Research On Generalized Thermoelastic Dynamic Response Of One Dimensional Hexagonal Quasicrystals

In 1984,Shechtman et al.observed icosahedral phase which has long range orientation and contains five fold rotational symmetry axis.It is a special material structure between crystal and non-crystal,namely quasicrystal(QC).Due to the unique particularity of symmetrical structure,QC has many special physical properties,such as high resistivity and low thermal conductivity.The classical thermoelasticity theory holds that heat propagates at an infinite speed,but the existence of heat waves means that heat propagates at a finite speed.For special material models(such as viscoelastic materials,porous materials,biological materials)and physical processes(such as abnormal conduction and abnormal diffusion),it is difficult to utilize the classical thermoelastic theory to describe their thermoelastic behavior.The fractional-order heat conduction equation obtained by introducing the fractional-order calculus operator into the non-Fourier’s heat conduction equation can explain the abnormal conduction and abnormal diffusion problems well.Subsequently,the fractional-order generalized thermoelasticity theories was established.Owing to the existence of phason field,the heat conduction problem of QCs is more complicated.In this paper,the thermoelastic behavior of one-dimensional(1D)hexagonal QCs is studied based on the generalized thermoelasticity theory and the fractional-order generalized thermoelasticity theory.In Chapter 1,the background,significance and present situation at home and abroad of QCs,the generalized thermoelasticity theories and the fractional order thermoelasticity theories,and the main work of this paper are introduced.In Chapter 2,based on the generalized thermoelasticity theory,the finite length 1D hexagonal piezoelectric QC rod is studied when the two ends are fixed and subjected to the action of moving heat source.The thermoelastic coupling equation of 1D hexagonal piezoelectric QCs is established and its numerical solution is obtained by the Laplace transform and inverse Laplace transform.Finally,the distributions of temperature,potential,displacement and stress in 1D hexagonal piezoelectric QCs are analyzed.The results reveal that due to the existence of phason field,the QC material subjected to the moving heat source is less disturbed than the classical material in the thermoelastic environment.In Chapter 3,based on the Sherief-type fractional-order thermoelasticity theory,the dynamic problem of a finite length 1D hexagonal QC rod with fixed ends subjected to a moving heat source is studied.The governing equation of this problem is obtained and solved by Laplace transform and its numerical inversion.Finally,the variation trends of displacement,temperature and stress with time,heat source velocity and fractional order parameter are obtained.It is found that the stress,displacement and temperature of 1D hexagonal QC increase with the increase of fractional order parameter when the speed of heat source and time keep constant,but the change in displacement is small.In Chapter 4,based on the Youssef-type fractional-order thermoelasticity theory,the dynamic response of a 1D hexagonal QC rod with fixed ends under the action of a moving heat source is studied.The results show that when the heat source velocity and time are constant,the absolute values of each physical quantity increase with the increase of the fractional-order parameter,but the fractional-order parameter have little influence on the displacement.