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The parametric vibrations are excited by a periodical force of Jacobi elliptic type.
In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement.
The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system.
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Their influence forms a non-sinusoidal periodical forcing function that simulates suitably the outdoor temperature fluctuations.
It is found that defects could be induced under external periodical forcing under the boundary, and then the wave emitted from the defects can keep balance with the waves excited from external forcing.
In both cases, the term Asin(Ω t) can be viewed as a periodical forcing or stimulus injected in the extracellular environment [ 22, 45].
Numerical simulations of nonlinear breaking AGW propagation to the middle and upper atmosphere from a horizontally periodical wave forcing near the ground were made.
According to the local people, sharing wells with livestock makes the water dirty and many times livestock destroy the wells hence forcing periodical maintenance.
Thus, significant periodical generalized exciting forces and resonance responses may occur in some higher modes of vibration of the cantilever deck.
As to long-span bridge, the wavelength of the mode shape of the fundamental mode is much longer than the load interval, so remarkable periodical generalized exciting forces cannot be formed in the fundamental mode and the resonance responses are not obvious in such cases.
The interrupted cutting process consists of several periodical characteristics, such as cutting force and time varying heat source.
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