坡形加热下的二维广义磁热黏弹性问题研究

STUDY ON A TWO-DIMENSIONAL GENERALIZED MAGNETO- THERMOVISCOELASTIC PROBLEM SUBJECTED TO RAMP-TYPE HEATING

运用具有一个热松弛时间的广义热黏弹性理论,研究了处于均布磁场中的二维磁热黏弹性问题．运用 Laplace变换(对时间变量)和Fourier变换(对于一个空间变量),得到了变换域内场量的精确表达式,并把结果应用到表面受到坡形加热的半空间问题．应用数值逆变换得到了时间-空间域内场量的解,对丙烯酸塑料给出场量的响应图．并把运用广义热黏弹性理论所得的结果与传统热黏弹性理论及热弹性理论下的结果进行了比较．

In this paper, a two-dimensional problem of magneto-thermoviscoelasticity with relaxation time in a perfectly conducting medium is studied. With Laplace transform （for time variable） and Fourier transform （for one space variable）, the exact expressions for field quantities are obtained in the transformed domain. The resulting formulations are applied to a semi-space problem subjected to ramp-type heating at the surface. Using numerical inverse method, the results are obtained and shown graphically when the acrylic plastic material is considered. Also a comparison is made between the results obtained using the generalized thermoviscoelastic theory and those obtained using the conventional thermoviscoelstic theory and thermoelastic theory.