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The proposed formulation employs the continuum mechanics based beam element with the warping displacement to model complex modes of deformation.
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Finally, the last part of the paper proposes a methodology allowing identification of experimental reduced models from the knowledge of the complex modes issued from the vibroacoustical modal analysis.
When finite element models are considered, iterative solvers are needed to calculate the complex modes and eigenvalues with good precision.
The procedure is based on a constrained error minimization approach and uses only experimentally identified complex modes and complex natural frequencies together with, for the non-viscous model, the mass matrix of the system.
Then, based on this model, a well adapted transformation is carried out to get the modal characteristics from the expression of complex modes, including the mode shapes.
The normal complex modes and generalized complex modes are defined.
In general relativity the corresponding complex modes of gravitational waves are known as quasi-normal modes.
Firstly, the state space form control model is formulated based on the complex mode theory.
Using PMA-induced ectodomain shedding of HB-EGF in human HT1080 fibrosarcoma cells as a model system, we demonstrate here a complex mode of regulation, involving ADAM17 protease activation as well as an apparent transport of substrate to and from the cell surface.
Most of the model updating techniques neglect damping and so these updated models cannot be used for accurate prediction of complex frequency response functions (FRFs) and complex mode shapes.
Figure 6 Illustration of a complex mode.
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