Method for Calculating the Steady-State Dynamic Response of Rigid-Body Machine Systems
The rigid-body equations of motion for conservative rotating machine systems with position-dependent moments of inertia are found to reduce to a single, second-order, inhomogeneous, nonlinear, ordinary differential equation with variable coefficients. Upon linearization this equation is reduced to first-order form. A rational proportionality between the periods of the variable coefficient and the in-homogeneous term implies that the steady-state rigid-body response will also be periodic. To solve for the steady-state rigid-body response the least common period of the system is divided into an appropriate number of sub-intervals, and the solution over each sub-interval is derived by assuming a constant value of the coefficient during that sub-interval. The final solution is computed by applying appropriate compatiblity and periodicity constraints. The solution algorithm is extended to systems for which the linearization assumptions do not apply through the application of a recursion scheme. Examples are included to illustrate the utility of the algorithm.
R. I. Zadoks and A. Midha, "Method for Calculating the Steady-State Dynamic Response of Rigid-Body Machine Systems," Journal of Mechanical Design, American Society of Mechanical Engineers (ASME), Jan 1987.
The definitive version is available at http://dx.doi.org/10.1115/1.3258814
Mechanical and Aerospace Engineering
Keywords and Phrases
Machinery; Dynamic Response; Steady State; Algorithms; Differential Equations; Equations of Motion; Rotational Inertia; Equations
Article - Journal
© 1987 American Society of Mechanical Engineers (ASME), All rights reserved.