Transition mechanism for a periodic bar-and-joint framework with limited degrees of freedom controlled by uniaxial load and internal stiffness

A specific periodic bar-and-joint framework with limited degrees of freedom is shown to have a transition mechanism when subjected to an external force. The static nonlinear elasticity of this framework under a uniaxial load is modelled with the two angular variables specifying the rotation and distortion of the linked square components. Numerically exploring the equilibrium paths then reveals a transition state of the structure at a critical value of the internal stiffness. A simplified formulation of the model with weak nonlinear terms yields an exact solution of its transition state. Load–displacement behaviour and stability for the two systems with or without approximation are analysed and compared.

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Localized Modes in Periodic Systems With Nonlinear Disorders

Journal of Applied Mechanics ◽

10.1115/1.2789003 ◽

1997 ◽

Vol 64 (4) ◽

pp. 940-945 ◽

Cited By ~ 10

Author(s):

C. W. Cai ◽

H. C. Chan ◽

Y. K. Cheung

Keyword(s):

Degrees Of Freedom ◽

Maximum Amplitude ◽

Critical Value ◽

Periodic Systems ◽

Algebraic Equations ◽

Localized Modes ◽

Transformation Technique ◽

Nonlinear Algebraic Equations ◽

Coupling Stiffness ◽

Localized Mode

The localized modes of periodic systems with infinite degrees-of-freedom and having one or two nonlinear disorders are examined by using the Lindstedt-Poincare (L-P) method. The set of nonlinear algebraic equations with infinite number of variables is derived and solved exactly by the U-transformation technique. It is shown that the localized modes exist for any amount of the ratio between the linear coupling stiffness kc and the coefficient γ of the nonlinear disordered term, and the nonsymmetric localized mode in the periodic system with two nonlinear disorders occurs as the ratio kc/γ, decreasing to a critical value depending on the maximum amplitude.

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DIGITAL ORIGIN OF COSMIC INFLATION

Modern Physics Letters A ◽

10.1142/s0217732310033219 ◽

2010 ◽

Vol 25 (18) ◽

pp. 1483-1489

Author(s):

CHUNG-HSIEN CHOU ◽

HOI-LAI YU

Keyword(s):

Degrees Of Freedom ◽

Dynamical Evolution ◽

Critical Value ◽

Cosmic Inflation ◽

The Past ◽

Physical Universe ◽

Communication Time ◽

Hubble Radius ◽

Time Required ◽

The Universe

Assuming our physical universe processes and registers information to determine its dynamical evolution, one can put serious constraints on the cosmology that our universe can bear, in particular, the origin of cosmic inflation. The universe evolves to gain her computation capacity which is linear in time t. On the other hand, the growth in content of degrees of freedom (i.e. by integrating in more galaxies) is as t3/2 through expansion. When the in flux of degrees of freedom of the universe grows beyond some value, the computation capacity of the universe becomes insufficient to determine its evolution, the universe fixes its Hubble radius and inflates away its degrees of freedom within its horizon to regain dynamical evolution. The length of inflation is determined by the communication time required by the universe to become aware of the dropping in the degrees of freedom below some critical value by inflation and is proportional to its Hubble radius. We predict that there can be multiple cosmic inflations. The next inflation era will stop after inflating for a period of 1019 sec if the past inflation period of our universe was 10-33 sec.

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Piecewise Exact Solution for a Bridge With Sliding Type Isolators Under Earthquakes

Volume 8: Seismic Engineering ◽

10.1115/pvp2007-26194 ◽

2007 ◽

Author(s):

C. S. Tsai ◽

Wen-Shin Chen ◽

T. C. Chiang ◽

B. J. Chen ◽

Kuei-Chi Chen

Keyword(s):

Exact Solution ◽

Computer Program ◽

Structural Control ◽

Degrees Of Freedom ◽

Large Degree ◽

System Response ◽

Analysis Process ◽

Nonlinear Stress ◽

Nonlinear Devices ◽

Isolated Bridge

In recent years, the earthquake proof technology has been applied to seismic mitigation of structures including buildings, bridges, etc. The bridge system possesses large degree of freedoms, and nonlinear characteristics when structural control devices are involved. Therefore, the analysis for a bridge with nonlinear devices will be time consuming. In this study, a piecewise exact solution for a bridge isolated with sliding type isolators has been derived to simplify the analysis process. In this study, the system is modeled as two degrees of freedom to reasonably represent a large number of degrees of freedom of a bridge with sliding type isolators for obtaining a piecewise exact solution for the system response during earthquakes. In the meantime, the NSAT (Nonlinear Stress Analysis Techniques) computer program has also been used to analyze the response of the bridge with sliding type isolators. By comparing the results from the piecewise exact solution and the NSAT computer program, it can be found that the piecewise exact solution not only simplifies the calculation process, but also obtains the seismic responses of the isolated bridge with good accuracy under earthquakes.

