Finding initial conditions

Joa

New member
Joined
Nov 26, 2019
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1
Hello,

I am trying to solve a differential equation corresponding to a model for visco-elastic material behavior. the model consists of 5 units of spring-dampers placed in parallel and should be solved for the strain \(\displaystyle \varepsilon(t)\). The material is subject to a constant stress \(\displaystyle \sigma_0\). I am able to come-up with a single fifth order differential equation but I am struggling to find the initial conditions. I have found the first initial condition as can be seen in the attached image, but don't know how to come-up with the remaining four conditions. Can anyone help me solve this problem?

Thanks in advance!

Joa

problem.png
 

sergiokp

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Nov 26, 2019
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I think that the key idea is that you can write a second order differential equation to describe the system. Anyway, I do not understand how you get those equations because whenever you use Newton's second law, since the acceleration appears, equations usually involve second derivatives.
 

Subhotosh Khan

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Jun 18, 2007
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I think that the key idea is that you can write a second order differential equation to describe the system. Anyway, I do not understand how you get those equations because whenever you use Newton's second law, since the acceleration appears, equations usually involve second derivatives.
For linear-elastic material ....................................stress = k*(strain)

For Visco-elastic Newtonian fluid.........................stress = k*(strain-rate)
 
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