# Neural Network-Based Prediction Model to Investigate the Influence of Temperature and Moisture on Vibration Characteristics of Skew Laminated Composite Sandwich Plates

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

^{0}FE formulation. Zenkour and Alghanmi [8] performed a static analysis of sandwich plates made of piezoelectric face sheets and a functionally graded core. The central deflection and the stresses generated in the sandwich plates acted upon by sinusoidal thermo-electro-mechanical loads were reported. Daikh et al. [24] utilized the higher-order shear deformation theory (HSDT) to investigate the static behavior of sandwich plates experiencing the thermo-mechanical loads. Temperature-dependent material properties were considered for the study. Ding et al. [25,26] experimentally investigated the effect of various harsh environmental aging on mechanical characteristics of the sandwich composites. Sandwich composites made of a PVC foam core and vinyl-ester-based composite face sheets were subject to salt-fog spray aging, hygrothermal aging, and solar radiation in combination with water vapor environmental aging.

_{c}/t

_{f}) ratio, fiber orientation, skew angle, and boundary constraints on the vibrational characteristics are investigated under various hygrothermal conditions.

## 2. Mathematical Model

**a**, and the width and thickness are symbolized as

**b**and

**H**, respectively. The face sheet thickness is denoted as

**h**(

**h**=

_{t}**h**=

_{b}**h**), and the core thickness is 2h

_{c}. Figure 1b exemplifies the kinematics of the deformation of an LCS plate in XZ- and YZ-planes. The angles

**α**,

_{x}**β**,

_{x}**φ**and

_{x}**α**,

_{y}**β**,

_{y}**φ**, signify the rotation in XZ- plane and YZ- planes, respectively. At midplane, the translational displacements along X, Y, and Z directions are denoted as x

_{y}_{0}, y

_{0}, and z

_{0}, respectively.

#### 2.1. Linear Strain Displacement Relations

- ε
_{x}, ε_{y}: Strains along x and y directions. - ε
_{xy}: In-plane shear strain. - ε
_{xz}, ε_{yz}: Transverse shear strains.

#### 2.2. Non-Linear Strain Displacement Relations

_{0,x}indicates a partial derivative of x

_{0}with respect to x, i.e., ${x}_{0,x}=\raisebox{1ex}{$\mathsf{\partial}{x}_{0}$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\partial}x$}\right.}$.

#### 2.3. Finite Element Model

_{0}, y

_{0}, z

_{0}) and six rotational (α

_{x}, α

_{y}, β

_{x}, β

_{y}, φ

_{x}, φ

_{y}) degrees of freedom are considered at each node. In general, the displacement vectors of any element can be articulated as

_{tra}and I

_{rot}are (3 × 3) and (6 × 6) identity matrices, respectively, and n

_{i}is the shape function of the natural coordinate associated with the i-th node.

#### 2.4. Elemental Stiffness Matrix

#### 2.5. Element Initial Stress Stiffness Matrix

_{1}and T

_{2}are transformation matrices of order 3 × 3 and 2 × 2 respectively, and,

- e
_{x}, e_{y}, e_{xy}: Non-mechanical strains - β
_{1}and β_{2}: Moisture coefficients - α
_{1}and α_{2}: Thermal coefficients - T and T
_{0}: Elevated and reference temperature - C and C
_{0}: Elevated and reference moisture profiles.

#### 2.6. Solution Process

_{e}], initial stress stiffness matrix [K

_{σ}], and mass matrix [M] are obtained by combining respective elemental matrices [K

^{e}

_{e}], [K

^{e}

_{σ}], and [M

^{e}], respectively. The obtained global matrices can be arranged to calculate the natural frequency of the system as

## 3. Material Properties

## 4. Results and Discussions

#### 4.1. Comparison with Previous Studies

#### 4.2. Artificial Neural Network

#### 4.3. Model Simulation Results

_{c}/t

_{f}ratio of 2 is considered for the simulation. The non-dimension frequency values for varying temperature and skew angle are presented in Figure 8. For both SSSS and CCCC boundary conditions, the natural frequency follows a decreasing trend with increasing temperature values. The frequency value increases with an increase in skew angle for all the temperature values considered. From Figure 8, it is also evident that the results predicted by the ANN model have good accuracy and show a similar trend to the results obtained from the numerical model.

