Dam-Reservoir Interaction Including the Effect of Vertical Component of Earthquake Acceleration on Hydrodynamic Pressure

2011 ◽  
Vol 255-260 ◽  
pp. 3493-3499
Author(s):  
Reza Attarnejad ◽  
Amirhossein Bagheri
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Transient Analysis ◽  
Separation Of Variables ◽  
Vertical Component ◽  
Hydrodynamic Pressure ◽  
Horizontal Component ◽  
Dam Reservoir ◽  
Vertical Accelerations ◽  
Infinite Reservoir

In this paper, time domain transient analysis of dam-reservoir interaction is studied. Resulting hydrodynamic pressure is exactly calculated including the effect of vertical component of earthquake acceleration as well as the horizontal component. Method of separation of variables is applied to solve resulting partial differential equation after applying Laplace transform. Sommerfeld’s boundary condition is used in far end of the infinite reservoir. Finally, a comparison is made between the results of the case involving both horizontal and vertical accelerations and the case of applying vertical component only using El Centro earthquake (1940) data.

Transient Analysis of Dam-Reservoir Interaction Based on Dynamic Stiffness of SBFEM

2011 ◽  
Vol 378-379 ◽  
pp. 213-217
Author(s):  
Shang Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Domain ◽  
Transient Analysis ◽  
Ground Motions ◽  
Dynamic Stiffness ◽  
Dam Reservoir ◽  
The Time Domain ◽  
Infinite Reservoir ◽  
Element Method

The scaled boundary finite element method (SBFEM) was extended to solve dam-reservoir interaction problems in the time domain and a dynamic stiffness used in the SBFEM of semi-infinite reservoir in the time domain was proposed, which was evaluated by the Bessel function. Based on the dynamic stiffness, transient responses subjected to horizontal ground motions were analyzed through coupling the SBFEM and finite element method (FEM). A dam was modeled by FEM, while the whole fluid in reservoir was modeled by the SBFEM alone or a combination of FEM and SBFEM. Two benchmark examples were considered to check the accuracy of the dynamic stiffness. Results were compared with those from analytical or substructure methods and good agreements were found.

Accurate analytical/numerical solution of the heat conduction equation

2014 ◽  
Vol 24 (7) ◽  
pp. 1519-1536 ◽  
Author(s):  
Antonio Campo ◽  
Abraham J. Salazar ◽  
Diego J. Celentano ◽  
Marcos Raydan
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Time Domain ◽  
Heat Conduction Equation ◽  
Separation Of Variables ◽  
Method Of Lines ◽  
Conduction Equation ◽  
Content Type ◽  
Entire Time

Purpose – The purpose of this paper is to address a novel method for solving parabolic partial differential equations (PDEs) in general, wherein the heat conduction equation constitutes an important particular case. The new method, appropriately named the Improved Transversal Method of Lines (ITMOL), is inspired in the Transversal Method of Lines (TMOL), with strong insight from the method of separation of variables. Design/methodology/approach – The essence of ITMOL revolves around an exponential variation of the dependent variable in the parabolic PDE for the evaluation of the time derivative. As will be demonstrated later, this key step is responsible for improving the accuracy of ITMOL over its predecessor TMOL. Throughout the paper, the theoretical properties of ITMOL, such as consistency, stability, convergence and accuracy are analyzed in depth. In addition, ITMOL has proven to be unconditionally stable in the Fourier sense. Findings – In a case study, the 1-D heat conduction equation for a large plate with symmetric Dirichlet boundary conditions is transformed into a nonlinear ordinary differential equation by means of ITMOL. The numerical solution of the resulting differential equation is straightforward and brings forth a nearly zero truncation error over the entire time domain, which is practically nonexistent. Originality/value – Accurate levels of the analytical/numerical solution of the 1-D heat conduction equation by ITMOL are easily established in the entire time domain.

scholarly journals Numerical Uncoupling of Domains in Dam-Reservoir Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Saba Golchin ◽  
Reza Attarnejad ◽  
Shahram Vahdani
Keyword(s):  
Numerical Model ◽  
Nonlinear Analysis ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Solution Method ◽  
Iterative Scheme ◽  
Hydrodynamic Pressure ◽  
Accurate Method ◽  
Dam Reservoir ◽  
Total Model

Flexibility of dam structure affects the hydrodynamic pressure acting on the dam. Several approaches have been proposed to consider this effect. Most of these approaches are involved with an iterative scheme. Of course solving the total numerical model including the dam and the reservoir is the most accurate method, but it has certain deficiencies. Using the frontal solution method of total model, dam structure, and fluid domain and keeping the interface degrees of freedom in the front is proposed in the current study. Having the solution of the interface degrees of freedom, the structure and fluid may be analyzed separately. The main advantage of the method lies in the fact that the accuracy of the results is the same as analysis of the total model, no iteration is necessary, combination of Lagrangian and Eulerian formulations for solid and fluid may be used, and the unknown variables are of the same order. Performing the analysis in time domain extends the method to nonlinear analysis if required.

