Investigation of Multi Linear Regression Methods on Estimation of Free Vibration Analysis of Laminated Composite Shallow Shells

This paper presents regression method's in estimating the free vibration analysis and compared with SDSST method. In this study, the free vibration analysis of the cross-ply laminated composite cylindrical shallow shells has been studied using shear deformation shallow shell theory (SDSST). First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution [1]. The results obtained by this solution are compared with the results obtained by (ANSYS) programs. In this article, regression method's and SDSST method's abilities in estimating the free vibration with the laminate number, aspect ratio, thickness ratio, curvature ratio and orthotropic ratio variables, are compared with different and similar aspects. In comparing with linear, interaction, quadratic and pure quadratic models, which are constructed with multiple linear regression approach, the quadratic model provides better results.