Non-Linear Torsional Vibration of a Two-Degree-of-Freedom System Having Variable Inertia

Abstract

A variant of Kryloff and Bogoliuboff's method is used to analyse the periodic vibrations of a non-linear two-degree-of-freedom system which is an idealization of the crankshaft of a two-cylinder in-line reciprocating engine. It is shown that there are two critical speed ranges associated with each normal mode of the system within which periodic harmonic or subharmonic vibrations of large amplitude can occur as a result of variable-inertia excitation. Extensions of the results to homogeneous in-line engines having any number of cylinders are indicated.