关于线粘弹性动力学中各种变分原理

ON THE VARIATIONAL PRINCIPLES FOR LINEAR THEORY OF DYNAMIC VISCOELASTICITY

本文提出一条简单而统一的新途径,系统地建立了线粘弹性动力学中各种简化Gurtin型变分原理,文中首先给出一个很有用的以卷积表示的积分关系式,然后从该式出发,系统地导出成互补关系的五类变量、四类变量、三类变量、二类变量及一类变量简化Gurtin型变分原理,并清楚地阐明它们之间的内在联系,而且,还发现当前在国际上有广泛影响的力学变分原理方面的名著[1]及文[2]中,所给出的四个变分原理的泛函式均有误.本文除给出这四个正确的泛函式外,还建立了一些新的更一般广义变分原理。

A unified new approach is proposed for the systematic Derivation of various simplified Gurtin-type variational principles in linear theory of dynamic viscoelasticity. The prime feature of this approach is the use of an important integral relation and generalized Le-gendre transformations given by the author. With this approach, it; is possible not only to derive the complementary functionals for the five-field, four-field, threefield, two-field and one-field simplified,Gurtin-type variational principles, but also to explain clearly the intrinsic relationship among various principles. Thus, in this paper, the simplified Gurtin-type variational prin-ciples are further generalized and systematized.