Application of Overlapping Finite Element for Free and Forced Vibration Analysis of 2D Linear Elastic Solids

Jiang, Zhilong; Li, Wei; Chai, Yingbin; Gui, Qiang

doi:10.1007/s42417-023-01098-x

Cited by 4 publications

(1 citation statement)

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“…Ladmek et al [181] performed an analytical solution to explore the FV performance of a novel FG-CNTRC NB with Winkler foundation (WF) created of NSGT and two variable HSDT. Furthermore, Jiang et al [182] explored the FV as well as the forced vibration behaviors of several 2D linear elastic structures, such as beams, by developing an overlapping FEM. Nonetheless, Mehrparvar et al [183] implemented the high order (HO) Haar wavelet methodology to examine the FV analysis of the Timoshenko beam.…”

Section: Beam Structurementioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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Section: Beam Structurementioning

confidence: 99%