Abstract
In this study, dynamic analysis of
axisymmetric circular plates subjected to two type of dynamic loads are theoretically
investigated. The solutions of damped response of the considered structure have
been obtained by the Laplace transform method and finite element method using
the two dimensional plane elements. Materials of the plate are assumed to be
isotropic, linear elastic and/or viscoelastic. In the viscoelastic material
case, the Kelvin model is employed. According to the correspondence principle
the material constants are replaced with their complex counterparts in the
Laplace domain. The governing equations of motion of the problem are first
obtained in the time domain. Laplace transform is then applied and the set of
simultaneous linear algebraic equations are solved numerically in the transferred
domain. The solutions obtained are transformed to the time domain using an
appropriate numerical inverse Laplace transform method. For the suggested
model, a finite element analysis computer program is coded in Fortran. Verification and
exactness of the written program is performed by comparing the results of the
present method and with those of ANSYS.
References
- [1] JAWAD, M. H., Theory and Design of Plate and Shell Structures. Chapman & Hall, New York – London, 1994.
- [2] GIBSON, J. E., “Thin shells computing and theory”, Pergamon Press, London. J.Acount.Soc.A, 35, 25 – 30, 1980.
- [3] WEAVER, W., JOHNSTON, P., Finite Elements for Structural Analysis, Prentice Hall, New Jersey. 1984.
- [4] BATHE, K. J., WILSON, E. L., “Numerical Methods in Finite Element Analysis”, Prentice Hall, Englewood Cliffs, 1976.
- [5] BHUTA, P. G., “Transient Response of A Thin Elastic Cylindrical Shell to A Moving Shock Wave”, J.Acount.Soc.A., 35, 25 – 30, 1963.
- [6] CASIMIR, J. B., NGUYEN, M. C., TAWFIQ, I., “Thick Shells of Revolution: Derivation of Stiffness Matrix of Continuous Elements and Application to A Tested Cylinder” , Comput. Struc., 85, 1845 – 1857, 2007.
- [7] TEMEL, B., ŞAHAN, M. F., “Transient Analysis Of Orthotropic, Viscoelastic Thick Plates in The Laplace Domain. Eur. J. Of Mech. A/Solids”, 37: 96 – 105, 2013.
- [8] BHIMARADDI, “Static And Transient Response of Cylindrical Shells”, Thin-Walled Struct., 19, 763 – 765, 1987.
- [9] SHIRMOHAMMADI, F., BAHRAMI, S., “Dynamic Response of Circular and Annular Circular Plates Using Spectral Element Method”, Applied Mathematical Modelling, 53, 156–166, 2018.
- [10] ZHOU, Z. H., WONG, K. W., XU, X.S., LEUNG A. Y. T., Natural Vibration of Circular and Annular Thin Plates by Hamiltonian Approach, Journal of Sound and Vibration 330, 1005–1017, 2011.
- [11] AL RJOUB, Y. S., ABDELJABER, O, “Free and Forced Vibration of Rectangular Plates Using The Finite Difference Method”, Materials and Civil Engineering, 627–633, 2015.
- [12] DURBIN, F.,“Numerical inversion of Laplace transforms: An Efficient İmprovement to Dubner and Abate’s Method”, Comput. J., 17:371 – 376, 1974.
- [13] TEMEL, B., ÇALIM, F. F., TÜTÜNCÜ, N., “Quasi-Static And Dynamic Response of Viscoelastic Helical Rods”, J. Sounds Vib., 271, 921 – 935, 2004.
- [14] ANSYS ® Mechanical APDL.
- [15] CHANDRUPATLA, T. R., BELEGUNDU, A. D., Introduction to Finite Elements in Engineering. Prentice Hall, New Jersey, 2002.
- [16] PEKEL, H., KELEŞ, I., TEMEL, B., TÜTÜNCÜ, N., “Transient response of FGM pressure vessels. In: Springer proceedings in Physics 139. Vibration problems ICOVP, 315 – 320, 2011.
- [17] BOLEY, B. A., WEINER, J. H., Theory of Thermal Stresses. John Wiley & Sons, New York, 1960.
- [18] ŞAHAN, M.F., Viskoelastik Kompozit Plakların Laplace Uzayında Dinamik Analizi. Doktora tezi, Çukurova Üniversitesi, Adana, 2012.
- [19] NOORI, A.R., Eksenel Dönel Simetrik Kabuk Problemlerinin Dinamik Analizi İçin Alternatif Çözüm Metodu. Yüksek Lisans tezi, Çukurova Üniversitesi, Adana, 2013.
- [20] NOORI A.R., ASLAN T. A., TEMEL B., “Damped Transient Response of in-Plane and out-of-Plane Loaded Stepped Curved Rods”. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 1-24, 2018.
Abstract
Bu çalışmada, eksenel dönel
simetrik dairesel plak problemlerin iki farklı dinamik yükleme altındaki davranışları
teorik olarak araştırılmıştır. Eksenel dönel simetrik dairesel plak cisimlerin
sönümlü titreşimleri, iki boyutlu düzlemsel eleman modeli kullanılarak, sonlu
elemanlar ve Laplace dönüşüm metotlarının birlikte kullanılması ile elde
edilmiştir. Plak malzemesi izotrop, lineer elastik veya viskoelastik kabul
edilmiştir. Viskoelastik malzeme durumunda Kelvin sönüm modeli kullanılmıştır.