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On drilling degrees of freedom in nonlinear elasticity and a hyperelastic material description in terms of the stretch tensor. Part 2: Application to membranes

Acta Mechanica ◽

10.1007/bf01187432 ◽

1996 ◽

Vol 115 (1-4) ◽

pp. 103-117 ◽

Cited By ~ 7

Author(s):

C. Sansour ◽

H. Bufler ◽

H. M�llersch�n

Keyword(s):

Nonlinear Elasticity ◽

Degrees Of Freedom ◽

Hyperelastic Material ◽

Stretch Tensor ◽

Drilling Degrees Of Freedom ◽

Tensor Part

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TWO MODELS OF NONSMOOTH DYNAMICAL SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411030180 ◽

2011 ◽

Vol 21 (10) ◽

pp. 2853-2860 ◽

Cited By ~ 4

Author(s):

MADELEINE PASCAL

Keyword(s):

Dry Friction ◽

Coupled Oscillators ◽

Degrees Of Freedom ◽

Analytical Form ◽

Critical Value ◽

Form Solution ◽

Nonsmooth Systems ◽

The Stability ◽

Close Form ◽

Nonsmooth Dynamical Systems

Two examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling.

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Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Journal of Mechanical Design ◽

10.1115/1.4046072 ◽

2020 ◽

Vol 142 (9) ◽

Cited By ~ 1

Author(s):

Nathan A. Pehrson ◽

Pietro Bilancia ◽

Spencer Magleby ◽

Larry Howell

Keyword(s):

Degrees Of Freedom ◽

Design Space ◽

Element Analysis ◽

Array Design ◽

Elastic Load ◽

In Series ◽

Load Displacement ◽

Stiffness Characteristics ◽

Tunable Stiffness ◽

Three Degrees Of Freedom

Abstract Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load–displacement for general serial–parallel formulations of LET arrays for three degrees-of-freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis, and to show variability of the LET array design space, several verification plots over a range of parameters are provided.

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Unbiased Atomistic Insight in the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation

10.1101/442889 ◽

2018 ◽

Author(s):

Faidon Z. Brotzakis ◽

Peter G. Bolhuis

Keyword(s):

Transition State ◽

Degrees Of Freedom ◽

Process Analysis ◽

Salt Bridge ◽

Underlying Mechanism ◽

Full Detail ◽

Hydration Water ◽

Native Contact ◽

Reorientation Dynamics

Association and dissociation of proteins are fundamental processes in nature. While this process is simple to understand conceptually, the details of the underlying mechanism and role of the solvent are poorly understood. Here we investigate the mechanism and solvent role for the dissociation of the hydrophilic β-lactoglobulin dimer by employing transition path sampling. Analysis of the sampled path ensembles indicates that dissociation (and association) occurs via a variety of mechanisms: 1) a direct aligned dissociation 2) a hopping and rebinding transition followed by unbinding 3) a sliding transition before unbinding. Reaction coordinate and transition state analysis predicts that, besides native contact and vicinity salt-bridge interactions, solvent degrees of freedom play an important role in the dissociation process. Analysis of the structure and dynamics of the solvent molecules reveals that the dry native interface induces enhanced populations of both disordered hydration water and hydration water with higher tetrahedrality, mainly nearby hydrophobic residues. Bridging waters, hydrogen bonded to both proteins, support contacts, and exhibit a faster decay and reorientation dynamics in the transition state than in the native state interface, which renders the proteins more mobile and assists in rebinding. While not exhaustive, our sampling of rare un-biased reactive molecular dynamics trajectories shows in full detail how proteins can dissociate via complex pathways including (multiple) rebinding events. The atomistic insight obtained assists in further understanding and control of the dynamics of protein-protein interaction including the role of solvent.PACS numbers:

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2P1-T03 External Force Estimation with Pneumatically Driven Forceps Manipulator with Redundant Degrees of Freedom(Surgical Robotics and Mechatronics(2))

The Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) ◽

10.1299/jsmermd.2012._2p1-t03_1 ◽

2012 ◽

Vol 2012 (0) ◽

pp. _2P1-T03_1-_2P1-T03_2

Author(s):

Masayoshi YAMAMOTO ◽

Kotaro TADANO ◽

Kenji KAWASHIMA

Keyword(s):

External Force ◽

Degrees Of Freedom ◽

Surgical Robotics ◽

Force Estimation

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Exact Solution of the Base-Isolated Structure With Sliding Type Base Isolator

Seismic Engineering, Volume 1 ◽

10.1115/pvp2004-2900 ◽

2004 ◽

Author(s):

C. S. Tsai ◽

Tsu-Cheng Chiang ◽

Bo-Jen Chen

Keyword(s):

Exact Solution ◽

Seismic Response ◽

Earthquake Engineering ◽

Degrees Of Freedom ◽

Good Accuracy ◽

Base Isolation ◽

Time History ◽

Relative Deformation ◽

History Analysis ◽

Base Isolator

The use of base isolation for enhancing the seismic resistibility has been proved as an efficiency way from experimental efforts and theoretical studies. It is usual to insert a flexible device in horizontal direction to permit the most relative deformation at this level. Because of the rigidity of the superstructure is much higher than that of the base isolator underneath the structure, therefore, the behavior of the superstructure can be idealized as a rigid body during earthquakes. In general, hundreds of degrees of freedom and a step-by-step time history analysis are the basic requisitions for calculating the seismic response of a base isolated structure under earthquakes. In order to develop a simple tool which can be easily adopted for calculating the sliding displacement and the shear force of the base isolator, an exact solution for predicting the seismic responses of base isolated structures has been derived in this study. The comparison between the experimental results conducted at National Center for Research on Earthquake Engineering (NCREE) in Taiwan and the analytical results obtained from the exact solution show that the exact formulation derived in this study can predict the seismic response of the base isolated structure with very good accuracy.

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