Free Vibrations of Uniform Timoshenko Beams With Attachments

Posiadała, B.

doi:10.1006/jsvi.1997.0952

Cited by 46 publications

(15 citation statements)

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“…Acting on the Lagrange multiplier formalism [11][12][13], the free vibration problem of the analyzed system has been formulated and the solution has been reduced to the matrix system of equations in the following form: [ ]…”

Section: Formulation and Solution Of The Problemmentioning

confidence: 99%

“…In this paper, the free vibration problem of the cantilever tapered beam has been formulated and solved with the help of the Lagrange multiplier formalism [11,12]. The beam has been circumscribed according to the Timoshenko theory.…”

Section: Introductionmentioning

confidence: 99%

“…A more detailed explanation and complement of the above-mentioned mathematical expressions are placed in works [11][12][13].…”

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confidence: 99%

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Free vibration of a cantilever tapered Timoshenko beam

Cekus¹

2012

Sci. Res. Inst. Math. Comp. Sci.

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Section: Formulation and Solution Of The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibration of a cantilever tapered Timoshenko beam

Cekus¹

2012

Sci. Res. Inst. Math. Comp. Sci.

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“…Lin and Chang (2005) studied free vibration analysis of multi-span Timoshenko beam with an arbitrary number of flexible constraints by TMM. Posiadala (1997) considered the transverse free vibration of Timoshenko beams having rotation and translation springs, concentrated mass with moment of inertia, linear undamped oscillators and additional supports, and obtained the frequency equation by Lagrange multiplier formalism. TMM is used with Holzer method for torsional vibration of systems with concentrated masses (Hurty & Rubinstein 1964), and with Myklestad-Thomson method for flexural vibrations of discrete systems with concentrated masses (Thomson 1981).…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods

Demirdağ

2008

Sadhana

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This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of fixity factor is used to define the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by finite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.

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“…But different methods were used to solve natural frequencies of beam carrying different types of attachments and only two articles [18,19] which give details of approach to analyze free vibration of beam with lumped attachments universally are found, the development of the general method for solving natural frequencies of the beam carrying spring-mass system with different distributions is necessary preparation for analysis of free vibration of those structures and become an important part of this article.…”

Section: Introductionmentioning

confidence: 99%

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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Abstract. The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. This manuscript develops a proposed analytical method as a general tool for solving the free vibration of varying cross-section beams carrying various types of attachments with different distributions and arbitrary boundary conditions. In current practice, the natural frequencies of beam carrying lumped and uniform sprung mass and resting on Pasternak soil are calculated and compared with those in references to verify the methodology firstly. Then, the natural frequencies of beam carrying non-uniform spring-mass systems and stepped beam on Pasternak soil are calculated by the proposed method to study free vibration of beam carrying attachments with non-uniform cross section or distribution. Finally, some important conclusions are derived from results, which reveal that distribution density of spring-mass system at peaks of the mode shape makes dominate effects on the change of the natural frequencies at that mode and the natural frequencies of the stepped beam resting on elastic foundation are more sensitive to the increase of soil parameters.

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Free Vibrations of Uniform Timoshenko Beams With Attachments

Cited by 46 publications

References 0 publications

Free vibration of a cantilever tapered Timoshenko beam

Free vibration of a cantilever tapered Timoshenko beam

Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

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