Kelvin modelinde elastik sabitler, elastik-viskoelastik analojisi yardımı ile
Laplace uzayında kompleks karşıtları ile yer değiştirmektedir. Sistemi idare
eden hareket denklemi öncelikle zaman uzayında elde edilmiştir. Ardından sistem
hareket denklemine Laplace dönüşümü uygulanarak elde edilen lineer cebrik
denklem takımı, sayısal olarak çözülmüştür. Dönüşmüş uzayda elde edilen çözümlerden
zaman uzayına geçmek için etkin bir sayısal ters Laplace dönüşüm metodu
kullanılmıştır. Bu işlem kullanılarak sonlu elemanlar yöntemine dayalı bir
bilgisayar programı hazırlanmıştır. Hazırlanan bilgisayar programının sonuçları, ANSYS sonlu eleman paket
programı kullanılarak hesaplanan sonuçlar ile karşılaştırılıp, bu yöntemin
doğruluğu ve üstünlüğü gösterilmiştir.
References
- [1] JAWAD, M. H., Theory and Design of Plate and Shell Structures. Chapman & Hall, New York – London, 1994.
- [2] GIBSON, J. E., “Thin shells computing and theory”, Pergamon Press, London. J.Acount.Soc.A, 35, 25 – 30, 1980.
- [3] WEAVER, W., JOHNSTON, P., Finite Elements for Structural Analysis, Prentice Hall, New Jersey. 1984.
- [4] BATHE, K. J., WILSON, E. L., “Numerical Methods in Finite Element Analysis”, Prentice Hall, Englewood Cliffs, 1976.
- [5] BHUTA, P. G., “Transient Response of A Thin Elastic Cylindrical Shell to A Moving Shock Wave”, J.Acount.Soc.A., 35, 25 – 30, 1963.
- [6] CASIMIR, J. B., NGUYEN, M. C., TAWFIQ, I., “Thick Shells of Revolution: Derivation of Stiffness Matrix of Continuous Elements and Application to A Tested Cylinder” , Comput. Struc., 85, 1845 – 1857, 2007.
- [7] TEMEL, B., ŞAHAN, M. F., “Transient Analysis Of Orthotropic, Viscoelastic Thick Plates in The Laplace Domain. Eur. J. Of Mech. A/Solids”, 37: 96 – 105, 2013.
- [8] BHIMARADDI, “Static And Transient Response of Cylindrical Shells”, Thin-Walled Struct., 19, 763 – 765, 1987.
- [9] SHIRMOHAMMADI, F., BAHRAMI, S., “Dynamic Response of Circular and Annular Circular Plates Using Spectral Element Method”, Applied Mathematical Modelling, 53, 156–166, 2018.
- [10] ZHOU, Z. H., WONG, K. W., XU, X.S., LEUNG A. Y. T., Natural Vibration of Circular and Annular Thin Plates by Hamiltonian Approach, Journal of Sound and Vibration 330, 1005–1017, 2011.
- [11] AL RJOUB, Y. S., ABDELJABER, O, “Free and Forced Vibration of Rectangular Plates Using The Finite Difference Method”, Materials and Civil Engineering, 627–633, 2015.
- [12] DURBIN, F.,“Numerical inversion of Laplace transforms: An Efficient İmprovement to Dubner and Abate’s Method”, Comput. J., 17:371 – 376, 1974.
- [13] TEMEL, B., ÇALIM, F. F., TÜTÜNCÜ, N., “Quasi-Static And Dynamic Response of Viscoelastic Helical Rods”, J. Sounds Vib., 271, 921 – 935, 2004.
- [14] ANSYS ® Mechanical APDL.
- [15] CHANDRUPATLA, T. R., BELEGUNDU, A. D., Introduction to Finite Elements in Engineering. Prentice Hall, New Jersey, 2002.
- [16] PEKEL, H., KELEŞ, I., TEMEL, B., TÜTÜNCÜ, N., “Transient response of FGM pressure vessels. In: Springer proceedings in Physics 139. Vibration problems ICOVP, 315 – 320, 2011.
- [17] BOLEY, B. A., WEINER, J. H., Theory of Thermal Stresses. John Wiley & Sons, New York, 1960.
- [18] ŞAHAN, M.F., Viskoelastik Kompozit Plakların Laplace Uzayında Dinamik Analizi. Doktora tezi, Çukurova Üniversitesi, Adana, 2012.
- [19] NOORI, A.R., Eksenel Dönel Simetrik Kabuk Problemlerinin Dinamik Analizi İçin Alternatif Çözüm Metodu. Yüksek Lisans tezi, Çukurova Üniversitesi, Adana, 2013.
- [20] NOORI A.R., ASLAN T. A., TEMEL B., “Damped Transient Response of in-Plane and out-of-Plane Loaded Stepped Curved Rods”. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 1-24, 2018.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Civil Engineering |
| Journal Section | Civil Engineering |
| Authors | |
| Publication Date | January 28, 2019 |
| Submission Date | July 13, 2018 |
| Acceptance Date | January 7, 2019 |
| Published in Issue | Year 2019 Volume: 8 Issue: 1 |
