scholarly journals Free energies of crystals computed using Einstein crystal with fixed center of mass and differing spring constants

2021 ◽  
Vol 154 (16) ◽  
pp. 164509
Author(s):  
Vikram Khanna ◽  
Jamshed Anwar ◽  
Daan Frenkel ◽  
Michael F. Doherty ◽  
Baron Peters
Keyword(s):  
Center Of Mass ◽  
Free Energies ◽  
Spring Constants ◽  
Fixed Center

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

The Appropriate Lumped Constants of Vibrating Shaft Systems

1943 ◽  
Vol 10 (4) ◽  
pp. A220-A224
Author(s):  
G. Horvay ◽  
J. Ormondroyd
Keyword(s):  
Total Mass ◽  
Spring Constant ◽  
New Method ◽  
Concentrated Mass ◽  
Shaft System ◽  
Spring Constants

Abstract The present paper is a theoretical supplement to the descriptive article, “Static and Dynamic Spring Constants.” It is concerned with the derivation of the constants (1a)Ki=ki+16miω2=ki(1+16ϵi2)(ϵi2=ω2mi/ki)(1b)Mi=μi+12(mleft+mright) of the appropriately lumped shaft system (Section 1), and with an estimate of the range of the new method (Sections 2, 3, 4). Term ki denotes the distributed static spring constant, mi the total mass of the ith (uniform) shaft section of the system; μi is the ith concentrated mass, ω the frequency of vibration.

High-Cycle Fatigue of Shafts due to Starting Transients in Drive Systems

1988 ◽  
Vol 202 (3) ◽  
pp. 201-209 ◽  
Author(s):  
S G Velonias ◽  
N A Aspragathos
Keyword(s):  
Structural Characteristics ◽  
Drive System ◽  
Suggested Approach ◽  
Loss Of Life ◽  
Speed Reducer ◽  
Starting Conditions ◽  
General Drive ◽  
Drive Systems ◽  
Non Linear System ◽  
Spring Constants

This paper investigates some of the effects that structural characteristics and main non-linearities of a drive system have on systems response and its shaft fatigue. In the suggested approach a general drive system, including a motor, load and speed reducers, is modelled as a multi-degree-of-freedom torsional vibrations non-linear system. The differential equations of the system are formed automatically. The user of the developed program must input just the constants of the components. An algorithm to compute the loss of life of the shafts due to fatigue is also incorporated into the program. As an example, a drive system, including a motor, a speed reducer and load is modelled and tested under starting conditions. The effects of changing spring constants of the shafts and the backlash of the speed reducer are investigated.

A CUBIC ARRANGED SPHERICAL DISCRETE ELEMENT MODEL

2014 ◽  
Vol 11 (05) ◽  
pp. 1350102 ◽  
Author(s):  
WEI GAO ◽  
YUANQIANG TAN ◽  
MENGYAN ZANG
Keyword(s):  
Strain Energy ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Laminated Plate ◽  
Discrete Elements ◽  
Elastic Continuum ◽  
Vibration Process ◽  
Spring Constants ◽  
Dem Model

A 3D discrete element model (DEM model) named cubic arranged discrete element model is proposed. The model treats the interaction between two connective discrete elements as an equivalent "beam" element. The spring constants between two connective elements are obtained based on the equivalence of strain energy stored in a unit volume of elastic continuum. Following that, the discrete element model proposed and its algorithm are implemented into the in-house developed code. To test the accuracy of the DEM model and its algorithm, the vibration process of the block, a homogeneous plate and laminated plate under impact loading are simulated in elastic range. By comparing the results with that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the DEM model and its algorithm proposed in this paper is proved.

A Numerical Method to Enhance the Accuracy of Mass-Spring Systems for Modeling Soft Tissue Deformations

2009 ◽  
Vol 25 (3) ◽  
pp. 271-278 ◽  
Author(s):  
Hadi Mohammadi
Keyword(s):  
Regular Function ◽  
Technical Note ◽  
Smooth Solutions ◽  
Governing Equations ◽  
Residual Function ◽  
Spring System ◽  
Mass Spring ◽  
Tissue Deformations ◽  
Spring Constants ◽  
Element Method

This technical note presents a numerical corrective technique that allows control of nonlinearity in a mass-spring system (MSS) independent of its spring constants or system topology. The governing equations of MSS in the form of ordinary differential equations or a regular function accompanied by any boundary or initial condition as known constraints, are employed to modify the results. A least-squares algorithm coupled with the finite difference method is used to discretize the basic residual function implemented in this corrective technique. This numerical solution is applicable to both static and dynamic MSS. This technique is easy to implement and has accuracy similar to that of the equivalent finite element method (FEM) solution to the same system whereas solutions are obtained in a fraction of the CPU time. The proposed technique can also be used to smooth solutions from other methods such as FEM or boundary element method (BEM).

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