References

Conclusion and outlooks

• The efficiency of the switch is critical for high damping performance

• The energy required for the switch is harvested from an additional piezo

• Minima and maxima detection obtained by a low pass filter

Piezo Sensor

Energy Harvesting

Switch

Piezo Actuator

Max Min detection

Testing and results

Introduction and objectives

Working principle of piezoelectric shunt damping

Stiffness compromise in the design for damping

Analytical modeling

Piezoelectric vibration damping using autonomous switching shunt

T. Delpero, A. Bergamini, P. Ermanni

Centre of Structure Technologies, ETH Zurich, CH-8092 Zurich, http://www.structures.ethz.ch

• Completely autonomous switching shunt with high damping performance and robust to changes in natural frequencies of the structure has been developed

• Very good agreement between analytical prediction and experimental values for the loss factor

• Importance of the concurrent design of stiffness and damping

1. Delpero T., Bergamini A., Ermanni P., “Shunted Piezoelectric Damping: Identification of the Electromechanical Parameters and Prediction of the Dissipated Energy”, Proc. ICAST 2011, 028

2. Delpero T., Di Lillo L., Bergamini A., Ermanni P., “Piezoelectric Vibration Damping Using Autonomous Synchronized Switching On Inductance”, Proc. SMASIS 2011, 5239

Self-powered SSDI enhanced by energy harvesting module

• The concurrent equal consideration of damping properties, geometry and material in the design phase is expected to allow for the development of systems able to fulfill more stringent requirements than the simply passive structure, or a passive structure augmented with adaptive materials.

• A concurrent approach (A-C) is expected to help find global optima of the design rather than local ones limited by a frozen design of the conventional structure obtained with a classical sequential design (A-B’-B), that applies the damping treatment once the host structure parameters are frozen.

Objectives

• To date, damping treatments are considered as an add-on to structures that are designed according to well established procedures based on conventional (i.e. non-adaptive) materials.

• This project will include the exploitation of damping treatments, such as shunted piezoelectric elements, as an additional variable in the design process.

Vo

lta

ge

Displacement

-γVM

VM

SSDS

SSDI

SSDV

SS

VM + Vs

-γVM - Vs

Resonant

• In the SSDI, the voltage on the piezo is in anti-phase with the velocity, so that the resulting force counteracts the vibrations of the structure

• The dissipated energy is

proportional to 1+𝛾

1−𝛾. The quality

factor of the switch γ is crucial for achieving high damping performance.

Shaker

Specimen

Force sensor Laser

PC with Labview

PXI Card (response)

PXI Card (stimulus)

Laser controller

Force Sensor

Laser

Amplifier Shaker Shunt

Oscilloscope

-25

-20

-15

-10

-5

0

38 40 42 44 46 48 50 52

Dis

pla

cem

en

t /

Forc

e [

dB

]

Frequency [Hz]

Open Circuit

Self-poweredSSDIResonant Shunt

Aluminum plate [200 x 60 x 2 mm] 2 piezo patches [100 x 30 x .2 mm]

-12.5 dB 77% amplitude reduction

0%

2%

4%

6%

8%

0 0.003 0.006 0.009 0.012

Loss

fa

cto

r η

Kij2

SSDI γ=.72

Resonant Shunt

SSDI γ=.33

SSDI γ=.60

A

B

C

B’

Shunting technique

SSD State Switching

SSDS Synchronized

Switching Damping on Short

Circuit

SSDI Synchronized

Switching Damping on Inductance

Resonant Shunt

Loss factor Kij

2

𝜋 4

Kij2

𝜋 4

1 + 𝛾

1 − 𝛾

Kij2

𝜋

Kij

2

Loss factor prediction using an energy approach

• Each shunting technique corresponds to a different hysteresis in the Voltage-Displacement diagram.

• The area of the hysteresis corresponds to the dissipated energy

Voltage in anti-phase with velocity Self-powered implementation

Experimental assembly Vibration reduction measurements

• The coupling coefficient Kij and the loss factor are measured for different specimen. • This diagram can be used for predicting the damping performance of the same shunts

on more complex structures, since it is based on non-dimensional parameters.

Stiffness compromise

Concurrent design

In the case of the SSDI, this approach leads to: 𝜂𝑆𝑆𝐷𝐼 = 4

𝜋

1+𝛾

1−𝛾

𝑘𝑖𝑗2

1−𝑘𝑖𝑗2

𝑈𝑝𝑖𝑒𝑧𝑜

𝑈𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒

Moreover, the obtained expression allows for the definition of a specific damping, with a strong

similarity with the viscous damping: 𝜂 = 𝜂𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑈𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑙𝑎𝑦𝑒𝑟

𝑈𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒

𝜂𝑠ℎ𝑢𝑛𝑡𝑒𝑑 𝑝𝑖𝑒𝑧𝑜

The relationship between the damping performance η, the generalized coupling coefficient Kij and strain energies U, suggest the need for a compromise between the stiffness of the structure and the piezoelectric:

Kij2 =

Upiezo

Ustructure

kij2

1 − kij2

The concurrent equal consideration of damping properties, geometry and material in the design phase is expected to allow for better design solution.

𝜂 = 𝜂(Upiezo

Ustructure, 𝑆ℎ𝑢𝑛𝑡 𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑦) 𝜂 = 𝜂(𝐾𝑖𝑗 , 𝑆ℎ𝑢𝑛𝑡 𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑦) Kij

2 =Upiezo

Ustructure

kij2

1 − kij2

Kij = Electromechanical coupling coefficient

Structure

Mechanical Energy

Piezoelectric Transducer

Electrical Energy

Electrical circuit

Energy Dissipated

Loss factor – coupling coefficient diagram