The Properties Of Non-steady Heat Conduction For Piezoelectric Materials Under Thermal Load

It is very important to study the problem of non-steady heat conduction, which can describe the distributions of temperature field and heat flux density of piezoelectric materials under high temperature load with development and application of heating technical in heat convection, aerospace, microwave heating and machining. So, the symplectic method was introduced to solve the unsteady heat conduction based on the two dimensional transient heat conduction theory, and the problems would be turned to solve the eigensolutions of zero eigenvalue and non-zeros eigenvalue with the methods of separation of variables and eigenfunction expansion in this present dissertation. The symplectic concept makes no hypothesis of deformation along the thickness direction and shows a rational derivation. Thus, the current method can precisely analyze thermal conduction with arbitrary depth-to-length ratio and time step. Numerical examples compared with other methods were given to illustrate the accuracy of the present symplectic approach and the effect of boundaries of temperature and heat flux under different thickness ratios and time were studied. Then, the problem of piezoelectric materials under thermal load had been studied with FEM, and the numerical solutions were obtained. And the temperature, electric field, stress and displacement caused by temperature of piezoelectric materials were discussed with numerical example under certain physical properties and different boundary conditions. The results showed that the symplectic method is very effective and practical to solve the transient heat conduction,which can quickly calculate the distribution of temperature under certain condition, and the results are high convergent. Moreover, the effect of boundaries will be more obvious increasing of thickness ratios,while temperature will attenuate quickly with the time increasing, and the heat flux changed little. The temperature will make great effect on stress, electric field and displacement of piezoelectric materials,but they do little donation to temperature of structures. The results above will provide basis theory and consult for designing and optimizing the piezoelectric material.