Analytical solution for a heterogeneous Timoshenko beam subjected to an arbitrary dynamic transverse load

Adámek, Vítězslav; Valeš, František

doi:10.1016/j.euromechsol.2014.07.016

Cited by 13 publications

(10 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is exactly the equation (10) obtained for homogeneous beams, except that K = k 2 is replaced by K. The roots are K + and K − , as given by (11), and the associated wavenumbers are:…”

Section: Available Exact Solutions For Free Vibrationsmentioning

confidence: 60%

“…Moreover, the interest in composite materials, exhibiting continuously varying effective material parameters at the macroscopic level, lead to numerous studies of the so-called functionally graded beams (FGBs). These works propose several ways to take into account a material heterogeneity in the transverse direction [10], in the axial direction [7,11], or in both directions [12]. Ultimately, beams that are both geometrically and materially heterogeneous are also considered [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

“…To help meet this need, the present paper proposes a fast enriched finite element method (FEM) to compute the motion of geometrically heterogeneous beams submitted to time-harmonic loadings. This method is expected to provide a basis for eigenfrequency search [23], modal analysis of beams [24], and time-domain simulations by Fourier synthesis [2,10,15,25].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Cornaggia

Darrigrand

Marrec

et al. 2020

Journal of Sound and Vibration

View full text Add to dashboard Cite

This work presents a new enriched finite element method dedicated to the vibrations of axially inhomogeneous Timoshenko beams. This method relies on the "half-hat" partition of unity and on an enrichment by solutions of the Timoshenko system corresponding to simple beams with a homogeneous or an exponentially-varying geometry. Moreover, the efficiency of the enrichment is considerably increased by introducing a new formulation based on a local rescaling of the Timoshenko problem, that accounts for the inhomogeneity of the beam. Validations using analytical solutions and comparisons with the classical high-order polynomial FEM, conduced for several inhomogeneous beams, show the efficiency of this approach in the time-harmonic domain. In particular low error levels are obtained over ranges of frequencies varying from a factor of one to thirty using fixed coarse meshes. Possible extensions to the research of natural frequencies of beams and to simulations of transient wave propagation are highlighted.

show abstract

“…This is exactly the equation (10) obtained for homogeneous beams, except that K = k 2 is replaced by K. The roots are K + and K − , as given by (11), and the associated wavenumbers are:…”

Section: Available Exact Solutions For Free Vibrationsmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Cornaggia

Darrigrand

Marrec

et al. 2020

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…This code has been previously tested and verified by authors on different transient wave problems (e.g. radial impact on a thin isotropic viscoelastic disc [7], transverse impact on an isotropic viscoelastic strip [2], impact on functionally graded beams [8] etc.) such that it can be said that its use does not mean the loss of analytical results accuracy.…”

Section: Analytical and Numerical Resultsmentioning

confidence: 99%

“…In this subsection, the Laplace transform will be applied to the simplified system (7) - (8). Introducing a new complex variable p and taking into account the zero initial conditions specified in the section 2, the transform of the system (7) -(8) takes the form…”

Section: Application Of Laplace and Fourier Transformsmentioning

confidence: 99%