Amplitude Modulation and Symmetry Breaking Bifurcation in Micro Devices

2012 ◽  
Author(s):  
Z. C. Feng ◽  
Mahmoud Almasri
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Amplitude Modulation ◽  
Dynamic Responses ◽  
Symmetric Structure ◽  
Different Types ◽  
Asymmetric Responses ◽  
Symmetric Response ◽  
Symmetry Breaking Bifurcation

Designs of many micro devices take advantage of the symmetry for better performance, immunity to noise, and for simpler analysis. When a symmetric structure is subjected to symmetric forcing, the symmetric response can become unstable leading to asymmetric responses. The occurrence of symmetry breaking bifurcation leads to complicated dynamic responses which often result in less desirable performances. In this paper, we obtain analytical criteria for the onset of symmetry breaking bifurcations. We also conduct numerical simulations to demonstrate different types of asymmetric dynamic responses resulting from the symmetry breaking bifurcation. In particular, we show the occurrence of amplitude modulated motions in such systems.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

GROUP THEORETICAL MODE INTERACTIONS WITH DIFFERENT SYMMETRIES

1994 ◽  
Vol 04 (01) ◽  
pp. 177-191 ◽  
Author(s):  
KARIN GATERMANN ◽  
BODO WERNER
Keyword(s):  
Group Theory ◽  
Symmetry Breaking ◽  
Irreducible Representations ◽  
Bifurcation Points ◽  
Mode Interactions ◽  
Different Types ◽  
Secondary Bifurcation ◽  
Two Parameter ◽  
Symmetry Breaking Bifurcation

In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the inner-connectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.

Scale-dependent merging of baroclinic vortices

1994 ◽  
Vol 264 ◽  
pp. 81-106 ◽  
Author(s):  
J. Verron ◽  
S. Valcke
Keyword(s):  
Numerical Simulations ◽  
Critical Point ◽  
Lower Layer ◽  
Interaction Mechanism ◽  
Competitive Effects ◽  
Different Types ◽  
Shape Effects ◽  
Baroclinic Vortices ◽  
The Relationship ◽  
Stratified Model

The influence of stratification on the merging of like-sign vortices of equal intensity and shape is investigated by numerical simulations in a quasi-geostrophic, two-layer stratified model. Two different types of vortices are considered: vortices defined as circular patches of uniform potential vorticity in the upper layer but no PV anomaly in the lower layer (referred to as PVI vortices), and vortices defined as circular patches of uniform relative vorticity in the upper layer but no motion in the lower layer (referred to as RVI vortices). In particular, it is found that, in the RVI case, the merging behaviour depends strongly on the magnitude of the stratification (i.e. the ratio of internal Rossby radius and vortex radius). The critical point here appears to be whether or not the initial eddies have a deep flow signature in terms of PV.The specific phenomenon of scale-dependent merging observed is interpreted in terms of the competitive effects of hetonic interaction and vortex shape. In the case of weaker stratification, the baroclinic structure of the eddies can be seen as dominated by a mechanism of hetonic interaction in which bottom flow appears to counteract the tendency of surface eddies to merge. In the case of larger stratification, the eddy interaction mechanism is shown to be barotropically dominated, although interface deformation still determines the actual eddy vorticity profile during the initialization stage. Repulsion (hetonic) effect therefore oppose attraction (barotropic shape) effects in a competitive process dependent on the relationship between the original eddy lengthscale and the first internal Rossby radius.A concluding discussion considers the implications of such analysis for real situations, in the ocean or in the laboratory.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

The Response of Nonlinear Systems to Modulated High-Frequency Input

1993 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Systems ◽  
Natural Frequency ◽  
Amplitude Modulation ◽  
Carrier Frequency ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Resonant Excitation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

scholarly journals Novel thick brane solutions with U(1) symmetry breaking

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Marzieh Peyravi ◽  
Nematollah Riazi ◽  
Francisco S. N. Lobo
Keyword(s):  
Symmetry Breaking ◽  
Scalar Fields ◽  
Einstein Tensor ◽  
Vacuum Structure ◽  
Different Types ◽  
Dimensional Gravity ◽  
Breaking Parameter ◽  
Symmetry Breaking Term ◽  
The Stability ◽  
Breaking Term

AbstractIn this work, using two scalar fields ($$\phi $$ ϕ , $$\psi $$ ψ ) coupled to 4 + 1 dimensional gravity, we construct novel topological brane solutions through an explicit U(1) symmetry breaking term. The potential of this model is constructed so that two distinct degenerate vacua in the $$\phi $$ ϕ field exist, in analogy to the $$\phi ^{4}$$ ϕ 4 potential. Therefore, brane solutions appear due to the vacuum structure of the $$\phi $$ ϕ field. However, the topology and vacuum structure in the $$\psi $$ ψ direction depends on the symmetry breaking parameter $$\beta ^{2}$$ β 2 , which leads to different types of branes. As a result, one can interpret the present model as a combination of a $$\phi ^{4}$$ ϕ 4 brane with an auxiliary field, which leads to deviations from the $$\phi ^{4}$$ ϕ 4 system with the brane achieving a richer internal structure. Furthermore, we analyse in detail the behaviour of the superpotentials, the warp factors, the Ricci and Kretschmann scalars and the Einstein tensor components. In addition to this, we explore the stability of the brane in terms of the free parameters of the model. The analysis presented here complements previous work and is sufficiently novel to be interesting.

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