PSI - Issue 81

Andrejs Kovalovs et al. / Procedia Structural Integrity 81 (2026) 388–395

391

2.2. Identification parameters The selection of identification parameters is guided by the anisotropic structure of CFRP laminates. In the case of the unidirectional composite, six independent engineering constants define the constitutive relations of a transversely isotropic ply: the longitudinal Young’s modulus E 1 , the transverse moduli E 2 = E 3 , the in-plane and out-of-plane shear moduli G 12 = G 13 and G 23 , and Poisson’s ratios ν 12 = ν 13 and ν 23 . For the twill-weave composite, the mechanical response is nearly orthotropic within the laminate plane ( E 1 = E 2 ) but remains distinct through the thickness; thus, six constants were again retained to represent the principal material directions. The bounds in Table 1 were chosen to cover the variability expected for aerospace-grade carbon/epoxy systems. These limits were determined from both literature data (Rikards, 2003; Matter et al., 2009) and manufacturer datasheets. The lower and upper limits correspond to ±20% deviations from nominal v alues to account for manufacturing scatter, fiber volume fraction differences, and potential uncertainties in manufacturing and curing conditions.

Table 1. Bounds of design experiments and reference elastic properties of unidirectional and twill-weave CFRP laminates.

Identification variables

Minimum value

Maximum value

Experimental data

Identification variables E 1 = E 2 (GPa)

Minimum value

Maximum value

Experimental data

E 1 (GPa)

130

150

139.37

60

80 10

73.87

E 2 = E 3 (GPa)

7

10

8.74

E 3 (GPa)

5

8.74

ν 12 = ν 13

0.2 0.3 3.5 1.0

0.3 0.4 6.5 2.0

0.268 0.325 4.858 1.289

0.01

0.10

0.029 0.286

ν 12

ν 13 = ν 23

0.2 5.0

0.4 7.0 5.0

ν 23

G 12 = G 13 (GPa)

G 12 (GPa)

6.19 4.86

G 23 (GPa)

G 13 = G 23 (GPa) 3.0

Unidirectional CFRP

Twill-weave CFRP

2.3. Virtual experiment results FE simulations were carried out for each of the 101 design points defined in the experimental matrix to obtain the first twelve natural frequencies and the corresponding mode shapes. The resulting dataset forms the numerical foundation for establishing the relationship between the elastic constants of the composite and the measurable modal parameters used in the inverse identification. The reference FE model described in Section 2.1 was used for all simulations. Each plate configuration was analyzed in the frequency domain using the Block Lanczos solver implemented in ANSYS Mechanical APDL. For every design point, the model provided twelve eigenfrequencies in the range up to 700 Hz and the associated displacement fields representing the global flexural and torsional vibration modes of the plate.

Table 2. Natural frequencies for unidirectional CFRP completely free plate.

Mode ( m , n )

Frequency (Hz)

Mode ( m , n )

Frequency (Hz)

Shape

No.

Shape

No.

1.

(1,1)

30.138

7.

(0,3)

172.34

2.

(0,2)

62.410

8.

(1,3)

194.16

268.61

3.

(1,2)

87.209

9.

(3,0)

4.

(2,0)

97.596

10.

(2,3)

270.44

114.54

11.

(3,1)

283.13

5.

(2,1)

6.

(2,2)

169.10

12.

(3,2)

330.05