New hybrid approach for free vibration and stability analyses of axially functionally graded Euler-Bernoulli beams with variable cross-section resting on uniform Winkler-Pasternak foundation

Abstract

In this paper, a new hybrid approach is presented based on the combination of the power series expansions and the Rayleigh-Ritz method for stability and free vibration analyses of axially functionally graded non-uniform beams resting on constant Winkler-Pasternak elastic foundation. In the proposed novel technique, the power series approximation is first adopted to solve the motion equation. Regarding this numerical methodology, the transverse displacement and all mechanical properties are expanded in terms of power series of a known degree. By solving the eigenvalue problem, one can acquire the fundamental natural frequencies. According to aforementioned method, the expression of vibrational mode shape is also determined. Based on the similarities existing between the vibrational and buckling deformation shapes, Rayleigh-Ritz method is finally employed to construct eigenvalue problem for obtaining the critical loads. In order to illustrate the correctness and convergence of the method, several numerical examples of axially non-homogeneous and homogeneous beams are conducted. The obtained outcomes are compared to the results of Finite Element Analysis in terms of ANSYS software and those of other available numerical and analytical solutions. The accuracy of the method is then remarked.

Vibration Characteristics of Nonuniform Blades Made of Functionally Graded Material

“…The results are compared with the ones given by Ref. [21]. Effect of the power law index parameter, α on the Modulus of Elasticity, E, of the beam is demonstrated in Figure 9.…”

Variable-Section Functional Gradient Beams on Pasternak Foundations: An Enhanced Interaction Theory for Construction Applications

“…Owing to its strength, stiffness, and lightweight nature, it finds widespread use in aerospace, automotive, marine, and defense engineering fields [2]. Functional gradient beams (FGBs), as the most fundamental structural element in aerospace, mechanical, and civil engineering, address the issue of delamination and stress concentration inherent in composite materials [4]. Various scholars use methods such as the differential quantization method (DQM) and generalized differential quantization method (GDQM) to investigate FGBs along different gradient directions.…”

“…Rajasekaran and Khaniki examined the vibration characteristics of nanobeams with bidirectional functional gradient variable sections on elastic foundations, utilizing the explicit and implicit finite element methods and the Wilsontheta method [20]. Hareram et al investigated the impact of different material grading parameters on the mechanical properties of axial FGBs on elastic foundations using the differential product method [9] (Soltani and Asgarian, 2019). By employing the differential transformation method, Shahba and Rajasekaran introduced the differential transformation element method to solve the displacement curve of a tapered beam with variable-section axia l functional gradient, significantly enhancing calculation convergence speed [15].…”

Transverse free vibration of Euler-Bernoulli beam with pre-axial pressure resting on a variable Pasternak elastic foundation under arbitrary boundary conditions

“…The model of beams resting on elastic foundation have a wide range of applications in civil engineering, such as underground pipelines, rails, strip foundations, pile foundations, etc. [1][2][3][4][5] Winkler elastic foundation is treated as a single-parameter model and commonly used by engineers and researchers, but this model ignores the shearing interaction between soil elements. Previous studies have shown that [6,7], the assumption always results in a huge deviation.…”