Nonlinear Dynamics

, Volume 92, Issue 2, pp 463–477 | Cite as

Autoparametric amplification of two nonlinear coupled mass–spring systems

  • Kareem Khirallah
Original Paper


This paper discusses a new excitation condition for two coupled mass–spring systems under autoparametric resonance. In particular, we are interested in analyzing the force and frequency response of the pitch–roll ship mathematical model. A new excitation condition of this model is investigated by directly exciting each degree of freedom using an external force while keeping the excitation frequency near the resonance frequency of each degree of freedom. We found that by choosing certain excitation parameters, the amplitude of oscillation of the primarily mode increases when the force that directly excites the secondary mode is elevated. This phenomenon has some similarity with the parametric amplification condition; therefore, we call this excitation condition the autoparametric amplification. Other interesting behaviors were captured such as autoparametric attenuation and two types of amplitude saturation. Finally, we show that a T-shaped microresonator can experience autoparametric amplification by choosing appropriate geometrical design and actuation conditions.


Autoparametric system Pitch–roll Parametric amplification 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringNortheastern UniversityBostonUSA

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