Solution of the Vibration Equations

  • Ahmed A. Shabana
Part of the Mechanical Engineering Series book series (MES)


It was shown in the preceding chapter that the application of Newton’s second law to study the motion of physical systems leads to second-order ordinary differential equations. The coefficients of the accelerations, velocities, and displacements in these differential equations represent physical parameters such as inertia, damping, and restoring elastic forces. These coefficients not only have a significant effect on the response of the mechanical and structural systems, but they also affect the stability as well as the speed of response of the system to a given excitation. Changes in these coefficients may result in a stable or unstable system, and/or an oscillatory or nonoscillatory system.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Ahmed A. Shabana
    • 1
  1. 1.Richard and Loan Hill, Professor of Engineering, Department of Mechanical & Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

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