The historical developments in the discipline of engineering dynamics are briefly reviewed, with attention paid to the formulation and solution of the dynamic behaviour of multi-body systems. It is shown that the dynamic characteristics of practical multi-body systems are dependent upon the interactions of many physical phenomena that can induce, restrain or constrain motion of parts. The long process of understanding and formulating the physics of multi-body motions, in some cases with pioneering contributions centuries old, together with continual refinements in numerical techniques and enhanced computing power has resulted in the solution of quite complex and practical engi- neering problems. Linking the historical developments to the fundamental physical phenomena and their interactions, the paper presents solutions to two complex multi-body dynamic problems. The practical implications of the approach in design of these systems are highlighted.

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Multi-body dynamics: Historical evolution and application:

Dynamic analysis of 3D beams with joints in presence of large rotations

In the first part of this study, dynamic models of single- and multi-cylinder reciprocating machines are presented, which may involve torsional flexibility in the crankshaft. These models take into account the dependence of the engine moment of inertia on the crankshaft rotation. In addition, both the driving and the resisting moments are expressed as functions of the crankshaft motion. This leads to dynamic models with equations of motion appearing in a strongly nonlinear form. Initially, an approximate analytical solution is presented for a linearized version of the equations of motion, by applying a suitable asymptotic method. This provides valuable insight into some aspects of the system dynamics. In the second part, numerical results are presented for linear and nonlinear engine models by applying appropriate methodologies, leading to direct determination of complete branches of steady-state response. These results illustrate the effect of the system parameters on its dynamics. Finally, some results are also presented in an effort to investigate the effect of engine misfire.

Linear and nonlinear dynamics of reciprocating engines

Vibration analysis of distributed-lumped rotor systems

This bibliography lists references to papers, conference proceedings, and theses/dissertations dealing with finite element vibration and dynamic response analysis of engineering structures that wer 

Finite element vibration and dynamic response analysis of engineering structures - A bibliography (1994-1998)

To simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The front pulley, timing gear, and the fly-wheel were idealized by a set of masses and moments of inertia. The main journal bearings were idealized by a set of linear springs and dash-pots. For each constituent member, the dynamic stiffness matrix was derived (in closed form) from the transfer matrix. Then the dynamic stiffness matrix for the total crankshaft system was constructed, and the natural frequencies and mode shapes were calculated. The modeling and analysis procedures were aplied to the analysis of free vibrations of four kinds of crankshafts: single cylinder, three-cylinder in-line, four-cylinder in-line, and V-six engines. The different coupling behavior of the three-dimensional vibrations in the planar-structure and the solid-structure crankshaft is discussed, and the influence of the bearing oil film stiffness on the crankshaft natural frequency is also analyzed

A. Shinno

Papers

Simple Modeling and Analysis for Crankshaft Three-Dimensional Vibrations, Part 1: Background and Application to Free Vibrations