scholarly journals A Discrete Approach to the Chaotic Representation Property

2001 ◽  
pp. 123-138 ◽  
Author(s):  
M. Émery
Keyword(s):  
Discrete Approach

scholarly journals Quantifying time-varying sources in magnetoencephalography—A discrete approach

2020 ◽  
Vol 14 (3) ◽  
pp. 1379-1408
Author(s):  
Zhigang Yao ◽  
Zengyan Fan ◽  
Masahito Hayashi ◽  
William F. Eddy
Keyword(s):  
Time Varying ◽  
Discrete Approach

scholarly journals Gradation trajectories as an analog of gradation curves in the metric CIE Lab space: discrete approach

2019 ◽  
Vol 43 (1) ◽  
pp. 132-136 ◽  
Author(s):  
D.A. Tarasov ◽  
◽  
O.B. Milder ◽  
Keyword(s):  
Discrete Approach ◽  
Cie Lab

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

2018 ◽  
Vol 423 ◽  
pp. 421-441
Author(s):  
Nirmal Ramachandran ◽  
Ranjan Ganguli
Keyword(s):  
Discrete Approach

Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

2022 ◽  
pp. 108128652110679
Author(s):  
Emilio Turco
Keyword(s):  
Kinetic Energy ◽  
Strain Energy ◽  
Nonlinear Vibrations ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Beam Model ◽  
Model Formulation ◽  
Discrete Approach ◽  
Numerical Integration Scheme ◽  
Proposed Model

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

A Semi-Discrete Approach for the Numerical Simulation of Freestanding Blocks

2016 ◽  
pp. 416-439
Author(s):  
Fernando Peña
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Numerical Modeling ◽  
Discrete Model ◽  
Mathematical Formulation ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Discrete Approach ◽  
Rocking Motion

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

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