_{c}/t

_{f}= 2) in the elevated thermal environment (325 K). Results indicate an upsurge in the frequency value with an increase in a/b and a/H ratios. As the length to thickness (a/H) ratio varies from 10 to 50, the plate transforms from a thick plate to a thin plate condition. As the a/b and a/H ratio increases, the ratio of the magnitude of the stiffness matrix to the mass matrix tends to increase continuously. Many researchers have reported similar observations for various composite structures [19,21,23]. The same trend in variation of natural frequency values for clamped boundary conditions can be observed, as presented in Figure 11.

_{c}/t

_{f}ratio are presented in Figure 14a. From the results, it is evident that the natural frequency considerably decreases with an increase in the t

_{c}/t

_{f}ratio at an elevated thermal environment. Previously, similar observations were reported by many researchers in ambient and elevated thermal environments [2,39,40]. The clamped LCS plates were also investigated in moisture environments to understand the impact of the t

_{c}/t

_{f}ratio on the natural frequency of the system. The results obtained for the LCS plate operating in a 1% moisture concentration environment are plotted in Figure 14b. From the results, it is evident that the frequency of the system decreases with an increase in moisture concentration value. It can also be observed that for both thermal and moisture cases, the influence of the t

_{c}/t

_{f}ratio is more prominent for higher values of a/b ratios.

_{c}/t

_{f}ratio, and skew angle were considered as 0.5, 2, and 0°, respectively, for the analysis. The results obtained for the LCS plate operating at a temperature of 375 K for various a/H ratios are presented in Figure 15.

## 5. Conclusions

_{c}/t

_{f}ratio. It is also noted that non-dimensional fundamental frequency considerably decreases with an increase in the fiber orientation of the face sheet.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## Appendix D

- N
_{x}, N_{y}, N_{xy}: In-plane initial internal force resultants per unit length - M
_{x}, M_{y}, M_{xy}: Initial internal moment resultants per unit length - Q
_{x}, Q_{y}: Initial transverse shear resultants.

## Appendix E

- w
_{1}and b_{1}are weight and bias of hidden layer - w
_{2}and b_{2}are weight and bias of hidden layer

