Mass,Spring, Damper vs Capacitor, Indcutor, Resistor vs ? analogy

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Discussion Overview

The discussion revolves around the analogies between mechanical systems (mass, spring, damper) and electrical components (capacitor, inductor, resistor), as well as exploring potential analogies in other fields such as thermal principles and hydraulics. Participants examine the underlying mathematical relationships and the applicability of these analogies across different domains.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the governing equations for mechanical and electrical systems are analogous due to their shared mathematical structure, particularly referencing the wave equation.
  • Claude expresses skepticism about the existence of a thermal analogy, suggesting that any additional analogies must exhibit wave-like behavior, which may not apply to thermal systems.
  • Others mention the existence of thermal circuit models in practical applications, indicating that thermal resistance and capacity exist, but question the existence of thermal inductance.
  • Claude questions the necessity for analogies to adhere strictly to the wave equation, arguing that circuit models can represent various types of differential equations, including higher-order and nonlinear forms.
  • There is a discussion about defining concepts such as thermal frequency, phase, and resonance, which raises doubts about the completeness of a thermal analogy.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence or validity of thermal analogies. There are competing views regarding the necessity of adhering to the wave equation and the definitions of thermal properties.

Contextual Notes

Limitations include the lack of clarity on the definitions of thermal properties and the potential for different mathematical frameworks to describe analogous systems. The discussion also highlights the need for further exploration of the conditions under which these analogies hold.

Who May Find This Useful

This discussion may be of interest to those studying control systems, thermal dynamics, and the mathematical modeling of physical systems across different domains.

MedievalMan
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From a mathematic, linear differential equation point of view, and energy storage point of view, the concepts I mentioned in the topics are the same (I remember this being a concept in modeling control systems.)

My question is, what are the same basic elements in other topics: thermal principes (I've heard of thermal resistance, is there thermal inductance?), hydraulics, etc?

-Matt
 
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These concepts are analogous because the equation that governs the interaction between the said quantities is exactly the same (namely the wave-equation).

Any additional analogies would have to obey the wave equation and thus have to exhibit some kind of wave-like behaviour, which is why I have my doubts there exists an appropriate thermal analogy. You could get an electromagnetic analogy using permittivity and permeability or an acoustic analogy using density and bulk modulus though.

Claude.
 
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While I am not familiar with the details, I know there are thermal circuit models used in real applications. In particular, the analyzer made by these people: http://www.klippel.de/ uses a circuit model for the thermal behavior of a loudspeaker.

Also, I don't see why these analogies have to obey the wave equation? Circuit models are another way of expressing constant coefficient differential equations, not just wave equations.
 
Can you define a thermal frequency? Can you define a thermal phase? Can you obtain a thermal resonance? These are the doubts I have as to whether one could obtain a perfect thermal analogy.
Nolen Ryba said:
Also, I don't see why these analogies have to obey the wave equation? Circuit models are another way of expressing constant coefficient differential equations, not just wave equations.
You could feasibly come up with a similar analogy that obeys a higher order differential equation, or even a nonlinear differential equation if one so wishes. The point was that all the parts of the analogy obey the same basic equation (even if all the terms represent completely different things). That's what makes an analogy so.

Claude.
 
MedievalMan said:
My question is, what are the same basic elements in other topics: thermal principes (I've heard of thermal resistance, is there thermal inductance?),

Although there is a thermal resistance and capacity, there is no thermal inductor.
 

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