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Related Concept Videos

Damped Oscillations01:07

Damped Oscillations

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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
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Types of Damping01:20

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If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
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Elasticity01:12

Elasticity

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Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
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Forced Oscillations01:06

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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
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Energy in Simple Harmonic Motion01:23

Energy in Simple Harmonic Motion

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To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Related Experiment Video

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Transient elasticity and polymeric fluids: Small-amplitude deformations.

Oliver Müller1, Mario Liu1, Harald Pleiner2

  • 1Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany.

Physical Review. E
|March 18, 2016
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Summary

Transient elasticity (TE) offers a thermodynamic framework to describe viscoelasticity and non-Newtonian fluid behavior. This theory effectively models various flow phenomena in soft matter, including the Weissenberg effect.

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Area of Science:

  • Rheology
  • Soft Matter Physics
  • Continuum Mechanics

Background:

  • Viscoelasticity describes materials with both viscous and elastic properties.
  • Non-Newtonian effects are common in polymeric fluids, granular media, and soft matter.
  • Existing models may lack thermodynamic consistency or simplicity.

Purpose of the Study:

  • To present a continuum-mechanical theory derived from transient elasticity (TE).
  • To demonstrate the theory's ability to describe non-Newtonian fluid behavior.
  • To validate the theory's applicability to various flow conditions in polymeric fluids.

Main Methods:

  • Development of a continuum-mechanical theory based on transient elasticity.
  • Application of the theory to analyze shear and elongational flows.
  • Focus on small-amplitude deformations for this study.

Main Results:

  • The theory provides a thermodynamically consistent generalization of viscoelasticity.
  • It accurately captures diverse phenomena in stationary, oscillatory, and transient flows.
  • The Weissenberg effect and flow down an inclined channel are well-described.

Conclusions:

  • Transient elasticity offers a powerful and simple framework for modeling soft matter.
  • The developed theory successfully predicts a wide range of non-Newtonian fluid behaviors.
  • This approach is applicable to both small and large amplitude deformations.