Abstract
The purpose of this paper is to develop a new analysis method, called Three Dimensional Time-Frequency Analysis, based on the well-known digital filter methodology. Using the method, we introduce the algorithm to analyze the sampled signal input, i.e. impulse and swept-sine signals. Second, we apply our method to forced vibrations of weakly nonlinear systems, described by the Duffing equation, to examine the difference between nonlinear and linear systems. Some typical examples were analyzed for the case of a primary and a secondary resonances, and then jump phenomena for primary resonance of the Duffing equation, and superharmonic resonance under the influence of monofrequency excitations are discussed. As a result, the effectiveness of our proposal method is confirmed.
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