... initial value method. Approximate and exact relations are also found. initial value problems shapes (structures) vibrations column vibration heavy support The vibration of a standing column under gravity is important for structures such as poles, antennas, and tall buildings. Systems...

... , “ Effect of Gravity on the Vibration of Vertical Cantilevers ,” Mech. Res. Commun. 0093-6413 , 34 , pp. 312 – 317 . 10.1016/j.mechrescom.2006.12.006 Wang , C. Y. , 2001 , “ Stability of a Heavy Segmented Column ,” Mech. Res. Commun. 0093-6413 , 28 ( 5 ), pp. 493 – 497 . 10.1016/S0093...