Piezoelectric transducers in conjunction with appropriate electric networks can be used as a mechanical energy dissipation device. Alternatively, undesired mechanical energy of a structure could be converted into electrical energy that can be dissipated through a shunt network in the form of Joule heating. This paper presents an experimental method to calculate damping energy in mechanical systems. However, the mathematical description of damping mechanism is much more complicated, and any process responsible for the occurrence of damping is very intricate. Structural and piezoelectric damping are calculated and analysed in the case of pulse switching or SSDI semiactive vibration control technique. This technique which was developed in the field of piezoelectric damping consists in triggering the inverting switch on each extremum of the piezoelectric voltage which induces an increase of the electromechanical energy conversion.

Vibration damping is one of the manifestations of mechanical energy dissipation related to motion in mechanical systems. Damping processes have been studied for a long time. Damping forces are small compared to the other interactions in a mechanical system and yet their mathematical description remains much more complicated. Actually, any process responsible for the occurrence of damping is very intricate and the knowledge of it is insufficient. Sometimes just changing the system’s stiffness or mass to alter the resonance frequencies can reduce the unwanted vibration as long as the excitation frequencies do not change. But in most cases, the vibrations need to be dissipated using damping materials or devices that are tuneable with vibration.

Several methods have been investigated in case of vibration damping. These methods have the forms of passive, semiactive, and active treatments which can be used for sound/vibration cancellation. Active control involves the use of active elements (actuators) along with sensors and controllers (analogue or digital) to produce an out-of-phase actuation to cancel the disturbance causing the noise/vibration [

Electronic damping using piezoelectric ceramics (Piezo-Shunt) is less temperature sensitive and more tuneable compared with viscoelastic damping treatments. In this damping technique, the mechanical energy of the structure is converted to electrical energy by piezoelectric material. The electrical energy, in turn is dissipated, as heat, in an electrical shunt circuit. These methods are interesting because they do not rely on any operative energy as in active control. They consist in the drive of a few solid-state switches (i.e., MOSFET transistor) requiring very few power and, in general, are simple to implement. Pulse switching damping technique [

Many various terms are used to represent vibration damping. These representations merely indicate the mathematical model used to represent the physical mechanism of damping that is still not clearly understood for many cases [

In vibration analyses, it is concerned with damping in terms of system response. The loss of energy from the oscillatory system results in the decay of free vibration amplitude. In steady-state forced vibration, the loss of energy is balanced by the energy which is supplied by the excitation. Energy dissipation is usually determined under conditions of cyclic oscillations. The energy dissipated per cycle due to a damping force

The experimental sample in this paper is a cantilever beam equipped with piezoelectric patches wired on a pulse switching cell (Figure

Cantilever beam where

The total outgoing current from the piezoelectric patches using their constitutive equations can be calculated as [

Strategy of pulse switching technique.

There are two types of damping: material damping (structural) and system damping. Material damping is the damping inherent in the material, while system damping includes the damping at adds damper devices to the system (such as, piezoelectric material), in addition to material damping. By calculating damping energy (

Experimental setup considered is a steel beam equipped with piezoelectric inserts. This structure corresponds to the description given in Table

Characteristics of the experimental structure.

Plate material | Steel |

Plate dimensions (free) | ^{3} |

Piezoelectric material | P189 |

Number of piezo elements | 12 (on each face) |

Piezo elements position | 10 mm from the clamping end |

Piezo elements dimensions | ^{3} |

Open-circuit resonance frequency | 56.48 Hz |

Inversion coefficient | 0.6 |

In practice, to measure the energy dissipated per cycle, using the concept of (

Figure

Variations of the capture signal amplitude versus the force amplitude in controlled and uncontrolled cases.

Figure

Variations of the capture signal attenuation in dB versus the force amplitude.

Figure

Variations of damping energy versus the square of capture signal amplitude.

This paper showed an experimental method to calculate the damping energy in mechanical system. However, the mathematical description of damping mechanism is much more complicated and any process responsible for the occurrence of damping is very intricate and the knowledge of it is insufficient. Structural damping and piezoelectric damping for pulse switching semiactive nonlinear control technique have been calculated and analysed. Pulse switching control technique is interesting for structural damping applications because it presents simultaneously good damping performances, a good robustness, and very low power requirements. Finally, it is important to consider that this technique is simple enough to be self-powered. Piezoelectric damping will increase with increase of force amplitude but its maximum value was limited and has its ultimate value.

The authors would like to thank Professor D. Guyomar and Professor C. Richard from LGEF-INSA for their kind help.