• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.87-95
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• 2000

The two eigenvalues (elastic critical load and natural frequency of lateral vibration) of sinusoidally tapered bats with simply supported ends were determined by the finite element method. For the convenience of structural engineers who are engaged in the structural design or vibration analysis of tapered beam-columns, eigenvalue coefficients were expressed by simple algebraic equations. The validity of each algebraic equation was confirmed by the value of unity for each correlation coefficient. The influence of axial thrust on the lateral vibration frequency was also investigated. For this purpose, the axial thrust was increased successively and the corresponding frequency was calculated. The approximate linear relationship between the axial thrust and the square of the frequency was confirmed lot each of the tapered members.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.263-270
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• 2000

It is generally known that the stress and displacement of a member or a system under dynamic load with frequency ω are magnified by the factor 1/[1-(ω/ω/sub 0/)sup/ 2/]. When the member assumes non-prismatic shape, the natural frequency, ω/sub 0/ is hard or impossible to determine if the conventional method are adopted. In these cases, the numerical methods are provide powerful tools for the solution of frequency problems. In this paper, finite element method is applied to determine the natural frequencies of the non-symmetrically tapered members. The shape of the member is assumed to change sinusoidally along its axis. The results obtained by finite element method are expressed by some simple algebraic equations. The estimated frequencies calculated by the proposed equations coincide well with those by the finite element method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.59-66
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• 2000

It is generally known that the lateral frequency( ω) of the vibration of a prismatic beam-column decreases according to the rele (equation omitted) (ω/sub 0/=natural frequency). In the cases of tapered members, the determination of P/ sub/ cr/(elastic critical load) and ω/ sub 0/ are not easy. Furthermore, the relationship between the compressive load and frequency can not be determined by the conventional analytical method. The axial force-frequency relationship of sinusolidally non-symmetrically tapered members with different shapes were investigated using the finite element method. To obtain the two eigenvalues, the axial thrust was increased step by step and the corresponding frequency was calculated. The result indicated that the axial thrust of the elastic critical load ratio and the square of the frequency ratio can be approximately represented in any case by a straight line. Finally, the linear relationship is also applicable to the sinusolidally non-symmetrically tapered member.