Abstract
Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktaların tam ankastre olduğu, kat kütlelerinin kat seviyelerinde topaklandığı, kolonların yayılı kütlesinin ve kayma deformasyonunun ihmal edildiği kabullerine sık rastlanmaktadır. Ancak uygulamada çoğu kez çerçevelerin zemine bağlandığı noktalar, zeminin elastik davranışı nedeni ile bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda çerçevenin zemine bağlandığı noktaya dönmeye ve ötelenmeye karşı elastik yaylar yerleştirilerek yarı-rijit mesnet davranışı modellenebilir. Bu çalışmada, zemine yarı-rijit bağlı tek katlı çerçevelerin serbest titreşim analizi kolonların yayılı kütlesi ve kayma deformasyonu dikkate alınarak yapılmış ve açısal frekansları elde edilmiştir. Kolon tabanındaki ötelenme ve dönme yay sabiti değerlerindeki artışın frekans değerlerinde meydana getirdiği artma ve kolon üst serbest ucundaki toplu kütlenin ve dönme ataletinin değerlerindeki artışın frekanslarda meydana getirdiği azalma grafiklerle sunulmuştur.
References
- Bapat, C.N., 1987, Natural frequencies of a beam with non-classical boundary conditions and concentrated masses, Sound Vib., 112, 1, 177-182.
- Chai, G.B., Low, K.H., 1993, On the natural frequencies of beams carrying a concentrated mass, Sound Vib., 160, 1, 161-166.
- DeRosa, M.A., Franciosi, C., Maurizi, M.J., 1996, On the dynamic behavior of slender beams with elastic ends carrying a concentrated mass, Comput. Struct., 58, 6, 1145-1159.
- Glabisz, W., 1999, Vibration and stability of a beam with elastic supports and concentrated masses under conservative and nonconservative forces, Comput. Struct., 70, 305-313.
- Goel, R.P., 1976, Free vibration of a beam-mass system with elastically restrained ends; Sound Vib., 47, 1, 9-14.
- Güler, K., 1996, Effects of soil flexibility on free vibrations of tower-like structures, Proceedings of the I. Symposium on Mathematical and Computational Applications, November 19-21, Manisa, Turkey.
- Laura, P.A.A., Maurizi, M.J., Pambo, J.L., 1975, A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end, Sound Vib., 41, 4, 397-405.
- Low, K.H., Lim, T.M., Chai, G.B., 1993, Experimental and analytical investigations of vibration frequencies for centre-loaded beams, Comput. Struct., 48, 6, 1157-1162.
- Low, K.H., 1994, An equivalent-center method for quick frequency analysis of beams carrying a concentrated mass, Comput. Struct., 50, 3, 409-419.
- Maurizi, M.J., Belles, P.M., 1991, Natural frequencies of the beam-mass system: Comparison of the two fundamental theories of beam vibrations, Sound Vib., 150, 2, 330-334.
- Maurizi, M.J., Belles, P.M., 1992, An additional evaluation of free vibration of beam-mass systems, Sound Vib., 154, 1, 182-186.
- Michaltsos, G.Th., Ermopoulos, J.Ch., 2001, Dynamic response of column bases; Eng. Struct., 23, 58-71.
Abstract
The assumptions of frame supports being fully rigid; storey masses being concentrated at the floor levels; distributed masses and shear deformations of the columns being neglected are frequently seen in dynamic analysis of frames because of less effort in calculation. In practice, however, columns may usually rotate and translate a little due to elastic behavior of soil. In this case, elastic support behavior can be modeled using elastic springs against translation and rotation at the column bases. In this study, free vibration of elastically supported columns is studied including shear deformation of the column and natural frequencies are obtained. Increasing effect of increasing rotational and translational spring coefficients at the column base and decreasing effect of increasing concentrated mass and its rotational inertia at the top of column on frequency values are presented in graphs.
References
- Bapat, C.N., 1987, Natural frequencies of a beam with non-classical boundary conditions and concentrated masses, Sound Vib., 112, 1, 177-182.
- Chai, G.B., Low, K.H., 1993, On the natural frequencies of beams carrying a concentrated mass, Sound Vib., 160, 1, 161-166.
- DeRosa, M.A., Franciosi, C., Maurizi, M.J., 1996, On the dynamic behavior of slender beams with elastic ends carrying a concentrated mass, Comput. Struct., 58, 6, 1145-1159.
- Glabisz, W., 1999, Vibration and stability of a beam with elastic supports and concentrated masses under conservative and nonconservative forces, Comput. Struct., 70, 305-313.
- Goel, R.P., 1976, Free vibration of a beam-mass system with elastically restrained ends; Sound Vib., 47, 1, 9-14.
- Güler, K., 1996, Effects of soil flexibility on free vibrations of tower-like structures, Proceedings of the I. Symposium on Mathematical and Computational Applications, November 19-21, Manisa, Turkey.
- Laura, P.A.A., Maurizi, M.J., Pambo, J.L., 1975, A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end, Sound Vib., 41, 4, 397-405.
- Low, K.H., Lim, T.M., Chai, G.B., 1993, Experimental and analytical investigations of vibration frequencies for centre-loaded beams, Comput. Struct., 48, 6, 1157-1162.
- Low, K.H., 1994, An equivalent-center method for quick frequency analysis of beams carrying a concentrated mass, Comput. Struct., 50, 3, 409-419.
- Maurizi, M.J., Belles, P.M., 1991, Natural frequencies of the beam-mass system: Comparison of the two fundamental theories of beam vibrations, Sound Vib., 150, 2, 330-334.
- Maurizi, M.J., Belles, P.M., 1992, An additional evaluation of free vibration of beam-mass systems, Sound Vib., 154, 1, 182-186.
- Michaltsos, G.Th., Ermopoulos, J.Ch., 2001, Dynamic response of column bases; Eng. Struct., 23, 58-71.
Details
| Other ID | JA48BJ33BG |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | September 1, 2005 |
| Published in Issue | Year 2005 Volume: 20 Issue: 3 |