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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where, ω is the imposed circular frequency, t (sec) is the time and φ (rad) is the displacement phase shift. 3. Computational Analyses In our study, the finite element program (ANSYS (2018)) has been used for the finite element analysis. The elements that have been used are the BEAM189 (ANSYS (2018)) which is a 2 node beam element, while for the pentamodes with confinement plates the PLANE183 (ANSYS (2018)) is used, which is a plate element with 8 nodes. Pentamodes are considered to be fully constrained at the bottom nodes, and a displacement of δ h or δ v is applied toward x- or z-axis, for different frequencies between the band 0.01Hz and 10Hz. In the following Fig. 1 the two types of pentamodes, without and with confinement plates, are presented.

(a)

(b)

Fig. 1. (a) Unit cell pentamode structure without confinement plates, (b) Unit cell pentamode structure with confinement plates

4. Results and Discussion At first, the convergence for the finite element method results is numerically checked. A pentamode with 3 unit cells toward x-axis, 2 unit cells towards z-axis and 1 unit cell towards y-axis and without confinement plates is examined. The bottom nodes are fully constrained, and a force F (=1kN) is applied to top nodes towards x-axis. Then, the displacements of top nodes are presented in Fig. 2.

Fig. 2. x-axis displacement at top nodes