One Degree of Freedom Systems

Reza N. Jazar
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Reza N. Jazar: RMIT University, School of Engineering

Chapter Chapter 6 in Advanced Vibrations, 2022, pp 483-590 from Springer

Abstract: Abstract Frequency response analysis of one-DOF systems is the most important analysis of vibrating systems in industry. A vast amount of vibrating systems can be modeled by a one-DOF mass–spring–damper system. The harmonic excitation is the most common excitation in industry. The response of a system to harmonic excitation will be harmonic. The frequency response is the steady-state solution of the equation of motion at each frequency, when the system is harmonically excited. In frequency response analysis, we are interested in the steady-state amplitude of the oscillation as a function of the excitation frequency. There are only four types of harmonically excited one-DOF systems: 1. base excitation, 2. eccentric excitation, 3. eccentric base excitation, 4. forced excitation. Base excitation is the most practical model for vertical vibration of mechanical systems. Eccentric excitation is a model for every type of rotary motor on a suspension. Eccentric base excitation is a model for the vibration of any equipment mounted on an engine. Forced excitation has almost no practical application; however, it is the simplest model to study forced vibration analysis methods. Forced excitation. The equation of motion of a harmonically forced system has the simplest differential equation of motion with great educational analysis, although there is no practical forced excited system in industry. Base excitation. The base excited system is a good model for a vehicle suspension system or any equipment that is mounted on a vibrating base. The base excited system is the most practical forced vibrating system in industry. Eccentric excitation. There is an unbalance mass at an eccentricity distance e that is rotating with an angular velocity. An eccentric excited vibrating system is the proper model for vibration analysis of an engine of a vehicle or any rotary motor that is mounted on a stationary base with flexible suspension. Eccentric base excitation. The base of a one-DOF eccentric base excited vibrating system has an unbalance mass at a eccentricity distance e that is rotating with angular velocity. The eccentric base excited system is the proper model for vibration analysis of different equipment that are attached to the engine of a vehicle, or any equipment mounted on a rotary motor. All kinds of frequency response of single-DOF harmonically excited systems can be expressed by eight equations.

Date: 2022
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DOI: 10.1007/978-3-031-16356-2_6

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