پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 161 |
| تعداد شمارهها | 6,484 |
| تعداد مقالات | 70,042 |
| تعداد مشاهده مقاله | 123,036,666 |
| تعداد دریافت فایل اصل مقاله | 96,270,464 |
A new approach for nonlinear vibration analysis of thin and moderately thick rectangular plates under inplane compressive load | ||
| Journal of Computational Applied Mechanics | ||
| مقاله 4، دوره 48، شماره 2، اسفند 2017، صفحه 185-198 اصل مقاله (1003.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2017.240726.181 | ||
| نویسندگان | ||
| Hesam Makvandi1؛ Shapour Moradi* 1؛ Davood Poorveis2؛ Kourosh Heydari Shirazi1 | ||
| 1Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| 2Department of Civil Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| چکیده | ||
| In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre- and post-buckled rectangular plates for the first time. This is an answer to an existing need to develope a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element, arc-length, harmonic balance and direct iterative methods. The governing differential equations of plate vibration have been extracted considering shear deformations and the initial geometric imperfection. The solution is assumed to be the sum of the static and dynamic parts which upon inserting them into the governing equations, convert them into two sets of nonlinear differential equations for static and dynamic behaviors of the plate. First, the static solution is calculated using a combination of the differential quadrature element method and an arc-length strategy. Then, putting the first step solutions into the dynamic nonlinear differential equations, the nonlinear frequencies and modal shapes of the plate are extracted using the harmonic balance and direct iterative methods. Comparing the obtained solutions with those published in the literature confirms the accuracy and the precision of the proposed method. The results show that an increase in the nonlinear vibration amplitude increases the nonlinear frequencies. | ||
| کلیدواژهها | ||
| BUCKLED PLATE؛ DIFFERENTIAL QUADRATURE ELEMENT METHOD؛ DIRECT ITERATIVE METHOD؛ HARMONIC BALANCE METHOD؛ Nonlinear vibration | ||
| مراجع | ||
|
[1] T. Wah, Large amplitude flexural vibration of rectangular plate, International Journal of Mechanical Science, Vol. 5, pp. 425-438, 1963. [2] C. Mei, Finite element displacement method for large amplitude free flexural vibrations of beams and plates, Computers & structures, Vol. 3, pp. 163-174, 1973. [3] N. Yamaki, M. Chiba, Nonlinear vibrations of clamped rectangular plate with initial deflection and initial edge displacement - part I: Theory., Thin-Walled Structures, Vol. 1, pp. 3-29, 1983. [4] C. Mei, K. Decha-umphai, A finite element method for nonlinear forced vibrations of rectangular plates, AIAA Journal, Vol. 23, No. 7, pp. 1104-1110, 1984. [5] Kapania, R.K., T. Y. Yang, Buckling, postbuckling, and nonlinear vibrations of imperfect plates, AIAA Journal, Vol. 25, pp. 1338-1346, 1987. [6] S. Hui-Shen, Postbuckling of rectangular plates under uniaxial compression combined with lateral pressure, Applied Mathematics and Mechanics, Vol. 10, pp. 55-63, 1989. [7] J. Woo, S. Nair, Nonlinear vibrations of rectangular laminated thin plates, AIAA Journal, Vol. 3, pp. 180-188, 1992. [8] E. Esmailzadeh, M. A. Jalali, Nonlinear oscillations of viscoelastic rectangular plates, Nonlinear dynamics, Vol. 18, pp. 311-319, 1999. [9] S. H. Chen, H. X. Cheung, H. X. Xing, Nonlinear Vibration of Plane Structures by Finite Element and Incremental Harmonic Balance Method, Nonlinear Dynamics, Vol. 26, No. 1, pp. 87–104, 2001. [10] L. Azrar, E. H. Boutyour, M. Potter-Ferry, Non-linear forced vibrations of plates by an asymptotic-numerical method, Journal of Sound and Vibration, Vol. 252, No. 4, pp. 657-674, 2002. [11] P. Ribeiro, A Hierarchical Finite Element for Geometrically Non-linear Vibration of Thick Plates, Meccanica, Vol. 38, No. 1, pp. 117–132, 2003. [12] K. E. Bikri, R. Benmar, M. Bennouna, Geometrically nonlinear free vibrations of clamped simply supported rectangular plates. Part I: the effects of large vibration amplitudes on the fundamental mode shape, Computers and Structures, Vol. 81, pp. 2029-2043, 2003. [13] M. Amabili, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers and Structures, Vol. 82, pp. 2587-2605, 2004. [14] M. Amabili, Non-linear vibrations of doubly curved shallow shells, International Journal of Non-linear Mechanics, Vol. 40, pp. 683-710, 2005. [15] M. Amabili, Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections, Journal of Sound and Vibration, Vol. 291, pp. 539-565, 2006. [16] M. A. Zarubinskaya, W. T. Van Horssen, On the Vibrations of a Simply Supported Square Plate on a Weakly Nonlinear Elastic Foundation, Nonlinear