Xiaogeng Tian

A high order theory for functionally graded piezoelectric shells

A high order theory is presented to examine the electromechanical behavior of piezoelectric generic shells with graded material properties in the thickness direction. Different types of charge equations, depending upon whether the driving signal of piezoelectrics is free charge or electric voltage, have been derived. The obtained equations can be readily reduced to typical structures, such as beams, plates and circular cylindrical shells. The high order theory has been used to study the sensing and actuating behavior of a simply supported inhomogeneous piezoelectric circular cylindrical shell and, for comparison and validation purposes, a homogeneous shell. Comparison between the obtained numerical results to those available exact solutions for homogeneous shell shows that the developed theory is accurate. The effects of graded material properties on the piezoelectrically induced displacements, stresses, electric potential and electric displacements distributions are also quantified, clearly showing the advantage of functionally graded piezoelectrics over homogeneous ones in terms of the usages as sensors and actuators.

State space approach to one-dimensional thermal shock problem for a semi-infinite piezoelectric rod

The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one-dimensional semi-infinite piezoelectric rod with its left boundary subjected to a sudden heat. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. Approximate small-time analytical solutions to stress, displacement and temperature are obtained by means of the Laplace transform and inverse transform. It is found that there are two discontinuous points in both stress and temperature solutions. Numerical calculation for stress, displacement and temperature is carried out and displayed graphically.

TRANSIENT MAGNETO-THERMOELASTIC RESPONSE FOR A SEMI-INFINITE BODY WITH VOIDS AND VARIABLE MATERIAL PROPERTIES DURING THERMAL SHOCK

In this work the magneto-thermoelastic problem of a semi-infinite body with voids and temperature-dependent material properties placed in a transverse magnetic field is investigated in the context of different theories of generalized thermoelasticity. The upper surface of the body is subjected to a zonal time-dependent heat shock. The solution is obtained by solving finite element governing equations of the problem. The results, including temperature, stresses, displacements, the change in volume fraction field, induced magnetic field and induced electric field are presented graphically. Comparisons are made in the results obtained under different theories of generalized thermoelasticity and three forms of temperature-dependent material properties (absolute temperature-dependent, reference temperature-dependent, and temperature-independent). Finally the voids effects in the theory of thermoelasticity are presented graphically.

Wave Characteristics of Two-Dimensional Hierarchical Hexagonal Lattice Structures

Hierarchical structures are structures that themselves contain structural elements. Hier-archical lattice structures are counterparts of the traditional lattice structures, whosewalls are replaced by some kind of structure. In this paper, wave propagation in two-dimensional hierarchical hexagonal lattice structures is calculated by the finite elementmethod with the Bloch theory. Attention is devoted to the comparison of the band gap,wave mode, dispersion surface, and phase and group velocities between the second-orderhierarchical hexagonal lattice structures and their first-order traditional counterpart.The results show that the former structures have more band gaps and similar isotropicwave behavior in the low frequency compared to the latter structure. The structure hier-archy is favorable for the periodic lattice structure to filtering or guiding wave at somecircumstances to meet the demands of engineering. [DOI: 10.1115/1.4025550]Keywords: Bloch theory, band gap, finite element method, hierarchical lattice structure

Pentamode metamaterials with asymmetric double-cone elements

Pentamode metamaterials are a very interesting set of artificial solids. They are difficult to compress but flow easily, hence imitating somehow the behaviours of liquids. In this paper, three-dimensional (3D) pentamode metamaterials based on the asymmetric double-cone element (ADCE) are proposed. The ADCE is composed by two connected truncated cones with different thin diameters. The phonon band structures of the ADCEs pentamode metamaterials are numerically analysed by using the finite element method (FEM). Besides the single phonon mode, the complete 3D band gaps are also found in the phonon band structures. Here, the influence of the degree of asymmetry of ADCE to the figure of merit (FOM), which is the ratio of bulk modulus and shear modulus, is discussed. The FOM can be increased by 21–30% (at FOM ≥ 103) when the degree of asymmetry m ranges from 0.4 to 0.6.

A size-dependent generalized thermoelastic diffusion theory and its application

ABSTRACT To capture the transient responses for the thermally and chemically shocked structure at micro or nanoscale, the present work is devoted to establish a size-dependent generalized thermoelastic diffusion theory within the thermodynamic framework. The uniqueness theorem and reciprocity theorem are, respectively, obtained. The corresponding generalized variational principle is developed using the semi-inverse method. In numerical implementation, a semi-infinite medium subjected to thermal and chemical shock at one end is considered and solved by the Laplace transformation. Numerical results are obtained and illustrated graphically. It can be concluded that the nonlocal scale parameter has a significant affect on the displacement and stress, which is excessively important in determining the material’s failure in complex environment. In addition, the numerical results show that the temperature, chemical potential, stress, and concentration are greatly influenced by the fractional order parameter.

Transient response for a half-space with variable thermal conductivity and diffusivity under thermal and chemical shock

ABSTRACT The present work aims to investigate the transient thermoelastic diffusive response for a half-space with variable thermal conductivity and diffusivity in the context of the generalized thermoelastic diffusion theory. The boundary plane of the half-space is assumed to be traction free and subjected to a time-dependent thermal and chemical shock. The governing equations of the problem are formulated by using Kirchhoff’s transformation. Due to the complexity of the equations, Laplace transformation method is applied to solve them. Numerical results are obtained and illustrated graphically. Parameter studies are performed to evaluate the effects of variable thermal conductivity and diffusivity on the response. The present investigation could be helpful for better understanding the multifield coupling effect of mechanical and thermal fields in real materials.

Effect of rotation on plane waves of generalized electromagnetothermoelastics with diffusion for a half-space

ABSTRACT This article is aimed at studying the effects of rotation on the model of generalized thermoelastic diffusion for a thermally, isotropic and electrically conducting half-space with rotation at the uniform angular velocity. The rotating half-space is initially placed in an external magnetic field with constant intensity and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load and chemical potential. The system of Maxwells equations is given and the generalized electromagnetothermoelastic diffusion coupled governing equations are established. The normal mode analysis is adopted to solve the problems and the exact expressions for the non-dimensional temperature, displacement, stress, induced magnetic field, induced electric field, chemical potential and concentration are gained and represented graphically. The effects of rotation are evaluated by comparing the results obtained in the presence and absence of rotation.

Atomistic modeling of electron relaxation effect on femtosecond laser-induced thermoelastic response of gold films

The thermoelastic response of thin gold films induced by femtosecond laser irradiation is numerically simulated using a modified combined two-temperature model (TTM) and molecular dynamics (MD) method, with focus placed upon the influence of the electron relaxation effect. The validity of the numerical approach is checked against existing experimental results. While the electron relaxation effect is found negligible when the laser duration is much longer than the electron thermal relaxation time, it becomes significant if the laser duration matches the electron relaxation time, especially when the former is much shorter than the latter. The characteristics of thermo-mechanical interaction in the thin film are analyzed, and the influence of temperature-dependent material properties upon the thermoelastic response of the film quantified.

Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions

ABSTRACT In this work, fractional order theory of thermoelasticity is applied to a bilayered structure being in imperfect thermal and mechanical contact. The model is subjected to a sudden heating at the traction-free end, assumed to be undisturbed at infinity. The heat conduction in each medium is described by the time-fractional heat conduction equations with two fractional order parameters, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are computed and represented graphically, from which the effects of fractional derivative parameters of both media, thermal contact resistance, elastic wave impedance ratio on the responses are discussed.