Data were obtained with forcing amplitude (peak-to-peak voltage to the speakers) at the air inlet of 20% of the mean velocity (half peak-to-peak amplitude of velocity oscillation to the bulk velocity) and the forcing frequency
could be varied between 50 and 400 Hz.
In each case, the variable frequency is used as the forcing frequency
and the resonant frequency for the mode shape identification.
Figure 4 shows, together with the bifurcation diagrams, all Lyapunov spectrum for 7 different values of forcing frequency
. Concerning Lyapunov exponents, periodic conditions, where all exponents are negative, quasiperiodic conditions, where the greater exponent vanishes, and chaotic conditions, where the greater exponent is positive, should be pointed out.
The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency
is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves.
With the advent of variable speed fans, one may be tempted to adjust the fan speed to control the input, forcing frequency
at the vibrating duct.
F(t) is the periodic signal, which can be described as A cos([omega]t + [theta]), and A and [omega], respectively, are the amplitude and forcing frequency
of the periodic signal.
However, it cannot be neglected if the capacitor value or the forcing frequency
are sufficiently large (objective 3).
: The frequency at which a shaker vibrates.
Vibration amplitude was decreased because the engine forcing frequency
was much higher than the natural frequency of the tree limb and also higher than the natural frequency of an airship mount.
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