Inertial Force in 4 DOF model

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dwsdolce
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Inertial Force in 4 DOF model

Post by dwsdolce » Tue May 02, 2017 6:09 am

Hi, I am new to the forum and just completed a course that Trevor Gore gave in the US on Modal Plate Tuning.

In reviewing equation 2.4-3 and 2.4-3 in the Contemporary Acoustic Guitar Design and Build book I am trying to understand where the term Kb(ys+yb) for both the side and back oscillator comes from? It appears to be two springs that are controlled by both the side and back movement and with one attached to the back and one to the sides.

Can anyone provide me some insight into where this term comes from and its physical meaning? Although other terms are pretty clear.

Regards
David Smith

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Trevor Gore
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Re: Inertial Force in 4 DOF model

Post by Trevor Gore » Tue May 02, 2017 9:07 am

Welcome, David.

Equations 2.4-2 sums the forces on the sides and 2.4-3 sums the forces on the back.

The Kb(yb + ys) term in 2.4.3 represent the restoring force on the back when it extends the spring representing the back stiffness (Kb) by an amount corresponding to the net movement of the back (yb) and sides (ys). Similarly for the restoring force for the movement of the sides in Equ. 2.4-2. The terms are spring restoring forces representing the (bending) stiffness of the parts rather than inertia forces (which are a mass * an acceleration).

Hey Martin (Kiwigeo), this topic may live better in the 4 DOF model thread in the book sub-forum here:

http://www.anzlf.com/viewtopic.php?f=33&t=4636

Cheers, Trevor.

dwsdolce
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Re: Inertial Force in 4 DOF model

Post by dwsdolce » Tue May 02, 2017 3:04 pm

I do see that the restoring force on the back and sides are both related to the sum of the movements times Kb.
I guess I do not see why it is done this way instead of:

2.42 having Ks*ys
and
2.44 having Kb*yb

I guess it is the rationale for why the restoring force is the same on both the back and sides and related to the sum of the displacements of the back and side instead of each being related to its own movement. I would have thought that the bending stiffness of the back and sides would be independent of each other.

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Trevor Gore
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Re: Inertial Force in 4 DOF model

Post by Trevor Gore » Tue May 02, 2017 7:08 pm

The sides aren't modeled with any bending stiffness (i.e. no Ks term), just as mass, with their in-plane motion ys. The sides move as a result of the reaction to forces exerted by the other components of the model through their coupling mechanisms (implying force equilibrium within the system as drawn).

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