scholarly journals Evaluation of Hydrodynamic Pressure Distribution in Reservoir of Concrete Gravity Dam under Vertical Vibration Using an Analytical Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Majid Pasbani Khiavi ◽  
Ali Sari
Keyword(s):  
Analytical Solution ◽  
Separation Of Variables ◽  
Vertical Component ◽  
Hydrodynamic Pressure ◽  
Vertical Vibration ◽  
Gravity Dam ◽  
Harmonic Load ◽  
Concrete Gravity Dam ◽  
Vertical Excitation ◽  
Hydrodynamic Wave

Fluid-structure interaction causes a hydrodynamic force, which can be exerted to the dam and affects its response. The effect of vertical excitation of ground motion on dynamic behavior of concrete gravity dam is the most important because of the interaction between foundation and reservoir. So, the foundation-reservoir interaction should be taken into account in designing concrete dams. In most studies, the effects of the vertical component of vibration have been ignored. While in vertical vibration, due to the interaction of the reservoir and the foundation, a significant hydrodynamic pressure is produced in the tank, which increases the dam response. In this study, the hydrodynamic pressure wave propagation in the reservoir of a concrete gravity dam caused by interaction with the foundation under vertical vibration is investigated using an analytical method. To achieve an analytical solution, the reservoir is assumed to be rectangular, and a harmonic load is vertically applied on the system from the foundation. Considering the acoustic nature of the reservoir fluid under harmonic vibration, a new method using the separation of variables method has been used for solution of hydrodynamic wave equation. The results show a significant effect of the vertical component of earthquake on the amount of induced pressure distributed in the reservoir, which has been omitted in most previous studies. Obtained results of the proposed model can be extended to more complicated models in terms of different loading and geometrical conditions.

Galilean Relativity

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Inertial Frame ◽  
Vertical Component ◽  
Horizontal Component ◽  
The Other ◽  
One Dimension ◽  
Everyday Experience ◽  
Low Speed ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Laws Of Motion

Galilean relativity is a useful description of nature at low speed. Galileo found that the vertical component of a projectile’s velocity evolves independently of its horizontal component. In a frame that moves horizontally along with the projectile, for example, the projectile appears to go straight up and down exactly as if it had been launched vertically. The laws of motion in one dimension are independent of any motion in the other dimensions. This leads to the idea that the laws of motion (and all other laws of physics) are equally valid in any inertial frame: the principle of relativity. This principle implies that no inertial frame can be considered “really stationary” or “really moving.” There is no absolute standard of velocity (contrast this with acceleration where Newton’s first law provides an absolute standard). We discuss some apparent counterexamples in everyday experience, and show how everyday experience can be misleading.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

Peripheral representation of antennal orientation by the scapal hair plate of the cockroach Periplaneta americana

2001 ◽  
Vol 204 (24) ◽  
pp. 4301-4309 ◽  
Author(s):  
J. Okada ◽  
Y. Toh
Keyword(s):  
Single Unit ◽  
Periplaneta Americana ◽  
Vertical Component ◽  
Horizontal Component ◽  
Vertical Position ◽  
Horizontal Position ◽  
Joint Movement ◽  
Basal Segment ◽  
Dynamic Phase ◽  
Hair Sensilla

SUMMARY Arthropods have hair plates that are clusters of mechanosensitive hairs, usually positioned close to joints, which function as proprioceptors for joint movement. We investigated how angular movements of the antenna of the cockroach (Periplaneta americana) are coded by antennal hair plates. A particular hair plate on the basal segment of the antenna, the scapal hair plate, can be divided into three subgroups: dorsal, lateral and medial. The dorsal group is adapted to encode the vertical component of antennal direction, while the lateral and medial groups are specialized for encoding the horizontal component. Of the three subgroups of hair sensilla, those of the lateral scapal hair plate may provide the most reliable information about the horizontal position of the antenna, irrespective of its vertical position. Extracellular recordings from representative sensilla of each scapal hair plate subgroup revealed the form of the single-unit impulses in response to hair deflection. The mechanoreceptors were characterized as typically phasic-tonic. The tonic discharge was sustained indefinitely (>20 min) as long as the hair was kept deflected. The spike frequency in the transient (dynamic) phase was both velocity- and displacement-dependent, while that in the sustained (steady) phase was displacement-dependent.

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