Stability and free vibration analysis of tapered sandwich columns with functionally graded core and flexible connections

• Published in: CEAS aeronautical journal Vol. 9; no. 4; pp. 629 - 648
• Main Authors: Rezaiee-Pajand, M., Mokhtari, M., Masoodi, Amir R.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.12.2018; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Beam theory (structures); Boundary conditions; Buckling; Differential equations; Engineering; Euler-Bernoulli beams; Exponential functions; Flexible connections; Free vibration; Functionally gradient materials; Least squares method; Mathematical analysis; Original Paper; Polynomials; Resonant frequencies; Ritz method; Stability analysis; Vibration analysis; Stability; Legendre polynomials; Natural frequencies; Tapered sandwich column; Functionally graded material
• ISSN: 1869-5582; 1869-5590
• DOI: 10.1007/s13272-018-0311-6

In this study, the buckling and free vibration behavior of tapered functionally graded material (FGM) sandwich columns is explored. The connections are considered to be semi-rigid. The core material is functionally graded along the beam depth according to the simple power law form. Euler–Bernoulli beam theory and the Ritz method will be employed to derive the governing equations. Legendre polynomials are chosen as auxiliary functions. After reducing the order of Euler’s buckling equation, an Emden–Fowler differential equation will be obtained. To reach a closed-form solution, the flexural rigidity of the column will be approximated with an exponential function by enforcing least-squares method. Non-dimensional natural frequencies and critical buckling loads will be presented for various cross-sectional types. The effects of FGM power, taper ratio, and spring rigidities on the critical buckling loads, and natural frequencies will be also investigated. Numerical results for various boundary conditions and configurations reveal the high accuracy of authors’ scheme.