Applications For Vibrational Coupling

If one is to start experimenting with Vibrational Coupling and combining this with EM to learn the connection between T E M in real life, if there will be found to be a connection, one needs the method and the math application to set up accurate designs. Getting a Ferrite core to go into vibrational resonance is something I have yet to experience. The following experiment now establishes some solid methods.

Toroidal Cores

Two large ferrite cores approximately 3" by 1/2" are selected from the junk box. They were removed from a power supply system some years back, and were the 60 Hz power input transfer toroids designed to handle power applications. Dimensions are carefully measured in metric for ease of calculation.

Toroidal Cores Picture

We now have several methods to couple these two toroids together vibrationally simply by sliding three plastic spacers between them at a fixed distance.
All formula will be calculated from the base center of mass, so the first calculation is to find this circles dimensions.

Vibrational Center of Mass

73.3 - 45.16 =  28.14 mm
28.14 / 2 =  14.07 mm = [width of the meat of the core]
45.16 + 14.07 =  59.23 mm = Diameter of the Vibrational Center

Diameter                         59.23 mm
Radius                             29.615 mm        [HEX segment length]
Circumference               186.077 mm

Toroid Thickness             13.0 mm
1/2 Thickness                     6.5 mm

Coupling Formula

HEX Coupling
Found above is the radius.
Spacer distance = Radius - Toroidal Thickness
Spacer Length =  29.615 - 13  =  16.615 mm

Polygon Coupling
Fractal Length = Diameter * (sine (1/2 the angle))  =  59.23 mm ( sine (1/2 the angle))

Perimeter Coupling
FS =  59.23 mm / X
FS = Fractal Segment Length

VE coupling can be applied for a 3D coupling of the standing vibrational form.

Triangle VE Coupling

Calculate the distance between top and bottom of the VE from opposing triangles.
Find the 3x polygon for the core circumference.

Square VE Coupling
Calculate the distance between top and bottom of the VE from opposing squares.
Find the 4x polygon for the core circumference.

Odd Coupling

7x Coupling
3x Coupling

1/2 pi  Resonant Lengths

Circumference               186.077 mm
1c         186.077
2c         292.289
3c         459.126
4c         721.194
5c       1132.849
6c       1779.475
7c       2795.194
8c       4390.68                  4.39068 meters
9c       6896.864
10c   10833.5698
11c   17017.3317
12c   26730.7622
13c   41988.5831
14c   65955.51
15c 103602.676             103.602676 meters

Phi Length

1c         186.077
1c phi    114.99   left spin
1c Phi    301.07   right spin

2c         292.289  
2c phi   180.634  
left spin  one layer in
2c Phi   472.92   right spin one layer in

3c         459.126

3c phi   283.74
3c Phi   742.8668

Dave L
c_s_s_p group
10 - 27 - 2009