Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Wu, Jian-Qiang; Chen, Lunting; Wu, Ruixian; Chen, Xiaochao

doi:10.1155/2021/6675125

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…Furthermore, nine diverse porosities were considered to study the functional gradient effect on the compressive strength of the structures both experimentally and numerically. The nonlinear forced vibration of bidirectional functionally graded porous material beams was researched by Wu et al, 16 the gradient of which changes in both thickness and axial directions. Results showed that the cyclic-fold bifurcation may occur once the beam is periodically motivated.…”

Section: Functional Gradient Structurementioning

confidence: 99%

Optimal design of a novel crash box with functional gradient negative Poisson’s ratio structure

Guan

Yan

Wang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part D:

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Crashworthiness and anti-vibration performance play critical roles in the performance of passenger cars. Aiming at enhancing the crash resistance and vibration resistance of vehicles thus providing good protection for passengers and drivers, a novel crash box with three-dimensional double arrow type negative Poisson’s ratio structure with functional gradient filling inner core (FGNPR crash box) is introduced in this paper and its performance is studied in detail through the comparison with the conventional crash box and the crash box filled with the uniform gradient negative Poisson’s ratio structure (NPR crash box) in crashworthiness and vibration resistance. Furthermore, range analysis is used to screen out the design variables that have little influence on the evaluation indexes and eliminate them. Based on these, neighborhood cultivation genetic algorithm (NCGA) and non-dominated sorting genetic algorithm-ii (NSGA-II) are selected as the optimization algorithms to carry out optimization design respectively and a comparison is made between the two suboptimal results screened out based on the normal boundary intersection (NBI) method to determine the overall optimal solution. Results show that the optimized FGNPR crash box has better crashworthiness and vibration resistance over the other crash boxes and its performance is further verified based on the peak acceleration of B-pillar in full vehicle crash condition. This paper provides some theoretical reference support for the development and exploration of automobile crash box systems.

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Section: Functional Gradient Structurementioning

confidence: 99%

Optimal design of a novel crash box with functional gradient negative Poisson’s ratio structure

Guan

Yan

Wang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part D:

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show abstract

“…Based on the neutral surface concept, nonlinear governing equations have simple forms which can be directly solved. Wu et al [11] investigated the nonlinear forced vibration of bidirectional FG porous material beams where the gradient of the material components changed in terms of both their thickness and axial direction. Vibration response curves and bifurcation diagrams were obtained using the pseudo-arclength technique, and it was found that the periodic motion of the beam may undergo cyclic fold bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Herişanu

Marinca

2023

Symmetry

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This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton’s principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function.

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“…To the best of the authors’ knowledge, only a few studies have investigated the nonlinear vibrations of porous structures made of BDFG materials. Recent works (Chen et al, 2021; Wu et al, 2021) focused on the nonlinear behavior of BDFG porous beams with different types of materials and porosity patterns. In these works, the equations of motion are formulated based on Timoshenko beam considering von Karman’s geometric nonlinearity and first-order deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Sari

Al‐Dahidi

Hammad

2022

Journal of Vibration and Control

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In this study, the free and forced vibrations of a bi-directional functionally graded porous beam are investigated. The governing equations of motion are derived by Hamilton’s principle, and the reduced temporal equation of motion with cubic and quintic nonlinear terms is obtained using the Galerkin approach. Analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves are established by the method of multiple scales. The effects of the axial and transverse functionally graded indexes, initial amplitude, porosity parameter, and the elastic and mass density ratios on the nonlinear frequencies and the forced responses are examined.

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Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Cited by 7 publications

References 31 publications

Optimal design of a novel crash box with functional gradient negative Poisson’s ratio structure

Optimal design of a novel crash box with functional gradient negative Poisson’s ratio structure

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

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