The Forced Vibration of a Beam With Viscoelastic Boundary Supports

Fan, Zi Jie; Lee, J.-H.; Kang, K. H.; Kim, K.-J.

doi:10.1006/jsvi.1997.1353

Cited by 24 publications

(5 citation statements)

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“…Donde 𝑎 es la amplitud transversal máxima no dimensional de la viga. Sustituyendo la función 𝜃 en la Ecuación (9). obtenemos el campo de desplazamiento acoplado transversal 𝑤, después de la integración se obtiene la Ecuación (14), existe concordancia conforme a las constantes 𝐸𝐼, 𝑘 y 𝐺𝐴 con el planteamiento de Austin et al [18], lo que nos indica que las funciones de rotación asumidas con correctas.…”

Section: D2) Función Admisible De Rotación -Caso Viga Empotradaapoyadaunclassified

“…Fan et al [9] desarrolló un método para responder a problemas de dinámica no lineal basado en el principio de Hamilton, el análisis espectral, el principio de Lagrange y el método de equilibrio armónico. Este enfoque reduce el problema dinámico a un conjunto de ecuaciones algebraicas no lineales que dependen de la matriz de masa y la rigidez clásica.…”

Section: Introductionunclassified

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Analysis of Forced Vibrations in Timoshenko Beams Using the Coupled Displacement Field Concept

Azaña-Margarito¹,

Zarate-Perez²,

Zarate-Perez³

2022

Proceedings of the 2nd LACCEI International Multiconference on Entrepreneurship, Innovation and Regional Development (LEIRD 202

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Modular construction is an excellent technique for achieving the rapid and safe development of facilities in light of the COVID-19pandemic. Beams are fundamental to modular construction. However, owing to various environmental conditions, novel methods are required to collect the characteristics for conducting structural analysis of beams according to the required needs. In this study, the performance of the coupled displacement field method in beam analysis was evaluated. The expressions for the transverse displacement were derived using an allowable function of total rotation. The function was obtained using the finite-element approximation method based on undetermined coefficients. Thus, the equation of motion was derived using the principle of conservation of energy. The Newmark method and mode superposition technique were then used to solve the obtained equations in MATLAB. The resultsshowed that the method used was suitable in applications that require the analysis of high-slenderness beams in modular constructions. In this method, strong vibrations were induced in the beam owing to its greater flexibility. The recommended method is less complex than other energy methods because the computational effort is halved. Therefore, this formulation can be applied to conduct the free vibration analysis of flexible structural members under various shears using Timoshenko beam models under various boundary conditions. Thus, the coupled displacement field method can be used to derive appropriate solutions to other complex problems, such as modular construction.

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Section: D2) Función Admisible De Rotación -Caso Viga Empotradaapoyadaunclassified

Section: Introductionunclassified

Analysis of Forced Vibrations in Timoshenko Beams Using the Coupled Displacement Field Concept

Azaña-Margarito¹,

Zarate-Perez²,

Zarate-Perez³

2022

Proceedings of the 2nd LACCEI International Multiconference on Entrepreneurship, Innovation and Regional Development (LEIRD 202

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“…In practical application occasion, the beam structure will be installed in different ways, and its dynamic behavior and vibration characteristics with various boundary conditions has been widely studied, such as the clamped-clamped boundaries (Maurizi and Bambill, 1987; Rao, 1989), the cantilevered boundary (Gürgöze et al, 1995), the general boundary restraints (Fan et al, 1998; Kang and Kim, 1996; Kim and Kim, 2001; Wang and Lin, 2001), and so on. These studies mentioned above are mainly performed by using Fourier series for the vibration characteristics analysis of the beam structure.…”

Section: Introductionmentioning

confidence: 99%

Vibration suppression and dynamic behavior analysis of an axially loaded beam with NES and nonlinear elastic supports

Zhao

Liu

2021

Journal of Vibration and Control

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Recently, dynamic analysis of a beam structure with nonlinear energy sink (NES) and various supports is attracting great attention. Most of the existing studies are about the beam structure with NES or nonlinear boundary supports with zero rotational restraint, respectively. However, there is little research accounting for such two types of complex factors simultaneously. In this work, the dynamic behavior of an axially loaded beam with both NES and general boundary supports is modeled and studied. The Galerkin truncated method (GTM) is employed to make the prediction of dynamic behavior of such a beam system, in which the mode functions of axially loaded Euler–Bernoulli beam with linear elastic boundary conditions are selected as the trail and weight functions. Then, the Galerkin condition is used to discretize the nonlinear governing equation of the beam system and establish the residual equations. The Runge–Kutta method is used to solve the residual matrix which consists of residual equations directly, and the harmonic balance method is also used to verify the results from the GTM. The influence of NES on vibration suppression and dynamic behavior of the beam structure is investigated and discussed. Results show that the vibration states of the beam structure can be transformed effectively through the change of NES parameters. On the other hand, the NES with suitable parameters has a beneficial effect on the vibration suppression at both ends of the beam structure.

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“…Governing differential equations were developed through variational calculus and solution algorithm involved Runge-Kutta method. Fan et al (1998) proposed a method for the forced response analysis of a beam with viscoelastic boundary supports, based on complex normal mode analysis. Wang and Chou (1998) carried out nonlinear dynamic analysis of a Timoshenko beam, under the coupling effect of external moving force with the self-weight of the beam, employing large deflection theory.…”

Section: Introductionmentioning

confidence: 99%

“…be separable in space and time(Fan et al 1998;Kadiri et al 2002) and can be approximately represented by sets of orthogonal coordinate functions…”

mentioning

confidence: 99%

Large amplitude forced vibration analysis of cross-beam system through energy method

Mitra¹,

Sahoo²,

Saha³

2010

Int. J. Eng. Sci. Tech

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Large amplitude forced vibration behaviour of cross-beam system under harmonic excitation is studied, incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak load value, thus reducing the problem to an equivalent static case. The two beams of the system are solved individually either by a direct substitution method employing successive relaxation technique or a multi-dimensional secant method, known as Broyden's method. An iterative scheme, based on the reaction force between the two beams of the system and equality of vibration amplitude at the contact of two beams, is developed to obtain the response of the system under external harmonic excitation. The present method is validated through results generated in ANSYS 11.0. The system response is studied for various loading type and contact location of the beams. The results are presented in terms of plots of vibration amplitude of the contact point versus frequency of forcing excitation in dimensional plane.

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The Forced Vibration of a Beam With Viscoelastic Boundary Supports

Cited by 24 publications

References 0 publications

Analysis of Forced Vibrations in Timoshenko Beams Using the Coupled Displacement Field Concept

Analysis of Forced Vibrations in Timoshenko Beams Using the Coupled Displacement Field Concept

Vibration suppression and dynamic behavior analysis of an axially loaded beam with NES and nonlinear elastic supports

Large amplitude forced vibration analysis of cross-beam system through energy method

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