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We present a hydrodynamic model to simulate the excitation by optical beating of plasma waves in nanometric field effect transistors. The biasing conditions are whatever possible from Ohmic to saturation conditions. The model provides a direct calculation of the time-dependent voltage response of the transistors, which can be separated into an average and a harmonic component. These quantities are interpreted by generalizing the concepts of plasma transit time and wave increment to the case of nonuniform channels. The possibilities to tune and to optimize the plasma resonance at room temperature by varying the drain voltage are demonstrated.