PSI - Issue 23

Zdeněk Machů et al. / Procedia Structural Integrity 23 (2019) 535 – 540 Zdeněk Machů / Structural Integrity Procedia 00 ( 2019) 000 – 000

536

2

Nomenclature a

crack length damping ratio

b r B E h i J y k K e 31 *

width of the beam piezoelectric modulus thickness of i -th layer bending stiffness elastic modulus

safety factor

K r,eff K appl K 0,c

effective R-Curve

stress intensity factor from kinematic excitation

intrinsic fracture toughness

L

length of the beam

m * M t

mass of the beam per unit of length

attached tip mass

R

connected resistive load

displacement amplitude of the beam’s clamped end

u 0

ü 0 max/crit maximal allowed acceleration amplitude with safety factor k

K =1.5 / k K =1.0

w W z Ti

z -component of displacement

thickness (height) of the multilayer structure z -coordinate of i - th layer’s geometrical centre

α

coefficient of thermal expansion

Δ T

temperature change

S 

permittivity measured at constant strain

33

ν ρ

Poisson ratio

density of the material thermal residual stresses

σ res σ appl ω , f

bending stress distribution induced by a kinematic excitation

forcing frequency

Ω 1

first undamped angular natural frequency

measuring systems) – Zielinski et al. (2014). One of the recently developing concepts of energy harvesters is in the form of a vibrating multilayer beam containing piezoelectric layers. Authors in many of the so-far published works, such as Erturk and Inman (2009 and 2011), Toudehdehghan et al. (2017), Phung-Van et al. (2015), modelled the electromechanical response of such piezoelectric harvesters, focusing only on the calculation of electrical quantities or on the calculation of displacement of a particular point on the centreline. They, however, did not consider the induced (residual/mechanical) stresses within the beam’s layers in their models. These stresses are, however, very important upon the design of such (ceramic) harvesters, since they suffer from a relatively low fracture toughness (caused by a high brittleness of the used materials), highly limiting their power possibilities. In other words, upon generation of electricity, the full potential of the device cannot be used, since too large deflections may cause damage to the device. Therefore, our main goal is to assess and tailor the fracture toughness of such a multilayer device (containing piezoelectric layers) in order to enable increase of the range of allowable deflections (and thus the output power) upon preservation of the system integrity. Such a goal can be achieved by means of a multilayer concept of the energy harvester containing high residual stresses in particular layers. Especially, strong compressive stresses can significantly improve the laminate’s resistance to a brittle failure as discussed e.g. in Sestakova et al. (2011) . If they take place in outer layers of the multilayer energy harvester, then such layers act as protective ones, i.e. they can help to prevent propagation of potential surface cracks through the laminate, and thus can help to prevent damage of piezo electric layers placed inside the laminate.