柔性连接杆的非线性动力学分析.doc

Non-linear dynamics of a flexible connecting rodAbstract: The present study investigates the dynamic response of single-cylinder reciprocating engine. In particular, simplified models of the classical slider–crank mechanism are examined, which take into account the flexibility of the connecting rod. Moreover, a main new feature of these models is that both the driving and the resisting moments are expressed as functions of the crankshaft motion, instead of prescribing the rotation of the crank. The equations of motion are first derived by application of Hamilton’s principle. These equations are then discretized geometrically and put in their final form by applying Galerkin’s method. Owing to the large rotations exhibited by the mechanism members and the form of the driving and the resisting moments, the resulting equations of motion involve strong non-linearities. As a consequence, their solution is obtained in both the time and the frequency domain by employing appropriate numerical methodologies. In particular, these methodologies include either determination of transient response by employing direct integration techniques or direct determination of complete branches of periodic steady state response by applying suitable methodologies. The first set of numerical results refers to the special case where the angular velocity of the engine crank can be considered as virtually constant. This case can be analysed more easily and provides valuable insight into some important aspects of the system dynamics. Then, the emphasis is shifted to the general case, corresponding to non-ideal forcing conditions. In all cases, the attention is focused on examining the influence of the parameters of the system on its dynamics during intervals with transient or under periodic steady state conditions.Keywords: engine mechanisms, flexible rod, non-ideal forcing, periodic steady state, chaotic response,Sommerfeld phenomena1 INTRODUCTIONDuring the last three decades, the rapid and cont