Research Article
Rotary Inertia and Higher Modes Effect on the Dynamic Response of Timoshenko Beams on Two-Parameter Elastic Foundation
Abstract
This study investigates the dynamic response of the axially loaded
Timoshenko beams on two-parameter foundation with generalized elastic end
conditions. A simplified modal analysis procedure is presented for the
vibration analysis by using the conventional separation of variables method.
The effects of higher modes and rotary inertia on the dynamic response of the
forced Timoshenko beam are highlighted. A numerical example is presented to
compare the modal responses of bending moment and shear force of the beams on
Winkler and Vlasov type foundations with and without the rotary inertia effect.
References
- Doyle, P.F. and Pavlovic, M., Vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10, 663–674, 1982.
- West, H. H. and Mafi, M., Eigenvalues for beam-columns on elastic supports. Journal of Structural Engineering, 110, 1305–1320, 1984.
- Çatal, H. H., Free vibration of partially supported piles with the effects of bending moment, axial and shear force. Engineering Structures, 24, 1615-1622, 2002.
- Çatal, H. H., Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear force. Engineering Structures, 28, 1911-1918, 2006.
- Yeşilce, Y. and Çatal, H. H., Free vibration of piles embedded in soil having different modulus of subgrade reaction. Applied Mathematical Modelling, 32(5), 889-900.
- Çatal, S., Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematical Modelling, 32(9), 1744-1757, 2008.
- Yeşilce, Y. and Çatal, S., Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method, Struct. Eng. Mech. 31(4), 453-475, 2009.
- Yeşilce, Y. and Çatal, H. H., Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method. Archive of Applied Mechanics, 81, 199-213, 2011.
- Sapountzakis, E. J. and Kampitsis, A. E., Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation, Computers and Structures, 88, 1206-1219, 2010.
- Çatal, S., Response of forced Euler-Bernoulli beams using differential transform method. Struct. Eng. Mech. 42(1), 95-119, 2012.
- Özturk, B. and Coşkun, S. B., Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions. Mathematical Problems in Engineering, 2013, 1-7, 2013.
- Pasternak P.L., On a new method of analysis on elastic foundation by means of two constants. Gosudarstvennoe Izdatel’stvo Literaturi po Stroitel’stvu i Arkhitekture, 1954.
- Vlasov, V.Z. and Leont’ev, U.N.: Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, 1966.
- Morfidis, K. and Avramidis, I. E., Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets. Computers and Structures, 80, 1919-1934, 2002.
- Yokoyama, T., Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundation. Computers and Structures, 61, 995-1007, 1996.
- Arboleda-Monsalve, L. G., Zapata-Medina, D. G. and Aristizabal-Ochoa, J. D., Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector. Journal of Sound and Vibration, 310, 1057-1079, 2008.
- Balkaya, M., Kaya, M. O. and Sağlamer, A., Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method. Arch. Appl. Mech. 79, 135-146, 2008.
- Celep, Z., Güler, K. and Demir, F., Response of a completely free beam on a tensionless Pasternak foundation subjected to dynamic load. Structural Engineering and Mechanics, 37, 61-77, 2011.
- Malekzadeh, P. and Karami, G., A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations. Applied Mathematical Modelling 32, 1381-1394, 2008.
- Morfidis, K., Vibration of Timoshenko beams on three-parameter elastic foundation. Computers and Structures, 88, 294-308, 2010.
- Calio, I. and Greco, A.: Free vibrations of Timoshenko beam-columns on Pasternak foundations. Journal of Vibration and Control. 19, 686-696, 2012.
- Hassan, M. T. and Nassar, M.: Analysis of stressed Timoshenko beams on two parameter foundations. KSCE Journal of Civil Engineering, 19, 173-179, 2014.
- Hızal, Ç. and Çatal, H. H., Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation. Structural Engineering and Mechanics, 57(6), 969-988, 2016.
- Zhaohua, F. and Cook, R.D., Beam elements on two-parameter elastic foundations. Journal of Engineering Mechanics, 109, 1390–402 (1983)
- De Rosa, M. A., Free Vibrations of Timoshenko Beams on Two Parameter Elastic Foundation. Computers and Structures, 57, 151-156, 1995.
