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Table 1 FEM computed and experimentally identified modal parameters

From: Physical modelling techniques for the dynamical characterization and sound synthesis of historical bells

Modal pair

FEM computations

Experimental modal identification

Rel. Diff

ERA

vs

FEM

(%)

Mode shapes

Frequency

(Hz)

Ratio

(fn/f2)

Frequency

(Hz)

Ratio

(fn/f2)

Damp

(%)

General

xy view

zx view

1st family

2nd family

1

(Hum)

1487.6

0.5133

1487.6

0.5139

0.02

0

1489.0

0.5137

1490.8

0.5150

0.02

0.12

2

(Prime)

2895.2

0.9989

2891.8

0.9989

0.03

0.12

2901.6

1.0011

2898.1

1.0011

0.02

0.12

3

(Tierce)

3597.6

1.2413

3593.8

1.2414

0.04

0.11

3599.1

1.2418

3594.0

1.2432

0.04

0.14

4

(Quint)

4831.1

1.6668

4854.4

1.6688

0.02

0.48

4841.4

1.6704

4855.9

1.6774

0.03

0.30

5

(Nominal)

6057.6

2.0900

6048.2

2.0925

0.03

0.16

6060.4

2.0909

6060.8

2.0934

0.03

0.01