## References

- Suresh Kumar, R.; Ray, M.C. Active constrained layer damping of smart laminated composite sandwich plates using 1-3 piezoelectric composites. Int. J. Mech. Mater. Des.
**2012**, 8, 197–218. [Google Scholar] [CrossRef] - Dat, N.D.; Quan, T.Q.; Mahesh, V.; Duc, N.D. Analytical solutions for nonlinear magneto-electro-elastic vibration of smart sandwich plate with carbon nanotube reinforced nanocomposite core in hygrothermal environment. Int. J. Mech. Sci.
**2020**, 186, 105906. [Google Scholar] [CrossRef] - Ryu, J.; Lho, S.H.; Lee, C.H.; Ju, Y.K. Flexural behavior of prestressed sandwich plate system composite beams. Eng. Struct.
**2020**, 215, 110705. [Google Scholar] [CrossRef] - Bouazza, M.; Zenkour, A.M. Hygro-thermo-mechanical buckling of laminated beam using hyperbolic refined shear deformation theory. Compos. Struct.
**2020**, 252, 112689. [Google Scholar] [CrossRef] - Khare, R.K.; Garg, A.K.; Kant, T. Free vibration of sandwich laminates with two higher-order shear deformable facet shell element models. J. Sandw. Struct. Mater.
**2005**, 7, 221–244. [Google Scholar] [CrossRef] - Biswal, M.; Sahu, S.K.; Asha, A.V. Experimental and numerical studies on free vibration of laminated composite shallow shells in hygrothermal environment. Compos. Struct.
**2015**, 127, 165–174. [Google Scholar] [CrossRef] - Parhi, P.K.; Bhattacharyya, S.K.; Sinha, P.K. Hygrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells. J. Sound Vib.
**2001**, 248, 195–214. [Google Scholar] [CrossRef] - Zenkour, A.M.; Alghanmi, R.A. Hygro-thermo-electro-mechanical bending analysis of sandwich plates with FG core and piezoelectric faces. Mech. Adv. Mater. Struct.
**2019**, 28, 282–294. [Google Scholar] [CrossRef] - Farrar, C.R.; Worden, K. An introduction to structural health monitoring. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2007**, 365, 303–315. [Google Scholar] [CrossRef] - Sharnappa Ganesan, N.; Sethuraman, R. Dynamic modeling of active constrained layer damping of composite beam under thermal environment. J. Sound Vib.
**2007**, 305, 728–749. [Google Scholar] [CrossRef] - Nguyen, N.D.; Nguyen, T.K.; Nguyen, T.N.; Thai, H.T. New Ritz-solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams. Compos. Struct.
**2018**, 184, 452–460. [Google Scholar] [CrossRef] - Sobhy, M. An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment. Int. J. Mech. Sci.
**2016**, 110, 62–77. [Google Scholar] [CrossRef] - Mehar, K.; Panda, S.K.; Sharma, N. Numerical investigation and experimental verification of thermal frequency of carbon nanotube-reinforced sandwich structure. Eng. Struct.
**2020**, 211, 110444. [Google Scholar] [CrossRef] - Dewangan, H.C.; Panda, S.K.; Sharma, N. Experimental Validation of Role of Cut-Out Parameters on Modal Responses of Laminated Composite—A Coupled FE Approach. Int. J. Appl. Mech.
**2020**, 12. [Google Scholar] [CrossRef] - Katariya, P.V.; Panda, S.K.; Mehar, K. Theoretical modelling and experimental verification of modal responses of skewed laminated sandwich structure with epoxy-filled softcore. Eng. Struct.
**2021**, 228, 111509. [Google Scholar] [CrossRef] - Biswal, M.; Sahu, S.K.; Asha, A.V. Dynamic Stability of Woven Fiber Laminated Composite Shallow Shells in Hygrothermal Environment. Int. J. Struct. Stab. Dyn.
**2017**, 17, 1–26. [Google Scholar] [CrossRef] - Sayyad, A.S.; Ghumare, S.M. Thermomechanical Bending Analysis of FG Sandwich Plates Using a Quasi-Three-Dimensional Theory. J. Aerosp. Eng.
**2021**, 34, 04021007. [Google Scholar] [CrossRef] - Zenkour, A.M.; El-Shahrany, H.D. Hygrothermal forced vibration of a viscoelastic laminated plate with magnetostrictive actuators resting on viscoelastic foundations. Int. J. Mech. Mater. Des.
**2021**, 17. [Google Scholar] [CrossRef] - Garg, N.; Karkhanis, R.S.; Sahoo, R.; Maiti, P.R.; Singh, B.N. Trigonometric zigzag theory for static analysis of laminated composite and sandwich plates under hygro-thermo-mechanical loading. Compos. Struct.
**2019**, 209, 460–471. [Google Scholar] [CrossRef] - Chandra, S.; Sepahvand, K.; Matsagar, V.A.; Marburg, S. Stochastic dynamic analysis of composite plate with random temperature increment. Compos. Struct.
**2019**, 226, 111159. [Google Scholar] [CrossRef] - Rath, M.K.; Sahu, S.K. Vibration of woven fiber laminated composite plates in hygrothermal environment. JVC/J. Vib. Control
**2012**, 18, 1957–1970. [Google Scholar] [CrossRef] - Sit, M.; Ray, C. Free vibration characteristics of glass and bamboo epoxy laminates under hygrothermal effect: A comparative approach. Compos. Part B Eng.
**2019**, 176, 107333. [Google Scholar] [CrossRef] - Padhi, A.; Pandit, M.K. Bending and free vibration response of sandwich laminate under hygrothermal load using improved zigzag theory. J. Strain Anal. Eng. Des.
**2017**, 52, 288–297. [Google Scholar] [CrossRef] - Daikh, A.A.; Bensaid, I.; Zenkour, A.M. Temperature dependent thermomechanical bending response of functionally graded sandwich plates. Eng. Res. Express
**2020**, 2. [Google Scholar] [CrossRef] - Ding, A.; Wang, J.; Ni, A.; Li, S. Hygroscopic ageing of nonstandard size sandwich composites with vinylester-based composite faces and PVC foam core. Compos. Struct.
**2018**, 206, 194–201. [Google Scholar] [CrossRef] - Ding, A.; Wang, J.; Ni, A.; Li, S. Assessment on the ageing of sandwich composites with vinylester-based composite faces and PVC foam core in various harsh environments. Compos. Struct.
**2019**, 213, 71–81. [Google Scholar] [CrossRef] - Salehi, H.; Burgueño, R. Emerging artificial intelligence methods in structural engineering. Eng. Struct.
**2018**, 171, 170–189. [Google Scholar] [CrossRef] - Atilla, D.; Sencan, C.; Goren Kiral, B.; Kiral, Z. Free vibration and buckling analyses of laminated composite plates with cutout. Arch. Appl. Mech.
**2020**, 90, 2433–2448. [Google Scholar] [CrossRef] - Elshafey, A.A.; Dawood, N.; Marzouk, H.; Haddara, M. Crack width in concrete using artificial neural networks. Eng. Struct.
**2013**, 52, 676–686. [Google Scholar] [CrossRef] - Sharma, N.; Swain, P.K.; Maiti, D.K.; Singh, B.N. Stochastic frequency analysis of laminated composite plate with curvilinear fiber. Mech. Adv. Mater. Struct.
**2020**, 1–16. [Google Scholar] [CrossRef] - Mouloodi, S.; Rahmanpanah, H.; Burvill, C.; Gohari, S.; Davies, H.M.S. Experimental, regression learner, numerical, and artificial neural network analyses on a complex composite structure subjected to compression loading. Mech. Adv. Mater. Struct.
**2020**, 1–17. [Google Scholar] [CrossRef] - Zenzen, R.; Khatir, S.; Belaidi, I.; Le Thanh, C.; Abdel Wahab, M. A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures. Compos. Struct.
**2020**, 248. [Google Scholar] [CrossRef] - Gomes, G.F.; de Almeida, F.A.; Junqueira, D.M.; da Cunha, S.S.; Ancelotti, A.C. Optimized damage identification in CFRP plates by reduced mode shapes and GA-ANN methods. Eng. Struct.
**2019**, 181, 111–123. [Google Scholar] [CrossRef] - Al Rjoub, Y.S.; Alshatnawi, J.A. Free vibration of functionally-graded porous cracked plates. Structures
**2020**, 28, 2392–2403. [Google Scholar] [CrossRef] - Oliver, G.A.; Ancelotti, A.C.; Gomes, G.F. Neural network-based damage identification in composite laminated plates using frequency shifts. Neural Comput. Appl.
**2020**, 3, 1–12. [Google Scholar] [CrossRef] - Jalal, M.; Grasley, Z.; Gurganus, C.; Bullard, J.W. A new nonlinear formulation-based prediction approach using artificial neural network (ANN) model for rubberized cement composite. Eng. Comput.
**2020**. [Google Scholar] [CrossRef] - Jodaei, A.; Jalal, M.; Yas, M.H. Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN. Compos. Part B Eng.
**2012**, 43, 340–353. [Google Scholar] [CrossRef] - Ram, K.S.S.; Sinha, P.K. Hygrothermal effects on the free vibration of laminated composite plates. J. Sound Vib.
**1992**, 158, 133–148. [Google Scholar] [CrossRef] - Kallannavar, V.; Kumaran, B.; Kattimani, S.C. Effect of temperature and moisture on free vibration characteristics of skew laminated hybrid composite and sandwich plates. Thin-Walled Struct.
**2020**, 157. [Google Scholar] [CrossRef] - Yuan, W.X.; Dawe, D.J. Free vibration of sandwich plates with laminated faces. Int. J. Numer. Methods Eng.
**2002**, 54, 195–217. [Google Scholar] [CrossRef] - Garg, A.K.; Khare, R.K.; Kant, T. Free vibration of skew fiber-reinforced composite and sandwich laminates using a shear deformable finite element model. J. Sandw. Struct. Mater.
**2006**, 8, 33–53. [Google Scholar] [CrossRef] - Behera, R.R.; Ghadai, R.K.; Kalita, K.; Banerjee, S. Simultaneous prediction of delamination and surface roughness in drilling GFRP composite using ANN. Int. J. Plast. Technol.
**2016**, 20, 424–450. [Google Scholar] [CrossRef] - Cascardi, A.; Micelli, F.; Aiello, M.A. An Artificial Neural Networks model for the prediction of the compressive strength of FRP-confined concrete circular columns. Eng. Struct.
**2017**, 140, 199–208. [Google Scholar] [CrossRef]

**Figure 1.**Graphical illustration of the (

**a**) Laminated Composite Sandwich (LCS) plate and (

**b**) kinematics of deformation of the LCS plate.

**Figure 2.**Properties of DYAD 606 viscoelastic material (

**a**) loss factor and (

**b**) shear modulus variations [10] (Adapted with permission from Elsevier B.V., License Number: 5077631407971).

**Figure 6.**Schematic representation of (

**a**) ANN training performance and (

**b**) histograms of error values of the developed predictive model.

**Figure 7.**Scatter plot to compare the target results and the ANN predicted fundamental natural frequency values.

**Figure 8.**Influence of thermal environment on the fundamental frequency of the LCS plate under (

**a**) SSSS and (

**b**) CCCC boundary conditions.

**Figure 9.**Influence of moisture environment on the fundamental frequency of the LCS plate under (

**a**) SSSS and (

**b**) CCCC boundary conditions.

**Figure 10.**Influence of skew angle on the simply supported skew LCS plate operating at elevated thermal environment (325 K) for varying a/b and a/H ratios (

**a**) a/b = 0.5 (

**b**) a/b = 1.0 (

**c**) a/b = 2.0.

**Figure 11.**Influence of skew angle on the clamped skew LCS plate operating in an elevated thermal environment (325 K) for varying a/b and a/H ratios (

**a**) a/b = 0.5 (

**b**) a/b = 1.0 (

**c**) a/b = 2.0.

**Figure 12.**Influence of skew angle on the SSSS skew LCS plate in presence of moisture (0.25%) for varying a/b and a/H ratios (

**a**) a/b = 0.5 (

**b**) a/b = 1.0 (

**c**) a/b = 2.0.

**Figure 13.**Influence of skew angle on the CCCC skew LCS plate in the presence of moisture (0.25%) for varying a/b and a/H ratios (

**a**) a / b = 0.5 (

**b**) a / b = 1.0 (

**c**) a / b = 2.0.

**Figure 14.**Influence of the t

_{c}/t

_{f}ratio on the clamped LCS plate in the presence of (

**a**) temperature (400 K) and (

**b**) moisture (1.0%) for varying a/b ratios.

**Figure 15.**Influence of the face sheet fiber orientation angle on the skew LCS plate in the presence of an elevated thermal environment (375 K) for varying a/H ratios operating under (

**a**) SSSS and (

**b**) CCCC boundary conditions.

**Figure 16.**Influence of the face sheet fiber orientation angle on the skew LCS plate in the presence of a moisture environment (0.75 %) for varying a/H ratios operating under (

