Stress Analysis for Viscoelastic Bodies

Lee, E.H.

doi:10.1016/b978-1-4832-2847-1.50005-2

Cited by 55 publications

(71 citation statements)

References 19 publications

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“…The correspondence principle [13,14,33,34] states that if a solution to a linear elasticity problem is known, the solution to the corresponding problem for a linearly viscoelastic material can be obtained by replacing each quantity which can depend on time by its Fourier Transform. In order that the elastic and viscoelastic solutions correspond, the interface between boundary regions under specified displacement and under specified stress must not change with time.…”

Section: Dynamic Effective Thickness By the Correspondence Principlementioning

confidence: 99%

Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

Pelayo

Aenlle

2017

Jnl of Sandwich Structures & Materials

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Multi-layered laminated glass panels are those with at least three monolithic glass layers and two viscoelastic interlayers. Multi-layered laminated glass panels are commonly used in floors, roofs and other horizontal glazing accessible to the public where a high level of security is required. Although the glass can be consider a linear-elastic material, the viscoelastic interlayers determine a non-linear behavior of the laminated structure that must be taken into consideration. In this paper, a dynamic effective thickness is proposed to predict the natural frequencies and damping ratios of multi-layered laminated glass beam-like structures with different boundary conditions and at different temperatures.Furthermore, the presented dynamic effective thickness can be also used to any frequency domain calculations such as displacements and stresses.To validate the proposed model, operational modal analysis was carried out on a multilayered laminated glass beam to obtain the experimental natural frequencies and damping ratios at 20, 25, 30 and 35 . Moreover, a finite element model of the beam was also assembly for the sake of comparison. The proposed model predicts the natural frequencies with errors less than 5% whereas the discrepancies in damping ratios are less than 50%. Greek lettersDensity of the polymeric interlayers Density of the glass layers

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Section: Dynamic Effective Thickness By the Correspondence Principlementioning

confidence: 99%

Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

Pelayo

Aenlle

2017

Jnl of Sandwich Structures & Materials

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“…According to the correspondence principle of linear viscoelasticity (LEE, 1955;RADOK, 1957), the Laplace transforms of quasi-static displacements due to a surface load are directly obtained from the solutions of the associated elastic problem by replacing Lame elastic constants with the S-dependent moduli and all of the time-dependent quantities with their Laplace transforms. Operation of the inverse Laplace transform on the S-dependent solutions yields the quasi-static displacement fields in the time domain.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…2. Derivation of the viscoelastic solutions is directly made by applying the correspondence principle of linear viscoelasticity (LEE, 1955;RADOK, 1957) to the associated elastic solutions. General features of the viscoelastic deformations are examined in Sec.…”

mentioning

confidence: 99%

Quasi-static crustal deformations due to a surface load: Rheological structure of the earth's crust and upper mantle.

Iwasaki

Matsu’ura

1982

J,Phys,Earth

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In this paper, we treat quasi-static displacement fields due to an axially symmetric load applied on the surface of a composite medium which consists of elastic layers overlying a stratified viscoelastic half-space. Integral representations of the surface displacements are obtained from those in the associated elastic problem by applying the correspondence principle of linear viscoelasticity. General features of the viscoelastic displacements are examined from various aspects through the computation of numerical examples for a three-layered model composed of an elastic surface layer, an intervening low viscosity layer and a viscoelastic substratum with relatively high viscosity.Uplift phenomena in two tectonically different regions, Fennoscandia and Lake Bonneville (the Basin and Range province), are analyzed to investigate regional difference in rheological structure of the earth's crust and upper mantle. The uplift data in Fennoscandia are well interpreted by a three-layered model which consists of a 100km thick elastic surface layer (lithosphere) and a 100-200km thick low viscosity layer (asthenosphere) overlying a relatively high

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“…Comparative values for the shift factors as derived by the two techniques are listed in Within the scope of small deformations and time-independent boundaries, the solutions can be obtained by application of the Laplace transform, which eliminates time dependence and reduces the viscoelastic problem to an associated elastic one (Lee, 1955).…”

Section: -12mentioning

confidence: 99%

Thermal Stress Investigation of Solid Propellant Grains. Volume I. Theory and Experiment

Jones¹,

Fitzgerald²,

Francis³

1963

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Stress Analysis for Viscoelastic Bodies

Cited by 55 publications

References 19 publications

Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

Quasi-static crustal deformations due to a surface load: Rheological structure of the earth's crust and upper mantle.

Thermal Stress Investigation of Solid Propellant Grains. Volume I. Theory and Experiment

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