clayey loess wetted to different levels of suctions under both isotropic and anisotropic stress states. The results show excellent agreement between the prediction by the proposed model and the experimental results.
文摘The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.
文摘A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.
