Finding initial conditions

[Joa]

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 [MATH]\varepsilon(t)[/MATH]. The material is subject to a constant stress [MATH]\sigma_0[/MATH]. 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

 

[sergiokp]

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.

 

[Deleted member 4993]

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)