Complementary formulations in vibrations: bond graph structures and modal transformations

Abstract

Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.