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A mode shape describes the displacement pattern of the system when it is vibrating or excited at a natural frequency (He and Fu 2001).
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A particular natural frequency and its corresponding mode shape describe one particular solution to the boundary value problem of the Timoshenko beam.
However, if the two closely spaced eigenvalues have a reasonable frequency distance to all other eigenvalues of the system, then a linear transformation exists between the set of perturbed and unperturbed mode shapes describing the significant changes as a rotation in the initial subspace defined by the two mode shapes.
Similar to former two, the mode shape properties that describe the participation of state variables in a particular mode are of vital importance for the safety and reliable operation of the system.
And then, double functions of Euler-Bernoulli beam can be utilized to describe mode shape of a TMW on basis of a span-by-span approach.
Reasons for the poor agreement are discussed; it is concluded that the only viable hypothesis is that mode shape statistics are not described by real Gaussian random functions.
The third mode shape in Fig. 3c describes oscillation of the rubber compound and top plate about z-axis.
Since the bottom plate is fixed, the motion of rubber compound and top plate describes each mode shape.
Thus, comparing the elements u i,k and u j,k describes the mode shape information between states i and j.
Cubic splines are used to describe the mode shape function and to satisfy the continuity and boundary conditions in conjunction with the Green function.
The first mode shape shown in Fig. 3a describes oscillatory (angular) motion of the rubber compound and top plate about x-axis of the draft pad.
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