PSI - Issue 47

Panagiotis N. Lymperopoulos et al. / Procedia Structural Integrity 47 (2023) 274–281 Panagiotis N. Lymperopoulos, Efstathios E. Theotokoglou / Structural Integrity Procedia 00 (2022) 000–000

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2

where a wave with a frequency inside the band can not propagate inside the material (Kadic et al. (2012), Norris (2014), Amendola et al. (2016)). Pentamodes have the possibility to confront different types of loading conditions. Therefore, there is a wide range of applications in which they can be used, such as antiseismic design (Fabbrocino et al. (2015), Mu et al. (2020), Lymperopoulos and Theotokoglou (2022)) and generally vibration isolation (Ji et al. (2021)). There is a lot of investigation on pentamodes characteristics (Fabbrocino et al. (2015), Amendola et al. (2016), Lymperopoulos et al. (2020), Cushing et al. (2022), Lymperopoulos and Theotokoglou (2022)). In addition, there is also investigation in order to describe pentamodes band gap (Kumara et al. (2022), Zhou et. al. (2023)). But in order to confront the seismic loading some affords have been done till now based on static loading conditions (Amendola et al. (2016), Lymperopoulos and Theotokoglou (2020)). Consequently, a study considering the dynamic nature of loading conditions should be taken place. Seismic waves have frequency between the band 0.01Hz to 10Hz, while the most catastrophic phenomena are between 0.01Hz and 2Hz (Masuda et al. (2020)). In this investigation, computational analyses have been carried out, to different pentamode structures, in order to understand the pentamodes behavior under harmonical loading conditions.

Nomenclature G c

Shear strength Bulk strength

E c F h F v δ h δ v H A D

Forces at bottom nodes of pentamodes toward x-axis Forces at bottom nodes of pentamodes toward z-axis Displacement at top nodes of pentamodes towards x-axis Displacement at top nodes of pentamodes towards z-axis

Height of pentamode Area of pentamode Rod big diameter Rod small diameter

d a

pentamode main dimension

2. Theoretical Consideration The shear and bulk strength of pentamodes, are given by the following equations ((Amendola et al. (2016), Lymperopoulos and Theotokoglou (2022)),

h FH

v FH

,

G

E

=

=

(1)

c

c

A

A

h δ

v δ

In this study, steel is considered as the material with the following properties (Table 1),

Table 1. Material Material

Young Modulus ( GPa)

Density (kg/m 3 )

Steel (Fabbrocino et al. (2015))

206

8000

In the case of static loading, a displacement of δ o =1mm is applied at the top nodes of the pentamode structure. In the case of harmonical loading, the displacement at the top nodes can be described by the following equation: ( ) 0 sin t δ δ ω φ = + (2)