A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed

Zhang, Y. F.; Liu, J. T.

doi:10.1038/s41598-018-37921-9

Cited by 3 publications

(2 citation statements)

References 46 publications

(34 reference statements)

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“…If the frequency of the object subjected to the external force is consistent with the natural frequency of the object, the amplitude of the displacement will become more intense. This phenomenon is called resonance [ 13 ]. For determination of the natural frequency of an object, let P (external force) = 0 in formula ( 1 ); then, the motion equation (formula ( 1 )) becomes the following: Assuming that the motion system has no damping, I = Ku , where K is the stiffness and u is the displacement.…”

Section: Methodsmentioning

confidence: 99%

Finite element analysis of the Union Plate in treating elderly acetabular fracture patients

et al. 2022

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Background Elderly acetabular fractures are one of the more difficult types of fractures to resolve. For patients at this age, the more common type of fracture is comminuted. How to better fix this type of fracture has always been an issue of concern. This study was performed to observe the mechanical properties of different internal fixation methods used in treating elderly acetabular fracture patients. Methods A model of a comminuted acetabular fracture in osteoporosis was established, consisting of an anterior column–posterior hemitransverse fracture with disruption of the quadrilateral surface. Fixation of the acetabular fracture model using a reconstruction plate and Union Plates was simulated. For the different internal fixation methods, static and transient modal analyses were performed under different loads, with an action time of 0.21 s and an analysis time of 0.7 s. The stress of the model was observed in the static analysis, and the displacement of the nodes and the entire model in the U1 direction was observed in the transient modal analysis. Results In the static analysis, the stress of the osteoporosis model, the suprapectineal pelvic reconstruction plate model, the infrapectineal quadrilateral surface buttress plate model, and the suprapectineal quadrilateral surface buttress plate model were 42.62 MPa, 37.49 MPa, 44.39 MPa, and 46.15 MPa, respectively. The stress was mainly distributed near the suprapubic branch. The corresponding displacement in the U1 direction was 0.1500 mm, 0.1020 mm, 0.0836 mm, and 0.0990 mm, respectively. In the transient modal analysis, there was a significant difference in displacement between the different models (P < 0.05). When different loads were applied with the same fixation method, there was no significant difference in model displacement (P > 0.05). Conclusion Static and transient modal analyses show that the infrapectineal quadrilateral surface buttress plate or the suprapectineal quadrilateral surface buttress plate has an advantage in maintaining the stability of fracture fragments when fixing comminuted acetabular fractures in elderly individuals. The infrapectineal quadrilateral surface buttress plate also presents better biomechanical results.

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Section: Methodsmentioning

confidence: 99%

Finite element analysis of the Union Plate in treating elderly acetabular fracture patients

et al. 2022

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“…For example, Shi et al 22 investigated carbon-nanotube-reinforced composite beams where different nanotube distributions were assumed including functionally graded distributions through the thickness of the beams. Other base models with functionally graded material distribution are also considered in recent literature, such as the work of Zhang and Liu 23 who investigated moving rectangular plates and the work of Ghamkhar et al 24 that discusses a three-layered cylinder shaped shell in which the central layer consists of functionally graded material. The static and dynamic characteristics of functionally graded materials are favorable in many scientific and engineering fields, such as aerospace, automobile, electronics, optics, chemistry, biomedical engineering, nuclear engineering and mechanical engineering 25 – 29 .…”

Section: Introductionmentioning

confidence: 99%

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Lelkes,

Bak,

Kalmár-Nagy

2024

Sci Rep

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Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted.

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1:1 internal resonance in a two d.o.f. complete system: a comprehensive analysis and its possible exploitation for design

2020

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A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed

Cited by 3 publications

References 46 publications

Finite element analysis of the Union Plate in treating elderly acetabular fracture patients

Finite element analysis of the Union Plate in treating elderly acetabular fracture patients

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

1:1 internal resonance in a two d.o.f. complete system: a comprehensive analysis and its possible exploitation for design

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