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Exact(4)
Analytical exProcedure for thexactstants integrationl equatiof are provided theuse for any lay-up sequence.
A single modal equation is used to analyze the qualitative behaviour of the system.
The solution to the modal equation is obtained utilizing assumed-modes method.
A dynamic response evolution parameter deduced from the primary-mode modal equation is used to characterize a transition from linear vibration to fully nonlinear dynamic snap-through.
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Analytical expressions for the constants in the modal equation are provided to use for any lay-up sequence.
Nonlinear modal equations are obtained through a modal reduction technique.
The modal equations are then employed for controller design and time domain simulation.
The derived dynamic modal equations, are further combined with optimization techniques to assist in designing feasible mechanical and robust dynamic passive and active control devices, to upgrade the serviceability of this bridge and user's comfort.
The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and the nonlinear coupled-modal equations are then transformed into a state space model in order to design controller.
This modal differential equation is discussed in terms of a fundamental matrix response.
By introducing quasi-modal parameter, modal analysis equation was decoupled under physical coordinate; hence, the modal parameters of each vibration mode are identified independently.
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