Application example summary text:
EXAMPLE=137
Dynamic axial or torsional response of a linear bar
Equation: K*A U,xx + Rho*A U,tt + Q_e = 0,
U = displacement, K = stiffness, A = area
Rho = mass density, Q_e = source per unit length
1 *---(K_e, A_e, Rho_e, Q_e)---* LT_N, Axial element in x
1 *---(G_e, I_e, Rho_e, Q_e)---* LT_N, Torsional element in x
Prop:    1    2      3    4

DATA_SET = 01 
Natural frequency of Biggs 4dof model
Bigg's spring mass system, via L3 elem
1 *---(K_e, A_e, Rho_e, Q_e)---* 2, Element in x
      1  k1    3   k2   5  k3    7
Fixed *----*---*---*----*---*----* Free
           2  m3   4   m5   6   m7
k1=6000 k2=4000 k3=2000 m2=2 m3=1 m4=1
approximate massless bar with Rho << 1

DATA_SET = 02 
drill string & collar system, via L3 elem
1 *---(G_e, I_e, Rho_e, Q_e)---* 2, Element in x
      1    2   3   4    5   6    7 Nodes
Fixed *----*---*---*----*---*----* Free
          (1)     (2)      (3)   J_collar
I_pipe = 9.4e-4 ft^4, I_collar = 1.593e-2 ft^4
G_steel = 1.728e9 lb/ft^2, Rho_steel = 15.22 lb s^2 / ft^2
Lumped 120' collar J = rho * L_c * I_c = 29.3 lb ft s^2
L_drill = 5000 ft, Freq = 2.41, 7.93 rad/s (approximately)

DATA_SET = 03 
drill string & collar system, via L3 elem
1 *---(G_e, I_e, Rho_e, Q_e)---* 2, Element in x
      1    2    3    4    5    6    7 8 9  Nodes
Fixed *----*----*----*----*----*----*-*-*  Free
          (1)       (2)       (3)    (4)    
I_pipe = 9.4e-4 ft^4, I_collar = 1.593e-2 ft^4
G_steel = 1.728e9 lb/ft^2, Rho_steel = 15.22 lb s^2 / ft^2
120' collar J = rho * L_c * I_c = 29.3 lb ft s^2
L_drill = 5000 ft, Freq = 2.41, 7.93 rad/s (approximately)