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Application of Integral Transform Method to Calculate Impedance Functions

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2011
Radisic-2011-Application_of_Integral_Transform_Method_to_Calculate_Impedance_Functions.pdf (1.795Mb)
Authors
Radišić, Marko
Nefovska-Danilović, Marija
Petronijević, Mira
Article (Updated Version)
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Abstract
To solve vibration problems of structure founded on the soil, the dynamic behavior of the soil needs to be understood and an accurate dynamic stiffness model of the soil has to be developed. Frequency dependent dynamic stiffness matrix of the massless, flexible soil-structure interface can be calculated analytically or numerically, depending on the complexity of the problem, using Boundary Element Method [1] or Thin Layer Method [3]. In this paper the impedance functions of a stiff rectangular foundation laying on a half-space are determined with the help of the Integral Transform Method (ITM) [4]. The Integral Transform Method is an efficient method to calculate wave propagation in an elastic homogeneous, or layered half-space. By the use of the decomposition of Helmholtz, the Lamé’s equations of elastodynamics are converted to a system of decoupled partial differential wave equations in space-time domain. With the help of a threefold Fourier Transform in the wave number-fr...equency domain wave equations can be transformed into a system of three decoupled ordinary differential equations which can be solved in the transformed domain. The results in the original domain can be finally obtained by an Inverse Fourier Transform. Using ITM method the dynamic stiffness of flexible foundation are determinate first. After that the impedance functions of the stiff foundation are obtained using kinematic transformation matrix. The obtained results are compared with impedance functions from literature.

Source:
Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics, 2011, 994-1006
Funding / projects:
  • Towards development of sustainable cities: influence of traffic induced vibrations on buildings and humans (RS-36046)

ISBN: 978-86-909973-3-6

[ Google Scholar ]
URI
https://grafar.grf.bg.ac.rs/handle/123456789/2145
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за техничку механику и теорију конструкција
Institution/Community
GraFar
TY  - JOUR
AU  - Radišić, Marko
AU  - Nefovska-Danilović, Marija
AU  - Petronijević, Mira
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2145
AB  - To solve vibration problems of structure founded on the soil, the dynamic
behavior of the soil needs to be understood and an accurate dynamic stiffness model of the
soil has to be developed. Frequency dependent dynamic stiffness matrix of the massless,
flexible soil-structure interface can be calculated analytically or numerically, depending on
the complexity of the problem, using Boundary Element Method [1] or Thin Layer Method
[3]. In this paper the impedance functions of a stiff rectangular foundation laying on a
half-space are determined with the help of the Integral Transform Method (ITM) [4]. The
Integral Transform Method is an efficient method to calculate wave propagation in an elastic
homogeneous, or layered half-space. By the use of the decomposition of Helmholtz, the
Lamé’s equations of elastodynamics are converted to a system of decoupled partial differential
wave equations in space-time domain. With the help of a threefold Fourier Transform in the
wave number-frequency domain wave equations can be transformed into a system of three
decoupled ordinary differential equations which can be solved in the transformed domain. The
results in the original domain can be finally obtained by an Inverse Fourier Transform. Using
ITM method the dynamic stiffness of flexible foundation are determinate first. After that
the impedance functions of the stiff foundation are obtained using kinematic transformation
matrix. The obtained results are compared with impedance functions from literature.
T2  - Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics
T1  - Application of Integral Transform Method to Calculate Impedance Functions
EP  - 1006
SP  - 994
ER  - 
@article{
author = "Radišić, Marko and Nefovska-Danilović, Marija and Petronijević, Mira",
year = "2011",
abstract = "To solve vibration problems of structure founded on the soil, the dynamic
behavior of the soil needs to be understood and an accurate dynamic stiffness model of the
soil has to be developed. Frequency dependent dynamic stiffness matrix of the massless,
flexible soil-structure interface can be calculated analytically or numerically, depending on
the complexity of the problem, using Boundary Element Method [1] or Thin Layer Method
[3]. In this paper the impedance functions of a stiff rectangular foundation laying on a
half-space are determined with the help of the Integral Transform Method (ITM) [4]. The
Integral Transform Method is an efficient method to calculate wave propagation in an elastic
homogeneous, or layered half-space. By the use of the decomposition of Helmholtz, the
Lamé’s equations of elastodynamics are converted to a system of decoupled partial differential
wave equations in space-time domain. With the help of a threefold Fourier Transform in the
wave number-frequency domain wave equations can be transformed into a system of three
decoupled ordinary differential equations which can be solved in the transformed domain. The
results in the original domain can be finally obtained by an Inverse Fourier Transform. Using
ITM method the dynamic stiffness of flexible foundation are determinate first. After that
the impedance functions of the stiff foundation are obtained using kinematic transformation
matrix. The obtained results are compared with impedance functions from literature.",
journal = "Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics",
title = "Application of Integral Transform Method to Calculate Impedance Functions",
pages = "1006-994"
}
Radišić, M., Nefovska-Danilović, M.,& Petronijević, M.. (2011). Application of Integral Transform Method to Calculate Impedance Functions. in Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics, 994-1006.
Radišić M, Nefovska-Danilović M, Petronijević M. Application of Integral Transform Method to Calculate Impedance Functions. in Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics. 2011;:994-1006..
Radišić, Marko, Nefovska-Danilović, Marija, Petronijević, Mira, "Application of Integral Transform Method to Calculate Impedance Functions" in Third Serbian (28th Yu) Congress on Theoretical and Applied Mechanics (2011):994-1006.

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