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This paper presents a simplified method to determine the vibrational amplitude produced by a four-cylinder engine when supported by a viscoelastic foundation. The pistons, connecting rods, and crankshaft are modeled as rigid bodies connected to the foundation by standard industrial rubber mounts which are modeled with spring and damping elements whose location, orientation, and stiffness can be easily configured for specific design analysis, or optimized to reduce vibration and noise in a design. The paper is presented in a general algorithmic form, with a detailed numerical example emphasizing the three parts of the analysis: the mechanism kinematics, the shaking force and torque determination on the engine block, and the three-dimensional vibrational analysis.

The use of the displacement matrix method in the dynamic analysis of suspension mechanisms is discussed and then demonstrated by simulating the dynamic motion of a McPherson suspension acting under a sinusoidal road force. The method of reduced systems in dynamic analysis is extended to include spatial mechanisms connected by spring and damping elements. The numerical example provides the position, velocity and acceleration of the wheel hub of the suspension along with all reaction forces, and is intended to be a problem for comparison, or for further study, using other methods in dynamic analysis.