PROGRAM HOLZER2a FOR HP-PRIME GRAPHING CALCULATOR


Version 1.021   Antonio Carlos R. Troyman (c) 1985 - 2014


This program calculates the torsional vibration of non-uniform
free-free shafts by the Transfer Matrix Method according to the
Holzer formulation.  As  a result the program delivers the 
natural frequencies and the corresponding normal modes together 
with the torsion moments distributions.  The natural frequencies
are determined using the bissection method for zeroes of 
functions calculation, so a searching interval is required.


Version 1.022   Antonio Carlos R. Troyman (c) 1985 - 2015


This version implements the use of the Terminal program in order
to bypass the limitations of the calculator common terminal.  The 
Terminal program was modified to set the light gray text background
color and the black text foreground color, as long as the colors 
and thickness of the scrollbar.  The Terminal program can be 
downloaded from the HP Prime Utilities section of www.hpcalc.org
site.  The user must modify the Terminal listings in order to
set his/her own colors.  The author set the following values:

line  3 - BackColor:=RGB(225,225,225);
line  4 - TextColor:=RGB(0,0,0);
line  5 - BarBColor:=RGB(128,128,128);
line  6 - BarFColor:=RGB(64,0,64);

line 39 - RECT_P(G9,312,0,319,239,BarBColor);
line 40 - RECT_P(G9,312,y,319,y+240/t,BarFColor);



USER INSTRUCTIONS

After starting the program from the Program Catalog, the 
following information are required:

ND : number of discs

Inert(I), I = 1, ..., ND : mass polar moment of inertia for 
                           each disc

Flexb(I), I = 1, ..., ND - 1 : torsional flexibility for each
                               shaft segment

FrqIni : initial frequency of the searching interval

FrqFin : final frequency of the searching interval

DltFrq : frequency increment of the searching interval

Tol : tolerance (precision) for convergence of the bissection
      method

The shaft segment flexibilities must be determined from the
torsion rigidities acording to the expression

            Flexb(i) = DX(i) / G * J(i)

where:

   DX(i) - lenght of the shaft segment i
   G     - Transversal Elasticity Modulus of the material
   J(i)  - polar area moment of inertiaof the shaft cross
           section

The user must be aware of the possibility of losing natural
frequencies depending on the assumed frequency increment.

The results of the program are presented on the calculator 
screen and the user must use the arrow keys in order to scroll 
the presentation.

As a means of testing the program after it is installed in the
HP Prime, the following example is provided:

ND = 6

Inert(1) = 46            Flexb(1) = 1.0896E-07
Inert(2) = 46            Flexb(2) = 1.7391E-07
Inert(3) = 46            Flexb(3) = 1.0896E-07
Inert(4) = 46            Flexb(4) = 1.4492E-07
Inert(5) = 1035          Flexb(5) = 4.3478E-06
Inert(6) = 460

FrqIni = 20
FrqFin = 800
DltFrq = 78
Tol    = 0.003

Results:

Vibration Mode = 1

Natural Frequency = 26.22467 rad/s

Angle Deflections   Left Torsion Moments  Right Torsion Mom.

      0.39225                0                    4.50519
      0.39090           -31635.73553
      0.38659           -63162.68802
      0.38257           -94342.13588
      0.37545          -125197.22416 
     -1                -806521.22416

Vibration Mode = 2

Natural Frequency = 149.11847 rad/s

Angle Deflections   Left Torsion Moments  Right Torsion Mom.

      1                      0                 1164.07077
      0.88882         -1022870.62194
      0.55283         -1932022.77611
      0.28137         -2497492.36420
     -0.12227         -2785301.22098
      0.00270            28742.90589


Vibration Mode = 3

Natural Frequency = 390.57379 rad/s

Angle Deflections   Left Torsion Moments  Right Torsion Mom.

      0.78576                0              1282674.51314
      0.18646         -7017202.78406
     -1               -8682386.61448
     -0.97881           248081.47809
      0.04482          8989338.47809
     -0.01456           -17381.67224


Vibration Mode = 3

Natural Frequency = 665.07812 rad/s

Angle Deflections   Left Torsion Moments  Right Torsion Mom.

      0.82540                0             13244143.32510
     -1              -20347133.70310
     -0.38217          4304028.42290
      0.84914         13725084.59640
     -0.01297         -7207295.04860
     -0.05377           -11368.66786


Vibration Mode = 5

Natural Frequency = 767.88165 rad/s

Angle Deflections   Left Torsion Moments  Right Torsion Mom.

      0.39620                0             11430302.34080
     -0.77182        -27123542.70660
      1               25714687.76660
     -0.84071        -42744686.28950
      0.00962         14809747.90620
     -0.01672           -15292.84160

It must be observed that all the frequencies must be in rad/s, 
not only the provided frequencies, but also the calculated ones. 

September, 8th, 2015