The maximum value of the amplitude decreases with increasing

damping coefficient of loading [b.sub.l], which also follows from equation (5).

In this model the damping properties are given as the combination of values of

damping coefficient [mu] and relaxation time [tau] = [[mu].sub.d]/G.

Third, the proposed method computes the stiffness parameters by inverse procedure of Hooke's law, and finally solves an estimation problem based on the proposed error metric to obtain a global optimal stiffness and

damping coefficient.

where m is the lumped mass of the system, [k.sub.iz] spring coefficient (stiffness), [c.sub.iz]

damping coefficient, [Z.sub.1] displacement amplitude of the forced excitation, [[omega].sub.iz] angular frequency, and t time.

The effect of parameters such as

damping coefficient, viscoelastic parameter, input voltage and excitation frequency is investigated.

Caption: Figure 10: Equivalent viscous

damping coefficient, he.

where [alpha] is the mass proportional

damping coefficient, M is the mass matrix, [beta] is the stiffness proportional

damping coefficient, and K is the stiffness matrix.

The

damping coefficient corresponding to the mode 101 Hz is identified as [c.sub.1] = 0.015.

The modified Duffing-Holmes equation is used to simulate the model; the vibrator (oscillator) movement state is related to the magnitude of the

damping coefficient ratio, k, and the amplitude of the excitation force, [gamma], of the periodic driving force.

where [L.sub.a] is inductance of the anchor; [r.sub.a] is resistance of the anchor; [U.sub.T] is the voltage at the terminals; [i.sub.a] is current of the anchor; [[omega].sub.mot] is motor speed; J is moment of inertia of the rotor; f is

damping coefficient of the rotor; [T.sub.L] is load torque.

Three predictive systems, adaptive neuro-fuzzy inference system (ANFIS), multi-layer perceptron (MLP) and multiple regression analysis method (MRM) were trained to predict the maximum shear modulus and the minimum

damping coefficient.

The

damping coefficient to a specific excitation frequency is defined as follows: