# Double Finite Sine Transform Method for Deflection Analysis of Isotropic Sandwich Plates Under Uniform Load

Double Finite Sine Transform Method for Deflection Analysis of Isotropic Sandwich Plates Under Uniform Load

Benjamin O. Mama Charles C. IkeClifford U. Nwoji Hyginus N. Onah

Department of Civil Engineering, University of Nigeria Nsukka, Enugu 400001, Nigeria

Department of Civil Engineering, Enugu State University of Science and Technology, Enugu 400001, Nigeria

Corresponding Author Email:
ikecc2007@yahoo.com
Page:
76-81
|
DOI:
https://doi.org/10.18280/ama_a.550206
11 April 2018
| |
Accepted:
10 June 2018
| | Citation

OPEN ACCESS

Abstract:

In this study, the double finite Fourier sine transform method was used to solve the governing partial differential equation of equilibrium of isotropic sandwich plates with all edges simply supported for the case of uniformly distributed transverse load over the entire plate domain.  The governing equation solved for the sandwich plate domain was obtained by Liaw Boen Dar by ignoring the linear terms in the Reissner’s plate equation to have a fourth order partial differential equation. Application of the double finite Fourier sine transformation, and use of the simply supported Dirichlet boundary conditions simplified the problem to an algebraic problem in terms of the double finite Fourier sine of the unknown deflection in the transform space. Inversion of the double finite Fourier sine transform yielded the unknown deflection in the physical domain space. Specific problem of uniformly distributed transverse load over the entire plate yielded rapidly convergent solutions for the deflection. The deflections are found to be expressible in terms of the sum of flexural and shear deflections for the case of general distributed load, and for the specific case of uniformly distributed load. Maximum deflections, found to occur at the plate center were found to be decomposed into flexural and shear components.

Keywords:

isotropic sandwich plate, double finite sine transform method, integral transformation, inverse Fourier sine transform, uniformly distributed load

1. Introduction
2. Theoretical Framework
3. Methodology
4. Results
5. Discussion
6. Conclusion
Nomenclature
References

[1] Petras A. (1999). Design of sandwich structures. PhD Dissertation. Cambridge University 114. https//doi.org/10.17863/CAM.13989

[2] Vrabie M, Chiriac R. (2014). Theoretical and numerical investigation regarding the bending behaviour of sandwich plates. Bul. Inst. Polit. Lasi. t. LX (LXIV). f. 4.

[3] Mama BO, Ike CC. (2018). Galerkin-Vlasov method for deflection analysis of isotropic sandwich plates under uniform load. Journal of Engineering Sciences (JES) 5(1): D15 – D19.

[4] Mama BO, Ike CC. (2018). Galerkin-Vlasov method for deflection analysis of isotropic sandwich plates under uniform load. Proceedings Faculty of Engineering, University of Nigeria First International Conference on Engineering and Technology as Tools for Sustainable Economic and Industrial Growth in the 21st Century, pp. 470-478.

[5] Jha AK. (2007). Free vibration analysis of sandwich panel. Master of Technology (Mechanical Engineering) Thesis. National Institute of Technology, Rourkela (Deomed University).

[6] Magnucka–Blandzi E, Wittenberg L. (2013). Approximate solutions of equilibrium equations of sandwich circular plate. AIP Conference Proceedings 1558(12352). https//doi/org/10.1063/1.48260.13

[7] Berthelot JM. (1999). Theory of sandwich plates. In Composite Materials, Mechanical Engineering Series, 382–391. http//doi.wg/10.1007/978-1-4612-0527-2_18

[8] Chiriac R, Vrabie M. (2016). The first order shear deformation theory for sandwich plates. Intersections/intersectii 13(1): 37–47.

[9] Magnucka–Blandzi E. (2011). Mathematical modelling of a rectangular sandwich plate with a metal foam core. Journal of Theoretical and Applied Mechanics 49(2): 439–455.

[10] Wang CM. (1995) Deflection of sandwich plates in terms of corresponding Kirchhoff’s plate solutions. Archive of Applied Mechanics 65(6): 408–414. https://doi.org/10.1007/BF00787534

[11] Kormenikova E, Manuzic I. (2011). Shear deformation laminabe theory used for sandwiches. Metabk 50(3): 193–196.

[12] Boen Dar L. (1968). Theory of bending of multilayer sandwich plates. PhD Thesis. Faculty of the Graduate School Oklahoma State University. August.