scholarly journals Calculation of response spectra from strong-motion earthquake records

1969 ◽  
Vol 59 (2) ◽  
pp. 909-922
Author(s):  
Navin C. Nigam ◽  
Paul C. Jennings
Keyword(s):  
Computing Time ◽  
Strong Motion ◽  
Response Spectra ◽  
Kutta Method ◽  
Third Order ◽  
Earthquake Records ◽  
Runge Kutta Method ◽  
Governing Differential Equation ◽  
Comparable Accuracy ◽  
Acceleration Record

abstract A numerical method for computing response spectra from strong-motion earthquake records is developed, based on the exact solution to the governing differential equation. The method gives a three to four-fold saving in computing time compared to a third order Runge-Kutta method of comparable accuracy. An analysis also is made of the errors introduced at various stages in the calculation of spectra so that allowable errors can be prescribed for the numerical integration. Using the proposed method of computing or other methods of comparable accuracy, example calculations show that the errors introduced by the numerical procedures are much less than the errors inherent in the digitization of the acceleration record.

Construction of strong motion response spectra from magnitude and distance data

1964 ◽  
Vol 54 (5A) ◽  
pp. 1257-1269
Author(s):  
John H. Wiggins
Keyword(s):  
Strong Motion ◽  
Response Spectra ◽  
Earthquake Magnitude ◽  
Empirical Equations ◽  
Maximum Acceleration ◽  
Period Range ◽  
Motion Response ◽  
Characteristic Period ◽  
Earthquake Records ◽  
Distance Data

Abstract Empirical equations are derived which relate maximum acceleration, velocity, and displacement computed from strong motion earthquake records to magnitude and distance from source to site. Over fifty earthquakes recorded at three California sites were used in the study. The equations show that earthquake magnitude governs not only the character of response spectra but also the characteristic period content of the earthquake. As an added feature, the reported Modified Mercalli intensities are shown to correlate best with computed response spectra which include only the low period range.

A High Order Time Advancement Scheme for Prediction of Solidification Processes

2010 ◽  
Vol 297-301 ◽  
pp. 779-784 ◽  
Author(s):  
A. Abbasnejad ◽  
M.J. Maghrebi ◽  
H. Basirat Tabrizi
Keyword(s):  
Analytical Solutions ◽  
Second Order ◽  
High Order ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
Solidification Processes ◽  
Order Scheme ◽  
High Order Time ◽  
Good Agreement

The aim of this study is the simulation of alloys and pure materials solidification. A third order compact Runge-Kutta method and second order scheme are used for time advancement and space derivative modeling. The results are compared with analytical and semi-analytical solutions and show very good agreement.

scholarly journals Strong motion earthquake records

1974 ◽  
Vol 7 (2) ◽  
pp. 53-61
Author(s):  
P. W. Taylor
Keyword(s):  
Strong Motion ◽  
Response Spectra ◽  
Elementary Level ◽  
Acceleration Response ◽  
Earthquake Intensity ◽  
Earthquake Records ◽  
Earthquake Resistant ◽  
Earthquake Resistant Structures ◽  
San Fernando ◽  
Initial Concept

This article reviews, at an elementary level, the ways in which information from strong-motion earthquake records may be presented. The various methods of presentation are illustrated with reference to the strong-motion records obtained at Pacoima Dam, in the San Fernando earthquake of 1971. As acceleration response spectra from the basis of most codes for the design of earthquake resistant structures, the historical development of response spectra is traced from the initial concept. Simplification of presentation by the use of 'pseudo' response spectra, and the use of spectra to define earthquake intensity are outlined.

Numerical Solution of the Flow Between Two Disks

1997 ◽  
Author(s):  
Wahid S. Ghaly ◽  
Georgios H. Vatistas
Keyword(s):  
Shooting Method ◽  
Static Pressure ◽  
Numerical Solutions ◽  
Kutta Method ◽  
Initial Value ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Pressure Distributions ◽  
Runge Kutta Method

Abstract This paper deals with the numerical solutions of converging and diverging flows, between two disks. The results are obtained by solving a nonlinear third order ordinary differential equation using a modified shooting method. The governing equation is written as a system of three nonlinear first order ODE’s and the resulting system is solved as an initial value problem via the Runge-Kutta method. The results are given in terms of velocity profiles and static pressure distributions. These are compared with previously reported experimental data obtained by others.

Numerical Simulations of a Polydisperse Sedimentation Model by Using Spectral WENO Method with Adaptive Multiresolution

2016 ◽  
Vol 13 (06) ◽  
pp. 1650037
Author(s):  
Carlos A. Vega ◽  
Francisco Arias
Keyword(s):  
Convergence Rates ◽  
Time Discretization ◽  
Strong Stability ◽  
Kutta Method ◽  
Strong Stability Preserving ◽  
Third Order ◽  
Runge Kutta Method ◽  
Sedimentation Model ◽  
Runge Kutta ◽  
Fifth Order

In this work, we apply adaptive multiresolution (Harten’s approach) characteristic-wise fifth-order Weighted Essentially Non-Oscillatory (WENO) for computing the numerical solution of a polydisperse sedimentation model, namely, the Höfler and Schwarzer model. In comparison to other related works, time discretization is carried out with the ten-stage fourth-order strong stability preserving Runge–Kutta method which is more efficient than the widely used optimal third-order TVD Runge–Kutta method. Numerical results with errors, convergence rates and CPU times are included for four and 11 species.

scholarly journals ANN-based modeling of third order runge kutta method

2015 ◽  
Vol 4 (1) ◽  
pp. 180
Author(s):  
M. Dehghanpour ◽  
A. Rahati ◽  
E. Dehghanian
Keyword(s):  
Differential Equations ◽  
Quantum Physics ◽  
Numerical Approach ◽  
Mathematical Explanation ◽  
Kutta Method ◽  
Specific System ◽  
Third Order ◽  
Runge Kutta Method ◽  
Numerical Solution Methods ◽  
Runge Kutta

<p>The world's common rules (Quantum Physics, Electronics, Computational Chemistry and Astronomy) find their normal mathematical explanation in language of differential equations, so finding optimum numerical solution methods for these equations are very important. In this paper, using an artificial neural network (ANN) a numerical approach is designed to solve a specific system of differential equations such that the training process of the ANN  calculates the  optimal values for the coefficients of third order Runge Kutta method. To validate our approach, we performed some experiments by solving two body problem using coefficients obtained by ANN and also two other well-known coefficients namely Classical and Heun. The results show that the ANN approach has a better performance in compare with two other approaches.</p>

scholarly journals Numerical Scheme Based on the Implicit Runge-Kutta Method and Spectral Method for Calculating Nonlinear Hyperbolic Evolution Equations

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 28
Author(s):  
Yasuhiro Takei ◽  
Yoritaka Iwata
Keyword(s):  
Spectral Method ◽  
Numerical Scheme ◽  
Evolution Equations ◽  
Unit Size ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
Klein Gordon ◽  
Runge Kutta ◽  
The Stability

A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-order accuracy is presented. The order of total calculation cost is O(Nlog2N). As a benchmark, the relations between numerical accuracy and discretization unit size and that between the stability of calculation and discretization unit size are demonstrated for both linear and nonlinear cases.

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