Table 1 Materials properties PZTG1195N T300/976 Young's Moduli (GPa) E11 63.0 150 E11= E33 63.0 9 Poisson's ratio ?23 0.3 0.3 ?12= ?13 0.3 0.3 Shear moduli (GPa) G23 24.2 7.1 G12=G13 24.2 2.5 Density [rho](kg/[m.sup.3]) 7600 1600 Piezoelectric constants (m/V) d31=d32 254 [10.sup.-12] Electrical permittivity (F/m) [epsilon]11= [epsilon]22 15.3 [10.sup.-9] [epsilon]33 15.0 [10.sup.-9] Table 2 The first five eigenfrequencies
(rad/s) Mode LAM et al Present Discrepancy  (%) 1 21.4657 21.4308 0.16 2 63.3491 63.0758 0.43 3 130.8221 129.1594 1.27 4 182.4224 182.1370 0.15 5 218.2750 216.7596 0.69 Table 3 Control parameters Control type Q R LQR 1 1/5/5 1/8.8/8.5 LQR 2 1/5/5 1/70/70 Control type [K.sub.p] [K.sub.i] [K.sub.d] PID 1 2 100 0.01 PID 2 2 400 0.03
(v) The eigenfrequencies
[[upsilon].sub.[mu]] are higher for a healthy periodontal tissue, which acts as a strong spring for the system, and are smaller for an affected periodontal tissue, which acts as a weaker spring.
In the case of linear time-invariant systems, the impulse response is the linear combination of specific shapes, called eigenvectors, vibrating at specific eigenfrequencies
. These invariant sets do not depend on initial conditions.
Before this first report in 1961, many geophysicists understood that the eigenfrequencies
of the modes were key for inferring the Earth's geophysical properties, following Lord Kelvin's estimation of the molten Earth.
Similar size effect results were obtained earlier for the vertical deflection of Cosserat plates for the case of bending and for the main eigenfrequencies
in the case of free vibration [10,11].
A new current eigenfrequencies
expression was introduced by Ma et al.
In terms of period lengths, the high eigenfrequencies
of the hydraulic system become visible at the bottom, approximately within a range of 10 min to 20 min, when the control loop reaches its limit.
 compared the eigenfrequencies
and vibration modes of a structure measured from test results and calculated by an FE model that included the soil-structure interaction.
Deformation characteristics and eigenfrequencies
of press-fit acetabular cups.
The criteria used are 1% for eigenfrequencies
, 5% for damping ratios and 99% for mode shape vectors (MAC).
Determination of the Eigenfrequencies
. In order to solve governing equation (3) of the problem, it is assumed that the principal elastic axes of the plate are parallel to its edges.
The effect of internal flow on the eigenfrequencies
manifests itself via the centrifugal and Coriolis forces.