Rotary Inertia and Higher Modes Effect on the Dynamic Response of Timoshenko Beams on Two-Parameter Elastic Foundation
Abstract
This study investigates the dynamic response of the axially loaded Timoshenko beams on two-parameter foundation with generalized elastic end conditions. A simplified modal analysis procedure is presented for the vibration analysis by using the conventional separation of variables method. The effects of higher modes and rotary inertia on the dynamic response of the forced Timoshenko beam are highlighted. A numerical example is presented to compare the modal responses of bending moment and shear force of the beams on Winkler and Vlasov type foundations with and without the rotary inertia effect.
References
- Doyle, P.F. and Pavlovic, M., Vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10, 663–674, 1982.
- West, H. H. and Mafi, M., Eigenvalues for beam-columns on elastic supports. Journal of Structural Engineering, 110, 1305–1320, 1984.
- Çatal, H. H., Free vibration of partially supported piles with the effects of bending moment, axial and shear force. Engineering Structures, 24, 1615-1622, 2002.
- Çatal, H. H., Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear force. Engineering Structures, 28, 1911-1918, 2006.
- Yeşilce, Y. and Çatal, H. H., Free vibration of piles embedded in soil having different modulus of subgrade reaction. Applied Mathematical Modelling, 32(5), 889-900.
- Çatal, S., Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematical Modelling, 32(9), 1744-1757, 2008.
- Yeşilce, Y. and Çatal, S., Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method, Struct. Eng. Mech. 31(4), 453-475, 2009.
- Yeşilce, Y. and Çatal, H. H., Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method. Archive of Applied Mechanics, 81, 199-213, 2011.
- Sapountzakis, E. J. and Kampitsis, A. E., Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation, Computers and Structures, 88, 1206-1219, 2010.
- Çatal, S., Response of forced Euler-Bernoulli beams using differential transform method. Struct. Eng. Mech. 42(1), 95-119, 2012.
- Özturk, B. and Coşkun, S. B., Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions. Mathematical Problems in Engineering, 2013, 1-7, 2013.
- Pasternak P.L., On a new method of analysis on elastic foundation by means of two constants. Gosudarstvennoe Izdatel’stvo Literaturi po Stroitel’stvu i Arkhitekture, 1954.
- Vlasov, V.Z. and Leont’ev, U.N.: Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, 1966.
- Morfidis, K. and Avramidis, I. E., Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets. Computers and Structures, 80, 1919-1934, 2002.
- Yokoyama, T., Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundation. Computers and Structures, 61, 995-1007, 1996.
- Arboleda-Monsalve, L. G., Zapata-Medina, D. G. and Aristizabal-Ochoa, J. D., Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector. Journal of Sound and Vibration, 310, 1057-1079, 2008.
- Balkaya, M., Kaya, M. O. and Sağlamer, A., Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method. Arch. Appl. Mech. 79, 135-146, 2008.
- Celep, Z., Güler, K. and Demir, F., Response of a completely free beam on a tensionless Pasternak foundation subjected to dynamic load. Structural Engineering and Mechanics, 37, 61-77, 2011.
- Malekzadeh, P. and Karami, G., A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations. Applied Mathematical Modelling 32, 1381-1394, 2008.
- Morfidis, K., Vibration of Timoshenko beams on three-parameter elastic foundation. Computers and Structures, 88, 294-308, 2010.
- Calio, I. and Greco, A.: Free vibrations of Timoshenko beam-columns on Pasternak foundations. Journal of Vibration and Control. 19, 686-696, 2012.
- Hassan, M. T. and Nassar, M.: Analysis of stressed Timoshenko beams on two parameter foundations. KSCE Journal of Civil Engineering, 19, 173-179, 2014.
- Hızal, Ç. and Çatal, H. H., Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation. Structural Engineering and Mechanics, 57(6), 969-988, 2016.
- Zhaohua, F. and Cook, R.D., Beam elements on two-parameter elastic foundations. Journal of Engineering Mechanics, 109, 1390–402 (1983)
- De Rosa, M. A., Free Vibrations of Timoshenko Beams on Two Parameter Elastic Foundation. Computers and Structures, 57, 151-156, 1995.
There are 25 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Civil Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | July 1, 2019 |
| Submission Date | March 23, 2018 |
| Published in Issue | Year 2019 Volume: 30 Issue: 4 |
