Dynamic Stability of the Flexible Connecting Rod of a Slider Crank Mechanism

The partial differential equation of motion of the flexible connecting rod of a slider crank is derived, under the assumption of small deflections. Application of the Galerkin procedure, leads to a system of linear ordinary differential equations, with respect to the modal coordinates of vibration of the rod. For periodic solutions, the foregoing system reduces to a system of coupled Hill equations. Application of Floquet theory, determines those values of the parameters: speed, input torque, geometry, and material properties that constitute the boundaries between the regions of stability and instability.