Dynamics, Vol. 40, No. 1, pp. 35–60, 2005. [17] J. Girish, L. S. Ramchandra, Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections, Journal of Sound and Vibration, Vol. 282, pp. 1137-1153, 2005. [18] C. P. Fung, C. S. Chen, Imperfection sensitivity in the nonlinear vibration of functionally graded plates, European Journal of Mechanics, Vol. 25, pp. 425-436, 2006. [19] A. Shooshtari, S. E. Khadem, A multiple scale method solution for the nonlinear vibration of rectangular plates, Scientica Iranica, Vol. 14, pp. 64-71, 2007. [20] F. Bakhtiari-Nejad, M. Nazari, Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate, Nonlinear Dynamics, Vol. 56, pp. 325, 2009. [21] A. Houmat, Nonlinear free vibration of a shear deformable laminated composite annular elliptical plate, Acta Mechanica, pp. 208-281, 2009. [22] M. K. Singha, R. Daripa, Nonlinear vibration and dynamic stability analysis of composite plates, Journal of Sound and Vibration, Vol. 328, pp. 541-554, 2009. [23] M. M. Rashidi, A. Shooshtari, O. Anwar Beg, Homotopy perturbation study of nonlinear vibration of von Karman rectangular plates, Computers and Structures, pp. 46-55, 2012. [24] S. Hashemi, E. Jaberzadeh, A finite strip formulation for nonlinear free vibration of plates, in 15 WCEE, Lisbon, 2012. [25] P. Malekzadeh, Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT, Composite Structures, Vol. 183, pp. 189-200, 2008. [26] P. Malekzadeh, M. Shojaee, Surface and nonlocal effects on the nonlinear free vibration on non-uniform nano beams, Composites: Part B, Vol. 82, pp. 84-92, 2013. [27] N. Ma, R. Wang, Q. Han, Y. Lu, Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions, Science China Physics, Mechanics & Astronomy, Vol. 57, No. 8, pp. 1536–1546, 2014. [28] A. A. Yazdi, Homotopy perturbation method for nonlinear vibration analysis of functionally graded plate, Journal of Vibration and Acoustics, Vol. 135, No. 2, 2013. [29] A. A. Yazdi, Assessment of Homotopy Perturbation Method for Study the Forced Nonlinear Vibration of Orthotropic Circular Plate on Elastic Foundation, Latin American Journal of Solid and Structures, Vol. 13, No. 2, pp. 243-256, 2016. [30] T. Detroux, L. Renson, G. Kerschen, The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems, Nonlinear Dynamics, Vol. 2, pp. 19-34, 2014. [31] T. Detroux, L. Renson, G. Kerschen, The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems, Nonlinear Dynamics, Vol. 1, pp. 65-82, 2016. [32] T. Detroux, L. Renson, L. Masset, G. Kerschen, The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems, Computer Methods in Applied Mechanics and Engineering, Vol. 296, No. 18-38, 2015. [33] A. Daneshmehr, Rajabpoor, A., Hadi, A., Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, Vol. 95, pp. 23-35, 2015. [34] C. Liu, Ke, L.L., Yang, J., Kitipornchai, S., Sheng, Y., Buckling and post-buckling analysis of size-dependent piezoelectric nanoplates, Theoretical & Applied Mechanics Letters, Vol. 6, No. 6, pp. 253-267, 2016. [35] K. KrishnaBhaskar, K. MeeraSaheb, Effects of aspect ratio on large amplitude free vibrations of simply supported and clamped rectangular Mindlin plates using coupled displacement field method, Journal of Mechanical Science and Technology, Vol. 31, pp. 2093-2103, 2017. [36] R. Bellman, B. G. Kashef, J. Casti, Differential Quadrature: A technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, Vol. 10, pp. 40-45, 1972. [37] J. R. Quan, C. T. Chang, New insights in solving distributed system of equations by quadrature-method, Computers & Chemical Engineering, Vol. 13, pp. 1017-1024, 1982. [38] X. Wang, Y. Wang, Free vibration analysis of multiple-stepped beams by the differential quadrature element method, Applied Mathematics and Computation, Vol. 219, No. 11, pp. 5802-5810., 2013. [39] X. Wang, 2015, Differential Quadrature and Differential Quadrature Based element Methods: Theory and Applications, Butterworth-Heinemann, [40] G. A. Wempner, Discrete approximation related to nonlinear theories of solids, International Journal of Solids and Structures, Vol. 7, pp. 1581-1599, 1971. [41] A. Riks, The application of Newton’s method to the problem of elastic stability, Journal of Applied Mechanics, Vol. 39, pp. 1060-1065, 1972. [42] B. D. R. Forde, S. F. Stiemer, Improved arc length orthogonality methods for nonlinear finite element analysis, Computers & Structures,, Vol. 27, pp. 625-630, 1987. [43] N. M. Krylov, N. N. Bogoliubov, 1943, Introduction to non-linear mechanics, Princeton University Press, [44] P. Ribeiro, M. Petyt, Geometrical non-linear, steady state, forced, periodic vibration of plates, part 1: model and convergence studies, Journal of Sound and Vibration, Vol. 226, No. 5, pp. 955-983, 1999. | ||
|
آمار تعداد مشاهده مقاله: 782 تعداد دریافت فایل اصل مقاله: 802 |
||