Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

Mapping Intimacies ◽

10.21741/9781644901755-65 ◽

2022 ◽

Author(s):

D.A. Kolesov

Keyword(s):

Mathematical Models ◽

Elastic Element ◽

Dynamic Processes ◽

Dimensional Chain ◽

Series Connection ◽

One Dimensional ◽

Nonlinear Mathematical Models ◽

Viscous Element ◽

Nonlinearly Elastic ◽

Elastic Elements

Abstract. To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

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PIPELINE ROBOTS WITH ELASTIC ELEMENTS

Transport ◽

10.3846/16483840.2002.10414039 ◽

2002 ◽

Vol 17 (5) ◽

pp. 177-181 ◽

Cited By ~ 2

Author(s):

Arvydas Matuliauskas ◽

Bronislovas Spruogis

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Degrees Of Freedom ◽

Vibration Exciter ◽

Motion Equations ◽

Two Degrees Of Freedom ◽

One Dimensional ◽

The Mathematical Model ◽

Original Construction ◽

Elastic Elements

In the article constructions of the pipeline robots with elastic elements are reviewed and the scheme of new original construction is presented. The mathematical models of a robot with one-dimensional vibration exciter with two degrees of freedom were developed and the equations of movement were formed and written. The mathematical model of the pipeline robot with circular elements is formed and its motion equations are presented.

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A new one-dimensional chain polymer based on [Zn2(OCO)2] rhomboid clusters

Журнал структурной химии ◽

10.26902/jsc_id39231 ◽

2019 ◽

Vol 60 (2) ◽

Keyword(s):

Dimensional Chain ◽

Chain Polymer ◽

One Dimensional

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Methodology for Increasing the Efficiency of Dynamic Process Calculations in Elastic Elements of Complex Engineering Constructions

Electronics ◽

10.3390/electronics10010040 ◽

2020 ◽

Vol 10 (1) ◽

pp. 40

Author(s):

Andriy Andrukhiv ◽

Maria Sokil ◽

Solomiia Fedushko ◽

Yuriy Syerov ◽

Yaryna Kalambet ◽

...

Keyword(s):

Dynamic Process ◽

Granular Media ◽

Homogeneous Medium ◽

Dynamic Processes ◽

Analytical Relationship ◽

Operational Parameters ◽

Protective Capacity ◽

Vibration Displacement ◽

Complex Engineering ◽

Elastic Elements

This study deals with a methodology for increasing the efficiency of dynamic process calculations in elastic elements of complex engineering constructions. We studied the complex dynamic processes in a simple engineering construction, a mechanical system of an elastic body–continuous flow of homogeneous medium. The developed methodology is based on the use of a priori information on some of the vibrations forms, the construction of a “simplified” mathematical model of system dynamics, and the obtaining of an analytical relationship that describe the overall range of factors on the elastic vibrations of system. The methodology is used for cases of complex vibrations of elastic bodies, and the obtained results can serve as a basis for choosing the main technological and operational parameters of elastic elements of mechanisms and machines that perform complex vibrations. The results obtained in this work are the basis for calculating the blast effect on the elements of protective structures in order to increase their protective capacity by improving the method of their attachment or by using additional reinforcement, buff load effects on the elements of drilling strings and dynamic processes that occur during surface strengthening by work hardening in order to avoid resonance phenomena, and technological processes of vibration displacement or vibration separation of granular media.

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A new one-dimensional CdIIcoordination polymer with a two-dimensional layered structure incorporating 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole and benzene-1,2-dicarboxylate ligands

Acta Crystallographica Section C Structural Chemistry ◽

10.1107/s2053229616007658 ◽

2016 ◽

Vol 72 (6) ◽

pp. 480-484 ◽

Cited By ~ 2

Author(s):

Qiu-Ying Huang ◽

Xiao-Yi Lin ◽

Xiang-Ru Meng

Keyword(s):

Layered Structure ◽

Room Temperature ◽

Weak Interactions ◽

Coordination Geometry ◽

Dimensional Chain ◽

Two Dimensional ◽

One Dimensional ◽

Heterocyclic Ligand ◽

Rich Variety ◽

Solvent Molecules

The N-heterocyclic ligand 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole (imb) has a rich variety of coordination modes and can lead to polymers with intriguing structures and interesting properties. In the coordination polymercatena-poly[[cadmium(II)-bis[μ-benzene-1,2-dicarboxylato-κ4O1,O1′:O2,O2′]-cadmium(II)-bis{μ-2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole}-κ2N2:N3;κ2N3:N2] dimethylformamide disolvate], {[Cd(C8H4O4)(C11H10N4)]·C3H7NO}n, (I), each CdIIion exhibits an irregular octahedral CdO4N2coordination geometry and is coordinated by four O atoms from two symmetry-related benzene-1,2-dicarboxylate (1,2-bdic2−) ligands and two N atoms from two symmetry-related imb ligands. Two CdIIions are connected by two benzene-1,2-dicarboxylate ligands to generate a binuclear [Cd2(1,2-bdic)2] unit. The binuclear units are further connected into a one-dimensional chain by pairs of bridging imb ligands. These one-dimensional chains are further connected through N—H...O hydrogen bonds and π–π interactions, leading to a two-dimensional layered structure. The dimethylformamide solvent molecules are organized in dimeric pairsviaweak interactions. In addition, the title polymer exhibits good fluorescence properties in the solid state at room temperature.

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The magneto-elastica : from self-buckling to self-assembly

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2013.0609 ◽

2014 ◽

Vol 470 (2162) ◽

pp. 20130609 ◽

Cited By ~ 30

Author(s):

Dominic Vella ◽

Emmanuel du Pontavice ◽

Cameron L. Hall ◽

Alain Goriely

Keyword(s):

Self Assembly ◽

Permanent Magnets ◽

Energy Estimates ◽

Dimensional Chain ◽

Elastic Rod ◽

Straight Chain ◽

One Dimensional ◽

Vibration Dynamics ◽

Magnetic Strength ◽

A Chain

Spherical neodymium–iron–boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.

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Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

Acta Crystallographica Section C Crystal Structure Communications ◽

10.1107/s0108270111055454 ◽

2012 ◽

Vol 68 (2) ◽

pp. m34-m36 ◽

Cited By ~ 1

Author(s):

Dong Liu

Keyword(s):

Title Complex ◽

Point Of View ◽

Solvothermal Reaction ◽

Dimensional Chain ◽

Two Dimensional ◽

One Dimensional ◽

Connected Network ◽

Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

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