On Dynamic Optimization of Timoshenko Beam

Cheng Keng-tung; Ding Hua

Volume 4 Issue 1

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Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(1): 69-76

Cheng Keng-tung, Ding Hua. On Dynamic Optimization of Timoshenko Beam[J]. Applied Mathematics and Mechanics, 1983, 4(1): 69-76.

Citation:

Cheng Keng-tung, Ding Hua. On Dynamic Optimization of Timoshenko Beam[J]. Applied Mathematics and Mechanics, 1983, 4(1): 69-76.

Citation:

Cheng Keng-tung, Ding Hua. On Dynamic Optimization of Timoshenko Beam[J]. Applied Mathematics and Mechanics, 1983, 4(1): 69-76.

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On Dynamic Optimization of Timoshenko Beam

Research Institute of Engineering Mechanics, Dalian Institute of Technology, Dalian

Received Date: 1982-06-24
Publish Date: 1983-02-15

Abstract

Abstract

The present paper discusses the minimum weight design problem for Timoshenko and Euler beams subjected to multi-frequency constraints. Taking the simply-supported symmetric beam as an example,we reveal the abnormal characteristics of optimal Timoshenko beams,i.e.,the frequency corresponding to the first symmetric vibration mode could be higher than the frequency of antisymmetric vibration mode if a very thin and high strip is suitably formed at the middle of the beam,and optimal Timoshenko beams subjected to two different sets of frequency constraints could have the same minimum weight. The above abnormal characteristics demonstrate the need for including maximum cross sectional area constraint in the problem formulation in order to have a well-posed problem.

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References(9)

References

[1]	Niordson,F.I.,On the optimal design of a vibrating beam,Quart.Appl.Mech.,23,(1965),47-53.
[2]	Olhoff,N.,Otimization of vibrating beams with respect to higher order natural frequencies,J.Struct.Mech.,4(1),(1976),87-122.
[3]	Cheng,K.T.and N.Olhoff,Regularized formulation for optimal design of axisymmetric plates,Int.J.of Solid and Struct.,17,(1981).
[4]	Kamat,M.P.,Effect of shear deformation and rotary inertia on optimum beam frequencies,Int.J.Numer.Methods.Eng.,9(1),(1975),51-62.
[5]	Pierson,B.L.,Minimum weight vibrating beam design,J.Struct.Mech.,5,(1977),147-178.
[6]	Warner,W.H.and D.J.Varrick,Optimal design in axial motion for several frequency constraints,J.Optim.Theory Appl.,15(1),(1975),157-166.
[7]	Kohn,R.V.and G.Strang,Structural design optimization,homogenization and relaxation of variationa1problems,Proc.of Conf.On Disordered Media,NYU,June(1981),Springer-Verlag.
[8]	Prager,W.,Unexpected results in structural optimization,J.Struct.Mech.9(1),(1981),71-90.
[9]	Pedersen,P.,Integrating finite element and linear programning in design,DCAMM Report,No.S 18,(March,1981).

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