Table 2 Fractals CMPPs metamaterials parameters and its acoustic absorption behavior of a two-unit cells.

1

S1

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 12.56% and \({\varphi }_{3}\) = 7.07% and \({\varphi }_{4}\) = 19.63

1000 Hz (α > 92%)

60%

2

S2

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 12.56% and \({\varphi }_{3}\) = 38.46% and \({\varphi }_{4}\) = 50.24%

1300 Hz (α > 60%)

39%

3

S3

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 19.63%and \({\varphi }_{3}\) = 12.56% and \({\varphi }_{4}\) = 28.26%

1100 Hz (α > 90%)

47.27%

4

S4

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 19.63%and \({\varphi }_{3}\) = 38.46% and \({\varphi }_{4}\) = 63.59%

1250 Hz (α = 80%)

40%

5

S5

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 12.56%and \({\varphi }_{3}\) = 19.63% and \({\varphi }_{4}\) = 63.59%

1250 Hz (α > 70%)

41%

6

S6

\({\varphi }_{1}\) = 7.07%, \({\varphi }_{2}\) = 19.63%and \({\varphi }_{3}\) = 12.56% and \({\varphi }_{4}\) = 63.59%

1050 Hz (α = 90%)

76% (800–1600 Hz)

One octave