Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

Yeşilce, Yusuf

doi:10.1155/2011/892736

Cited by 14 publications

(9 citation statements)

References 28 publications

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“…Numerous authors have studied the free and/or forced response of beams carrying in-span mass or spring-mass systems. In most investigations on the free vibration, different authors have used analytical methods to determine the exact solutions for the natural frequencies and mode shapes (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13] and references mentioned therein).…”

Section: Introductionmentioning

confidence: 99%

On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

Barry

Oguamanam

2014

Shock and Vibration

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The exact natural frequencies, mode shapes, and the corresponding orthogonality relations are important in forced vibration analysis via modal expansion. In the present paper, a free vibration analysis is conducted to determine the exact natural frequencies and mode shapes of an axially loaded beam carrying several absorbers. An explicit expression is presented for the generalized orthogonality relations. These generalized orthogonality conditions are employed along with the assumed modes method to perform forced vibration analysis. The present approach is compared to other approximate methods in the literature with the classical orthogonality relations and different choice of mode shapes. The results indicate that the use of the generalized orthogonality relation with the exact mode shapes is required for a precise investigation of the dynamic response of a beam with mass-spring-mass-damper system.

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Section: Introductionmentioning

confidence: 99%

On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

Barry

Oguamanam

2014

Shock and Vibration

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“…When investigating the forced vibration of beams, the traditional methods are direct integration method and mode superposition approach. Kim and Dickinson (1988), Yesilce and Demirdag (2008), and Yesilce (2013) studied the forced vibration of beams by mode superposition method. Green’s function is another method to deal with the definite solution problem.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

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This paper aims to investigate forced vibrations of Timoshenko nanobeam, which is under axially loaded. The material is assumed to be magneto-electro-elastic coupling and surface effect is considered. The governing equations and the corresponding boundary conditions are derived, with the Hamilton principle. For steady-state forced vibrations, the variable separation and the Laplace transform methods are employed to obtain the Green’s function, for three typical kinds of beams, namely Hinged-Hinged, Clamped-Clamped, and Clamped-Free. Numerical examples are performed to check the validity of the present solutions and to evaluate the influence of magneto-electric coupling and surface effect on the forced vibration of the beams.

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“…They concluded that increasing the axial compressive force leads to reduction in natural frequency unlike increasing the relative stiffness and the stiffness ratio which leads to increasing in natural frequency. Yesilce (2011) investigated the free vibration analysis of multi-span beams carrying multiple spring-mass systems based on TSDT. They used the exact solutions for the natural frequencies and mode shapes.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of cracked beam based on Reddy beam theory by finite element method

Taima

El-Sayed

Shehab

et al. 2022

Journal of Vibration and Control

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The lateral vibration of cracked isotropic thick beams is investigated. Generally, the analysis of thick beam based on line elements can be undertaken using either Timoshenko beam theory or a third order beam theory (TSDT) such as Reddy beam theory. TSDT is superior to Timoshenko beam theory, as it eliminates the need for a shear correction coefficient. However, there is no available solution for a cracked beam based on Reddy beam theory which is the main focus of this paper. The investigated beam is divided into several elements where their stiffness and mass matrices are derived using Reddy beam theory. Each element has two nodes with 3 degrees of freedom (1 lateral and 2 rotational) at each node. The crack was modeled using two rotating springs with stiffnesses that varied with crack depth. These elements are used to connect the adjacent beam elements. The impact of boundary conditions, slenderness ratio, crack location, and crack depth are investigated. In addition, experimental and finite element analyses of cracked steel beams is undertaken to validate the results of the present model. The results show that the maximum deviation between the analytical and the experimental results is less than 3% up to the third mode shape.

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Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

Cited by 14 publications

References 28 publications

On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Vibration analysis of cracked beam based on Reddy beam theory by finite element method

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