Note on Lord Rayleigh's Reciprocal Theorems in Elastic System

Extract

Reciprocal theorems are valuable devices in the attack on strength, stiffness and vibration problems in structures, often leading to elegant and simple solutions. Reciprocity is a fairly common property in various coefficients which arise in mathematical physics, as for example coefficients of mutual potential, capacity, induction, and so on. It is inevitably encountered both in theory and practice in almost any branch of physical science. So far as the stiffness of structures is concerned it seems that while Hooke is the mainspring of the theory of elasticity Rayleigh is the regulator of reciprocal relations in elastic systems.