Dynamic analysis and non-standard continualization of a Timoshenko beam lattice

Gómez-Silva, F.; Zaera, R.

doi:10.1016/j.ijmecsci.2021.106873

Cited by 13 publications

(6 citation statements)

References 62 publications

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“…In this section, the continualization method proposed by Polyzos and Fotiadis [34] for axial lattice systems is applied for the first time to a square lattice system like the one presented in this work. This continualization technique has also been applied by Gómez-Silva and Zaera to Euler-Bernoulli [41,42] and Timoshenko [46] beam lattices, and consists in expanding the displacement variables in the energy density expressions of the lattice system. For this purpose, the cell shown in Fig.…”

Section: Standard II Modelmentioning

confidence: 99%

See 1 more Smart Citation

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Gómez-Silva

Zaera²

2022

Thin-Walled Structures

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Section: Standard II Modelmentioning

confidence: 99%

“…A modified semi-continuum Euler beam model with relaxation phenomenon is developed by Shen and Li in [43], where they present the bending deformation of a extreme-thin beam with micro/nano-scale thickness. Shear deformations have been also included in [44][45][46] in order to achieve non-classical Timoshenko beam models.…”

Section: Introductionmentioning

confidence: 99%

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Gómez-Silva

Zaera²

2022

Thin-Walled Structures

Self Cite

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“…Among the homogenization schemes, we find asymptotic methods [26][27][28][29][30][31][32]; asymptotic variational methods [33][34][35]; and computational methods [36][37][38][39][40][41]. Among the continualization methods, we include the so-called standard methods [42][43][44][45][46][47][48][49], the standard energy-based methods [44,46,[50][51][52][53], the improved and enhanced methods [47,48,[54][55][56][57][58][59][60] and also the improved energy-based methods [61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Dynamic continualization of mechanical metamaterials with quasi-periodic microstructure

Del Toro,

De Bellis,

Bacigalupo

2024

Phil. Trans. R. Soc. A.

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This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet–Bloch theory to validate the proposed scheme. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1).’

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“…Other researchers [24] to [27] proposed a Timoshenko beam consisting of a chain of masses and straight segments, accounting for the bending and shear deformations of the linear rotational and transverse springs. Zhan et al [28] and Si et al [29] studied the free vibrations of axially-loaded multicracked Timoshenko beams with different boundary conditions, such as hinged, cramped, clamped-hinged, and cramped-free.…”

Section: Introductionmentioning

confidence: 99%

“…Comparison between vibration response test and theoretical results of ring die pelletizer system; a) test results, and b) theoretical resultsStrojniški vestnik -Journal of Mechanical Engineering 69(2023)[1][2][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] …”

mentioning

confidence: 99%

Analysis of the Dynamic Characteristics of a Gear-Rotor-Bearing System with External Excitation

Na¹,

Jia²,

Miao³

et al. 2023

sv-jme

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The dynamic response of the rotor system in a ring die granulator is complex and difficult to solve when it operates under joint external, support and gear mesh forces. To solve this problem, a finite element method and extrusion theory was applied in this study to develop a dynamic coupling model for a hollow overhung rotor with external load excitation. A Newmark-β numerical integration method was used to solve for the dynamic response of the overhung rotor under multiple excitation forces. The results included time-domain response diagrams, frequency-domain response diagrams, phase diagrams, Poincaré section diagrams, and bifurcation diagrams. The model and the method were verified by testing a ring die granulator. On this basis, the dynamic response of the system is predicted according to the influence of different parameters. As the bearing support distance increased, the roller eccentricity decreased, the bearing clearance decreased, the response of the rotor system was significantly optimized, and the system tended to stabilize gradually. Therefore, this paper provides a theoretical basis and experimental verification for the optimization of a pelleting machine transmission structure.

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Dynamic analysis and non-standard continualization of a Timoshenko beam lattice

Cited by 13 publications

References 62 publications

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Dynamic continualization of mechanical metamaterials with quasi-periodic microstructure

Analysis of the Dynamic Characteristics of a Gear-Rotor-Bearing System with External Excitation

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