Torsional Analysis of a Four-Stroke Engine

Reciprocating machines fall into many categories. Despite different applications and designs, e.g. pumps or internal combustion engines with a varying number of pistons, a simple approach to determine torsional modes of regardless which crankshaft assembly can be investigated. The resulting natural frequencies are required by ISO 3046 for rotor dynamic analysis.

Internal Combustion Engine with piston and flywheel geometry
Figure 1 Internal Combustion Engine with piston and flywheel geometry, (https://www.quora.com/What-is-a-starter-flywheel)

Below, a common way to express a crankshaft assembly with massless shaft and mass-inertia elements is presented, whereas the reciprocating and revolving mass around the crack can be expressed as follows:
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