**a**) SSSS and (

**b**) CCCC boundary conditions.

Properties | Units | Graphite-Epoxy [38] | Viscoelastic Core [10] |
---|---|---|---|

Elastic Moduli | GPa | Table 2a,b | Figure 2 |

Density | kg/m^{3} | 1600 | 1200 |

Poisson’s Ratio | m/m | υ12 = 0.3 | υ12 = 0.49 |

Coefficient of moisture expansion | - | β1 = 0 β2 = 0.44 | - |

Coefficient of thermal expansion | /K | α1 = −0.3 × 10^{−6} α2 = 28.1 × 10 ^{−6} | - |

(a) | |||||

Elastic Moduli (GPa) | 0.00 | 0.25 | 0.50 | 0.75 | 1.00 |

E1 | 130 | 130 | 130 | 130 | 130 |

E2 | 9.50 | 9.25 | 9.00 | 8.75 | 8.50 |

G12 = G13 | 6.0 | 6.0 | 6.0 | 6.0 | 6.0 |

(b) | |||||

Elastic Moduli (GPa) | 300 | 325 | 350 | 375 | 400 |

E1 | 130 | 130 | 130 | 130 | 130 |

E2 | 9.50 | 8.50 | 8.00 | 7.50 | 7.00 |

G12 = G13 | 6.0 | 6.0 | 5.5 | 5.0 | 4.75 |

**Table 3.**Influence of hygrothermal environment on the non-dimensional frequency of the clamped skew composite plate.

Skew Angle | Mesh Size | Temperature (K) | Moisture Concentration (%) | ||||||
---|---|---|---|---|---|---|---|---|---|

300 | 325 | 350 | 375 | 0.00 | 0.25 | 0.50 | 0.75 | ||

0° | 4 × 4 | 34.2394 | 34.2046 | 34.1697 | 34.1350 | 34.2394 | 34.1720 | 34.1048 | 34.0377 |

8 × 8 | 35.6470 | 35.6113 | 35.5756 | 35.5399 | 35.6470 | 35.5775 | 35.5080 | 35.4386 | |

12 × 12 | 35.8753 | 35.8404 | 35.8054 | 35.7705 | 35.8753 | 35.8066 | 35.7381 | 35.6696 | |

Ref. [39] | 35.8753 | 35.8404 | 35.8054 | 35.7705 | 35.8753 | 35.8066 | 35.7381 | 35.6696 | |

15° | 4 × 4 | 34.6184 | 34.5807 | 34.5431 | 34.5055 | 34.6184 | 34.5470 | 34.4758 | 34.4047 |

8 × 8 | 36.0444 | 36.0060 | 35.9675 | 35.9292 | 36.0444 | 35.9710 | 35.8977 | 35.8246 | |

12 × 12 | 36.2630 | 36.2253 | 36.1875 | 36.1498 | 36.2630 | 36.1904 | 36.1179 | 36.0455 | |

Ref. [39] | 36.2630 | 36.2253 | 36.1875 | 36.1498 | 36.2630 | 36.1904 | 36.1179 | 36.0455 | |

30° | 4 × 4 | 35.9073 | 35.8608 | 35.8143 | 35.7679 | 35.9073 | 35.8232 | 35.7392 | 35.6555 |

8 × 8 | 37.3947 | 37.3477 | 37.3008 | 37.2540 | 37.3947 | 37.3092 | 37.2240 | 37.1390 | |

12 × 12 | 37.5810 | 37.5345 | 37.4880 | 37.4415 | 37.5810 | 37.4960 | 37.4111 | 37.3265 | |

Ref. [39] | 37.5810 | 37.5345 | 37.4880 | 37.4415 | 37.5810 | 37.4960 | 37.4111 | 37.3265 | |

45° | 4 × 4 | 38.7608 | 38.6980 | 38.6352 | 38.5725 | 38.7608 | 38.6532 | 38.5459 | 38.4389 |

8 × 8 | 40.3527 | 40.2904 | 40.2282 | 40.1661 | 40.3527 | 40.2455 | 40.1385 | 40.0319 | |

