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The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity. Packages such as MATLAB may be used to run simulations of such models. [1]
An animated cobweb diagram of the logistic map = (), showing chaotic behaviour for most values of >. A cobweb plot , known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions , such as the logistic map .
Diagram of a Maxwell material. The Maxwell model is represented by a purely viscous damper and a purely elastic spring connected in series, [4] as shown in the diagram. If, instead, we connect these two elements in parallel, [4] we get the generalized model of a solid Kelvin–Voigt material.
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
The first, referred to as the Maxwell arm, contains a spring (=) and dashpot (viscosity ) in series. [2] The other system contains only a spring ( E = E 1 {\displaystyle E=E_{1}} ). These relationships help relate the various stresses and strains in the overall system and the Maxwell arm:
2 Equations. 3 See also. 4 Sources. 5 Further reading. Toggle the table of contents. List of equations in fluid mechanics. 1 language. ... −2 [T] −1: Momentum ...
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being ...
The curve represents a plot of equation with p 1, v 1, c 0, and s known. If p 1 = 0, the curve will intersect the specific volume axis at the point v 1. Hugoniot elastic limit in the p-v plane for a shock in an elastic-plastic material. For shocks in solids, a closed form expression such as equation cannot be derived from first principles.