Planar internal Lamb problem: Waves in the epicentral zone of a vertical power source

Kuznetsov, S. V.; Terentjeva, E. O.

doi:10.1134/s1063771015030112

Cited by 31 publications

(12 citation statements)

References 49 publications

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“…Note that these angles are invariant under the (same) linear transformation of the axes. 51 Instead of finding angles ψ, more consistent results can be achieved at computing the scalar product of the following unit vectors…”

Section: Physical Propertiesmentioning

confidence: 99%

On infinite group velocity in composite plates

Kuznetsov

2023

Jnl of Sandwich Structures & Materials

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The analytical and geometrical conditions for the possible appearance of the infinite group velocity (IGV) points belonging to the dispersion curves of Lamb waves propagating in traction-free plates are studied by a combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method. According to the obtained geometrical condition, the IGV corresponds to the coincidence of a tangent line to any of the dispersion curves with a straight line passing through the origin. The developed technique is demonstrated by applying to the analysis of Lamb wave dispersion in three-layered plates with a soft inner core.

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Section: Physical Propertiesmentioning

confidence: 99%

On infinite group velocity in composite plates

Kuznetsov

2023

Jnl of Sandwich Structures & Materials

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“…3). This distance depends on the source depth h and the physical properties of the medium [25][26][27], and…”

Section: Head Sp Wavesmentioning

confidence: 99%

“…3 wave S 1 falls on the free surface, forming reflected waves: transversal (SS 1 ) and longitudinal (SP 1 ), in a similar way, wave S 2 falls on the free surface, forming reflected waves (SS 2 ) and longitudinal (SP 2 ), the latter moves parallel to the free surface by forming a head wave. The angle at which the S 2 wave falls is called the critical angle, it is determined by the following expression [27]:…”

Section: Head Sp Wavesmentioning

confidence: 99%

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Seismic Barriers for Protection Against Surface and Headwaves: Multiple Scatters and Metamaterials

2021

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“…Метод конечных элементов (МКЭ) является эффективным способом решения задач дифракции волн в различных средах. Применения КЭ моделирования к учету диссипации энергии в конструкциях, к наложению неотражающих граничных условий, к моделированию сейсмических источников и к сейсмической защите рассмотрены в работах [3] и [5][6][7][8][9][10][11][12].…”

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Drucker-Prager Models for Dynamic Analysis of Granular Metamaterials in Earthquake Engineering

A.A.

2021

Construction Materials and Products

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Problem of developing methods for protecting buildings and structures from the vibrations transmitted to them from the soil under the action of seismic effects is extremely important to date. One of these modern methods is seismic pads. The purpose of this work was to study the effectiveness of adding a pad of granu-lar metamaterials under the foundation of the building to decrease influence of seismic shear waves. The Finite Element Analysis of Mohr-Coulomb models was used to achieve this goal. The FE model consists of a ten-story superstructure rested on the slab foundation, under which there is a layer of granular metamateri-als. The values of five variables that affect the mechanical properties of these metamaterials were analyzed (density – cohesion – internal friction angle – Young's modulus – Poisson's ratio) for two different pad thicknesses. The dynamic analysis performed using the software package Abaqus/CAE showed the effec-tiveness of the granular metamaterials in their ability to significantly reduce magnitudes of displacements, velocities and accelerations in the building compared to the same values in the absence of these metamateri-als. The analysis also revealed that among the studied variables, the cohesion is the parameter most influenc-ing the effectiveness of metamaterials in their ability to dissipate seismic waves, while no significant effect was observed for the other parameters

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Planar internal Lamb problem: Waves in the epicentral zone of a vertical power source

Abstract: We analyze the field in the epicentral zone for the internal Lamb problem of the action of a con centrated force within an elastic half plane. We compare the solutions obtained using integral representa tions, geometric optical methods, and finite element approximations.

Cited by 31 publications

References 49 publications

On infinite group velocity in composite plates

On infinite group velocity in composite plates

Seismic Barriers for Protection Against Surface and Headwaves: Multiple Scatters and Metamaterials

Drucker-Prager Models for Dynamic Analysis of Granular Metamaterials in Earthquake Engineering

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