Effective system properties and spectral density in random vibration with parametric excitation

The characteristic frequency and bandwidth of the random response to parametric excitation may be influenced by the excitation process. It is demonstrated that the effrective stiffness and damping properties can be expressed as conditional mean values for given displacement and energy levels, respectively. These properties are used to describe response in terms of its probability density function and its spectral density function. An example demonstrates the accuracy in predicting the change of frequency and damping of a praametrically excited oscillator, and another example extends the method to a self-excited oscillator with domains of negative damping.