The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines

Tang Shou-gao; Yuan Si

Volume 13 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(6): 505-513

Tang Shou-gao, Yuan Si. The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines[J]. Applied Mathematics and Mechanics, 1992, 13(6): 505-513.

Citation:

Tang Shou-gao, Yuan Si. The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines[J]. Applied Mathematics and Mechanics, 1992, 13(6): 505-513.

Citation:

Tang Shou-gao, Yuan Si. The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines[J]. Applied Mathematics and Mechanics, 1992, 13(6): 505-513.

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The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines

Tang Shou-gao¹,
Yuan Si²

1.
Tongji University, Shanghai;
2.
Qinghua University, Beijing

Received Date: 1991-04-01
Publish Date: 1992-06-15

Abstract

Abstract

The method of lines based on Hu Hai-chang's theory for the vibration and stability of moderate thick plates is developed.The standard nonlinear ordinary differential equation(ODE) system for natural frequencies and critical load is given by use of ODE techniques,and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition.Numerical examples show that the present method is very effective and reliable.
- moderate thick plate,
- vibration,
- stability,
- method of lines

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References(9)

References

[1]	胡海昌,《弹性力学的变分原理及其应用》,科学出版社,北京(1981).
[2]	Ascher,U.and R.D.Russell,Reformulation of boundary value problems into standard form,SIAM Rev.,23(1981),238-254.
[3]	唐寿高,薄板的振动问题的线法,江西工业大学学报.13(2)(1991),273-279.
[4]	Liskovets,O.A.,The method of lines(Review),Differential Equations,1(1965),1308-1323..
[5]	Xanthis,L.S.,The numerical method of lines and ODE solvers can provide a new powerful computational fracture mechanics tool,Int.Conference on Computational Mechanics,Tokyo,Japan(1986).
[6]	Ascher,U.,J.Christianscn and R.D.Russell,Collocation software for boundary-value ODEs,ACE Trans.Math.Software,7,2(1981),209-222.
[7]	Ascher,U.,J.Christiansen and R.D.Russell,Algorithm 569,COLSYS:collocation software for boundary-value ODEs D2,ACM Trans.Math.Software,7,2(1981),223-229.
[8]	Bader,G.and U.Ascher,A new basis implementation for a mixed order boundary value ODE solver,SIAM J.Sci.Stat.Comput.,8(1987),483-500.
[9]	中科院力学所,《夹层板壳的弯曲、稳定和振动》,科学出版社,北京(1977).

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