6 marker shows the experimental characteristics of the LM of vibration action for the mode of the

steady-state vibration amplitude [X.sub.am] = 0.007 m.

For

steady-state vibration, let [u.sup.L.sub.r]: = [R.sub.2][U.sup.L.sub.[eta]][e.sup.i[omega]t], [[phi].sup.L] = [R.sup.3.sub.2][[bar.[phi]].sup.L][e.sup.i[omega]t].

We can see that these dispersive curve equations are relevant to nonlinear small perturbation [epsilon], coefficient before nonlinear term [bar.[GAMMA]], and steady-state vibration amplitude of the pure Duffing oscillator [absolute value of [A.sub.2.sup.(0)].

From Figures 8 and 9, some time later, the vibration amplitude of each shell and oscillator no longer attenuates but has stabilized; the displacement-velocity phase diagrams of the shell and the oscillator both consist of a circle, and all the shells and oscillators of this periodic structure have achieved steady-state vibration.

Thus, the

steady-state vibration response of each DOF has a single frequency, and the vibration frequency is the same as the excitation frequency when an MDOF system is subjected to a single frequency excitation.

The

steady-state vibration of a periodically supported beam on an elastic half-space under a uniformly moving harmonic load has been studied in [15].

Thus, in such a formulation, we solve an unsteady heat conductivity problem in which internal heat sources are simulated by a dissipative function calculated in the

steady-state vibration problem.

It performs both static displacement and vibration measurements but cannot be used for fast transients because time averaging is required on

steady-state vibration modes.

Realizing that an engine at idle is very close to sinusoidal

steady-state vibration, and since we are only concerned with the magnitude of the transfer function, we are left with the final equation with which the entire system can be modeled: This equation relates the output sinusoid to the input sinusoid and will be optimized as the magnitude of this equation approaches zero.

Transient vibrations characterized by larger amplitudes and quick dissipation are more easily tolerated by humans than a continuous

steady-state vibration [44].

Mbaye, "A nonlinear component mode synthesis method for the computation of

steady-state vibrations in nonconservative systems," Mechanical Systems and Signal Processing, vol.

Kenney, "

Steady-state vibrations of beam on elastic foundation for moving load," Journal of Applied Mechanics, vol.