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To accurately separate the electromechanical modes from trivial modes, the generalized inverse of SSI is used to estimate another state matrix.
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The transformations are applied to each subsystem, with consecutive use being made of free interface undamped modes in the existing physical co-ordinates followed by fixed interface damped modes in the generalized co-ordinates.
Such changes can be explained by the most unstable modes in the generalized Eady model.
The most common narrative mode is the generalized past.
The "mode generation function" φ, and the "generalized ray generation function" B u) are introduced for a stratified wave-guide.
The solution is expressed in the form of an infinite sum of orthogonal natural modes multiplied by the generalized displacements.
The performed analyses led to the development of a number of charts that can be used to identify the natural frequency, the mode shapes and the generalized mass and stiffness of conical tanks for both the fundamental and the cos-modes of vibration.
Mode representation and the "generalized ray" representation satisfy the Poisson summation formula.
With elementary beam theory modelling, numerical results are obtained for the frequencies, mode shapes and the generalized modal mass of this elastically coupled system, for a range of values of the spring constants and cantilevered beam stiffness and inertia values.
Because of the defective characteristic of the system, we have to use an invariant sub-space recursive method with numerical stability to calculate the generalized modes of the defective and near defective systems.
Furthermore, a dynamic equation of the workpiece-fixture system considering the external damping factor is proposed using the Lagrangian method in terms of all the mode shape function and the generalized coordinate, and the response of system under the dynamic cutting force is calculated to evaluate the stability of the milling process under damping control.
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