Basic Theorems in Dynamic Elasticity - UNAM

Reciprocity Theorem(Betti’s Theorem)Betti’s theorem remains true even if quantities associated with bothdisplacement fields u and v are evaluated at two different times t 1and t 2 , respectively.Let us suppose that u and v are everywhere zero throughout V before agiven time t 0 . If we take t 1 = t and t 2 = τ – t, and time integrate thereciprocity equality from zero to τ, then Betti’s formula becomes:This major result relates, in a straightforward manner, bothdisplacement fields throughout V, the body forces that originatethem and the associated traction vectors they induce over S.