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Determination of the stability chart and transition curves of parametric differential equations are extremely important in design, optimization, and study of parametric systems. Besides several approximate methods that are capable of determining the stability chart of parametric systems, the energy-rate method is the most exact one. In this chapter we review this analytics-numerical method to determine stable, unstable, and periodic response of differential equations that their stability depends on relation between parameters. We will use the Mathieu equation as the principal example to develop the method.
KeywordsEnergy-rate method Mathieu stability chart Mathieu equation Parametric vibrations Stability of Mathieu equation Stability chart
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