Table 2 Optimal stiffness and damping values.

From: Flexural band gaps and response attenuation of periodic piping systems enhanced with localized and distributed resonators

Support condition

Type #1

Type #2

α

0.05

0.16

0.25

0.05

0.16

0.25

P with LLR

\({k}_{t,\alpha }\,(N/m)\)

1.30E6

2.87E6

3.05E6

1.37E6

3.05E6

3.99E6

\({c}_{t,\alpha }\,(Ns/m)\)

3.59E3

1.19E4

2.44E4

3.16E3

1.09E4

1.80E4

\(Z\)

2.08E-3

8.03E-7

6.77E-8

2.83E-3

1.10E-6

4.94E-9

P with \({P}_{1,\alpha }\)

\({k}_{{P}_{1,\alpha }}\,(N/m)\)

1.05E1

2.46E6

1.47E6

1.53E1

2.49E6

1.72E6

\({c}_{{P}_{1,\alpha }}(Ns/m)\)

1.51E3

6.38E3

8.17E3

9.51E2

6.74E3

7.07E3

\(Z\)

8.93E-1

7.61E-3

2.55E-4

8.97E-1

8.93E-3

2.55E-4

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