Dynamic analysis of viscoelastic functionally graded porous beams using an improved Bernstein polynomials algorithm

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2024-11-02 DOI:10.1016/j.chaos.2024.115698
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Abstract

Functionally graded porous (FGP) materials have significant application potential because they can achieve many specific applications by controlling porosity and material composition. However, most current research has little emphasis on the vibration characteristics of FGP materials with viscoelastic properties. To address this issue, this article presents an improved Bernstein polynomials algorithm to establish the governing equation for analyzing the vibration response of fractional-order viscoelastic FGP beams. This method effectively resolves instability problems associated with boundary conditions. Single step Adams scheme and Newmark-β method are then utilized to solve the governing equation of the viscoelastic FGP beams. The accuracy of the proposed method is confirmed through comparison with the results obtained from the finite element method. A parametric investigation is conducted to explore the impact of porosity and its distribution pattern, power law index, boundary condition, fractional order, and viscoelasticity coefficient on the vibration characteristics of the viscoelastic FGP beams. These findings suggest that desirable dynamic properties for FGP beams can be achieved through tailoring their material gradient and porosity distribution.
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使用改进伯恩斯坦多项式算法对粘弹性功能分级多孔梁进行动态分析
功能分级多孔(FGP)材料具有巨大的应用潜力,因为它们可以通过控制孔隙率和材料成分实现许多特定应用。然而,目前大多数研究很少关注具有粘弹特性的 FGP 材料的振动特性。针对这一问题,本文提出了一种改进的伯恩斯坦多项式算法,用于建立分析分数阶粘弹性 FGP 梁振动响应的控制方程。该方法可有效解决与边界条件相关的不稳定性问题。然后利用单步 Adams 方案和 Newmark-β 方法求解粘弹性 FGP 梁的控制方程。通过与有限元法得出的结果进行比较,证实了所提方法的准确性。通过参数化研究,探讨了孔隙率及其分布模式、幂律指数、边界条件、分数阶数和粘弹性系数对粘弹性 FGP 梁振动特性的影响。这些研究结果表明,通过调整 FGP 梁的材料梯度和孔隙率分布,可以获得理想的动态特性。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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