12 × 12 | 40.4746 | 40.4122 | 40.3498 | 40.2875 | 40.4746 | 40.3669 | 40.2594 | 40.1523 | |

Ref. [39] | 40.4746 | 40.4122 | 40.3498 | 40.2875 | 40.4746 | 40.3669 | 40.2594 | 40.1523 | |

60° | 4 × 4 | 45.2802 | 45.1912 | 45.1024 | 45.0137 | 45.2802 | 45.1346 | 44.9893 | 44.8446 |

8 × 8 | 46.9400 | 46.8524 | 46.7650 | 46.6778 | 46.9400 | 46.7961 | 46.6526 | 46.5097 | |

12 × 12 | 46.9691 | 46.8804 | 46.7920 | 46.7037 | 46.9691 | 46.8233 | 46.6781 | 46.5335 | |

Ref. [39] | 46.9691 | 46.8804 | 46.7920 | 46.7037 | 46.9691 | 46.8233 | 46.6781 | 46.5335 |

Lamination Scheme | Source | Skew Angles | ||
---|---|---|---|---|

0° | 15° | 30° | ||

90°/0°/C/0°/90° | FSDT [41] | 172.7237 | 184.5342 | 225.9660 |

HSDT [41] | 158.0954 | 167.8775 | 201.7029 | |

Spline finite strip method [40] | 159.30 | - | - | |

Present | 157.20 | 165.10 | 190.85 | |

0°/90°/C/0°/90° | FSDT [41] | 166.3086 | 177.6942 | 217.7630 |

HSDT [41] | 152.2992 | 161.7182 | 194.3770 | |

Spline finite strip method [40] | 152.58 | - | - | |

Present | 150.78 | 158.48 | 183.61 | |

0°/90°/C/90°/0° | FSDT [41] | 159.8275 | 170.7568 | 209.3430 |

HSDT [41] | 146.5089 | 155.5495 | 186.9801 | |

Spline finite strip method [40] | 145.99 | - | - | |

Present | 144.40 | 151.88 | 176.31 |

Parameters | Range |
---|---|

Temperature (K) | 300, 325, 350, 375, 400 |

Moisture (%) | 0, 0.25, 0.5, 0.75, 1 |

Boundary conditions | SSSS, CCCC |

Length to breadth (a/b) ratio | 0.5, 1, 2 |

Length to thickness (a/H) ratio | 10, 20, 50 |

Core thickness to thickness of face sheet (t_{c}/t_{f}) ratio | 2, 5, 10, 50 |

Fiber orientation of composite face sheets | 0°, 30°, 45°, 60° |

Skew angle | 0°, 15°, 30°, 45° |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kallannavar, V.; Kattimani, S.; Soudagar, M.E.M.; Mujtaba, M.A.; Alshahrani, S.; Imran, M.
Neural Network-Based Prediction Model to Investigate the Influence of Temperature and Moisture on Vibration Characteristics of Skew Laminated Composite Sandwich Plates. *Materials* **2021**, *14*, 3170.
https://doi.org/10.3390/ma14123170

**AMA Style**

Kallannavar V, Kattimani S, Soudagar MEM, Mujtaba MA, Alshahrani S, Imran M.
Neural Network-Based Prediction Model to Investigate the Influence of Temperature and Moisture on Vibration Characteristics of Skew Laminated Composite Sandwich Plates. *Materials*. 2021; 14(12):3170.
https://doi.org/10.3390/ma14123170

**Chicago/Turabian Style**

Kallannavar, Vinayak, Subhaschandra Kattimani, Manzoore Elahi M. Soudagar, M. A. Mujtaba, Saad Alshahrani, and Muhammad Imran.
2021. "Neural Network-Based Prediction Model to Investigate the Influence of Temperature and Moisture on Vibration Characteristics of Skew Laminated Composite Sandwich Plates" *Materials* 14, no. 12: 3170.
https://doi.org/10.3390/ma14123170