An elastodynamic reciprocity theorem for linear, viscoelastic media

✍ Scribed by Hoop, A. T.

• Publisher: Springer
• Year: 1966
• Tongue: English
• Weight: 291 KB
• Volume: 16
• Category: Article
• ISSN: 0003-6994
• DOI: 10.1007/bf00384053

✦ Synopsis

A reciprocity t h e o r e m for impulsive d i s t u r b a n c e s in a linear, viscoelastic m e d i u m is derived. A p a r t from t h e condition t h a t t h e m e d i u m be linear a n d viscoelastic of t h e B o l t z m a n n type, no restrictions as to t h e properties of t h e m e d i u m are imposed. Hence, t h e reciprocity t h e o r e m is applicable to d i s t u r b a n c e s in inhomogeneous a n d anisotropic media.

As an illustration of its usefulness t h e reciprocity t h e o r e m is used to derive a n integral r e p r e s e n t a t i o n of t h e Kirchhoff t y p e for t h e d i s p l a c e m e n t vector in a linear, viscoelastic m e d i u m .

F o r reference, also t h e Laplace t r a n s f o r m version 0f t h e o b t a i n e d results is given.