Nonlinear vibration analysis of harmonically excited cracked beams on viscoelastic foundations

Younesian, Davood; Marjani, Seyed Rahim; Esmailzadeh, Ebrahim

doi:10.1007/s11071-012-0644-3

Cited by 20 publications

(3 citation statements)

References 18 publications

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“…By the Extended Finite Element Method and generalized Heaviside function, Zhang et al [26] numerically investigated the deformations in a viscoelastic cracked body such as crack opening and sliding displacements. Combining the Galerkin method and multiple scale method, Younesian et al [27] analyzed the frequency response of a cracked beam supported by a nonlinear viscoelastic foundation. Based on the Fourier transform and the principle of virtual work, Sarvestan et al [28] presented a spectral finite element model for vibration analysis of the Euler-Bernoulli Kelvin-Voigt cracked beam.…”

Section: Introductionmentioning

confidence: 99%

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Yang

2021

Advances in Civil Engineering

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Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additionally, the effects of the time, slenderness ratio, and crack depth on the bending deformations of the different cracked beam models are revealed.

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Section: Introductionmentioning

confidence: 99%

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Yang

2021

Advances in Civil Engineering

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“…Harmonically excited vibrations of a cracked beam were scrutinized using the MSM. Accordingly, the frequency response of the cracked beam was obtained, and the effect of different parameters, namely the geometry and location of the crack, loading position and the linear and nonlinear foundation parameters on the frequency response solution were studied (Younesian et al., 2013). Three-to-one internal resonances in a hinged–clamped beam were studied by Chin and Nayfeh (1997).…”

Section: Introductionmentioning

confidence: 99%

Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations

Saadatnia

Argani

Esmailzadeh

2017

Journal of Vibration and Control

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The multi-frequency excitation of a microbeam, resting on a nonlinear foundation, is investigated and the governing equation of motion of the microbeam system is developed. The viscoelastic-type foundation is considered by assuming nonlinear parameters for both Pasternak and Winkler coefficients. The well-known Galerkin approach is utilized to discretize the governing equation of motion and to obtain its nonlinear ordinary differential equations. The multiple time-scales method is employed to study the multi-frequency excitation of the microbeam. Furthermore, the resonant conditions due to the external excitation as well as the combination resonances for the first two modes are investigated. The influences of different parameters, namely the Pasternak and Winkler coefficients, the position of the applied force and the geometrical factors on the frequency response of the system are examined.

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“…More recently, Esmailzadeh (2010, 2011) studied the free and the forced nonlinear vibrations of rotary blades by utilizing the multiple scales method. They have also investigated the nonlinear vibration of harmonically excited beams on viscoelastic foundations (Younesian et al (2006(Younesian et al ( , 2008(Younesian et al ( , 2013.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of circular annular plates subjected to peripheral rotating transverse loads

Younesian

Aleghafourian

Esmailzadeh

2013

Journal of Vibration and Control

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Vibration of a hollow circular plate subjected to a rotating peripheral force is analytically studied in this paper. Closed-form solutions are developed in a series form for the plate deflection as well as the distributions of the strain and stress. The Galerkin approach is adopted as the solution method and a finite element model has also been developed. Computer simulations were performed to verify the model and solution methods were adopted. Close agreement is observed when comparing the numerical results with those obtained from the analytical technique. The acoustic pressure field is eventually obtained in front of the vibrating plate surface using the Rayleigh integral method. The solution procedure presented and the numerical results obtained can be extensively utilized in the noise source separation. This has always been a significant challenge in many engineering applications such as the railway wheel-rail dynamics or that of the automotive gear trains.

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Nonlinear vibration analysis of harmonically excited cracked beams on viscoelastic foundations

Cited by 20 publications

References 18 publications

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations

Vibration analysis of circular annular plates subjected to peripheral rotating transverse loads

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