Dynamic response of a poro-elastic soil to the action of long water waves: Determination of the maximum liquefaction depth as an eigenvalue problem

2017 ◽  
Vol 67 ◽  
pp. 213-224 ◽  
Author(s):  
E. Arcos ◽  
E. Bautista ◽  
F. Méndez
Keyword(s):  
Eigenvalue Problem ◽  
Dynamic Response ◽  
Water Waves ◽  
Elastic Soil

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

Elastic Layer Pressed Against a Half Space

1974 ◽  
Vol 41 (3) ◽  
pp. 703-707 ◽  
Author(s):  
K. C. Tsai ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Layer ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Auxiliary Functions ◽  
Receding Contact ◽  
Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

Calculation of Coupled Modes for Vibro-Acoustic Problems

2012 ◽  
Vol 488-489 ◽  
pp. 1691-1696
Author(s):  
M. Beldi ◽  
Z. Lamia
Keyword(s):  
Numerical Methods ◽  
Eigenvalue Problem ◽  
Numerical Method ◽  
Stiffness Matrix ◽  
Fluid Pressure ◽  
Singular Matrix ◽  
Coupled Modes ◽  
Acoustic Modes ◽  
Change Of Variable

A new numerical method for the study of elasto-acoustic structures coupled with fluid-filled cavities has been developed. This method essentially consists of solving the eigenvalue problem for the determination of elasto-acoustic modes. The Numerical methods commonly used for its resolution is based on the mass coupling. However, this approach requires for it is resolution the inversion of a singular matrix, "the stiffness matrix of the fluid". We then propose a new numerical method based on stiffness coupling by using modal superposition techniques through a change of variable which shows a symmetric and regular problem in terms of displacement of the elastic structure and in terms of fluid pressure in the cavity.

Dynamic Response of a Porous Seabed and an Offshore Pile to Linear Water Waves

2008 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Dynamic Response ◽  
Water Waves ◽  
Coupled Model ◽  
Expansion Method ◽  
Wave Theory ◽  
Horizontal Displacement ◽  
Element Model ◽  
Wave Force ◽  
Acoustic Medium ◽  
Linear Wave

In this study, a coupled model is proposed to investigate dynamic response of a porous seabed and an offshore pile to ocean wave loadings. Both the offshore pile and the porous seabed are treated as a saturated poro-elastic medium, while the seawater is considered as a conventional acoustic medium. The coupled boundary element model is established by the continuity conditions along the interfaces between the three media. In the system, wave force is considered as an external load and it is evaluated via the wave function expansion method in the context of a linear wave theory. Numerical results show that the increase of the modulus ratio between the pile and the seabed can reduce the horizontal displacement of the pile and the pore pressures of the seabed around the pile. Furthermore, the maximum pore pressure of the seabed usually occurs at the upper part of the seabed around the pile.

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