PSI - Issue 25

P.N. Lymperopoulos et al. / Procedia Structural Integrity 25 (2020) 172–179

173

2 Panagiotis N. Lymperopoulos, Efstathios E. Theotokoglou, Ioannis A. Antoniadis / Structural Integrity Procedia 00 (2019) 000–000

In addition, metamaterials appears to have band gap, waves with frequency inside this band, can not propagate through the metamaterial (Chronopoulos et.al. (2015)),(Sapountzakis et.al. (2015)). This phenomenon is under inves tigation in order to use metamaterials for seismic-resistance design and aircrafts design. The antiseismic design of old buildings and modern buildings is a significant factor during the design process for seismic protection. Seismic waves appear to have frequencies inside a band from 0.0001 Hz to 1000Hz (Shearer (2009)).

Nomenclature

G shear modulus G c shear modulus of pentamode structure G r shear modulus of isolators K bulk modulus D max diameter of a pentamode rod d min diameter of a pentamode rod α length of pentamode R length of a pentamode rod

In this research, an initial approach onthe design of pentamode related to a computational analysis is taken place. A finite element model is proposed in order to confront multi rows pentamode. According to the proposed analysis, an optimum diameter for the rods considered in pentamodes results. The proposed pentamodes behave similarly with isolators (Fabbrocino et.al. (2015)).

2. Theoretical Consideration

Pentamodes have been studied from several researchers. Analytical approaches have been proposed by (Norris A. (2014)), (Fabbrocino et.al. (2015)) and (Kadic et.al. (2012)), where the ratio G K has been calculated, which is very essential for pentamodes design. The following equations (1), (2) have been proposed by (Fabbrocino et.al. (2015)) and (Kadic et.al. (2012)), respectively :

G K =

8(2 D + dD + d 2 ) R 2 27 d 2 D 2

( 4

1

(1)

) −

9 +

2 R

G K =

(( R

1

(2)

D ) −

d )

In order to calculate the shear modulus, the equation (3) has been proposed (Amendolad et.al. (2016)) :

F h H d h A

G c =

(3)

where d h is the constant displacement, that the top nodes are forced to have, when nodes at the bottom are restrained. F h is the force that is calculated to the restrained bottom nodes. H is the height of the pentamode, and A is the area of the pentamode.