Reciprocal theorems in structural dynamics including initial conditions. - Panagiotopoulos, C. G.
For completeness purposes, as well as for practical reasons, this work investigates the well-known Betti?Rayleigh reciprocal theorem for structural dynamics in a way which includes the effect of initial conditions. It then presents a natural and consistent way for introducing the Duhamel integral for the transient response of a dynamical system through the aforementioned reciprocal theorem.
Keywords: Dynamic reciprocity; Betti?Rayleigh theorem; Duhamel integral; Riemann convolution; Initial conditions