Taha Selman Cakir
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8th week

Forced vibrations:

Vibrations are usually classified as free or forced. In the case of forced vibration, the body is subjected to external force functions that make it vibrate with the frequency of the exciting force. An alternating external force system may arise as a consequence of many natural phenomena such as waves, sound, blast, earthquake, and heavy vehicular traffic on highway pavements and bridges, as well as from any mechanically produced causes. In each case the wave motion of the disturbance will vibrate a structure at the frequency of the oscillating force. A condition of resonance will occur if the frequency of the applied force system coincides with one of the natural free frequencies of the body. At the resonant condition the amplitude of vibration will approach infinity with time. In practical situations, however, the amplitude of vibration may exceed allowable values in a short period of time, with the subsequent loss of structural integrity.

(Fertis D. G., Mechanical and structural vibrations, 1995, p. 9,10)

Piezoelectric materials:

Piezo derives from the Greek verb piezin- "to press"- and piezoelectricity is a seperation of charge that occurs when pressure is applied to a piezoelectric material. The piezoelectric effect occurs only in certain crystalline electrical insulators, and the charge seperation is manifested by an electrical potential difference between opposite faces of a crystal. A converse effect to piezoelectricity also exists; when an electrical field is applied to a piezoelectric crystal, the crystal becomes distorted as long as the field is present.

Most piezoelectric materials are ionic salts, which consists of positively charged cations and negatively charged anions. In the solid state, these ions form a regular lattice that is described by a unit cell-the smallest group of ions that represent the whole structure of the cell- and a crystal can be thought of as a three-dimensional array of unit cells. A few piezoelectric materials are highly polar crystalline polymers, such as polyvinylidene chloride.

(Marshall Cavendish Corporation, How it works: science and technology, 2002, p. 1744)

Free vibrations:

This type of motion is characterized by an oscillation that occurs with a linear spring and mass system without any external force or excitation. The system is initially streched beyond a static equilibrium position and then released. Typical free-vibration problems provide the value of the initial displacement (deformation), denoted by x0, and require solutions for the amplitude, velocity, period, and/or natural frequency at a given time or position.

(Olia M., Casparian A. S., How to prepare for the fundamentals of engineering, FE/EIT exam, 1999, p. 91)

Semi-active actuators:

The power at the output port of the actuator can be expressed as a function of the conjugate variables as:

PTrans =F. v

for translational output mechanical energy, and:

PRot = T . w

for rotational mechanical energy.

Semiactive actuators are those whose output mechanical power is not positive: PTrans <0 or Prot <0. This means that the energy level in the plant is reduced. Semiactive actuators dissipate the energy of the plant they are coupled to.

Semiactive actuators can actively modulate power dissipation, but the effort they supply (whether a force or a torque) can only oppose the flow in the plant (whether a velocity or an angular rate)

(Pons J. L., Emerging actuator technologies: a micromechatronic approach, Ed. 1st, p. 33, 34)