Objet Introduction Random vibrations and earthquakes Conclusions
Acc´el´erogram characteristics comparison Ph.Maurel December 2008
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Introduction The engineering problem
Random vibrations and earthquakes Simplification for simulated time histories Numerical examples and comparisons
Conclusions
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
What we need and what is available ?
I
For the seismic analysis of buildings and equipments, we frequently need time histories to perform transient (linear or non-linear) analysis.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
What we need and what is available ?
I
For the seismic analysis of buildings and equipments, we frequently need time histories to perform transient (linear or non-linear) analysis.
I
The basic data are site (free filed) response spectra for several damping values.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
The possible solutions
I
Obtain time histories from data bases of natural earthquakes,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
The possible solutions
I
Obtain time histories from data bases of natural earthquakes,
I
Build synthetic time histories from natural earthquakes,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
The possible solutions
I
Obtain time histories from data bases of natural earthquakes,
I
Build synthetic time histories from natural earthquakes,
I
Generate artificial time histories,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
Natural, synthetic or artificial ? I
In natural earthquakes data bases, there are very few accelerograms that match the magnitude, epicentral distance and PGA of a site ! These accelerograms are not correlated, but provide response spectra that poorly match the site response spectra.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
Natural, synthetic or artificial ? I
In natural earthquakes data bases, there are very few accelerograms that match the magnitude, epicentral distance and PGA of a site ! These accelerograms are not correlated, but provide response spectra that poorly match the site response spectra.
I
Synthetic accelerograms are obtained using regression coefficients on some parameters (PGA, IA, T soil) from natural earthquakes data bases. Generally, the phase content is kept, but the number of ’pic’ ground accelerations is different. Depending on the way they are computed, they can be not correlated, non stationary, but provide response spectra that do not match very well the target response spectra.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
Natural, synthetic or artificial ? I
In natural earthquakes data bases, there are very few accelerograms that match the magnitude, epicentral distance and PGA of a site ! These accelerograms are not correlated, but provide response spectra that poorly match the site response spectra.
I
Synthetic accelerograms are obtained using regression coefficients on some parameters (PGA, IA, T soil) from natural earthquakes data bases. Generally, the phase content is kept, but the number of ’pic’ ground accelerations is different. Depending on the way they are computed, they can be not correlated, non stationary, but provide response spectra that do not match very well the target response spectra.
I
We will discuss about artificial tim histories. Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
How to match a specified response spectrum ? I
Some guidelines are given in the following documents : • ASCE 4-98 • EUROCODE-8 • ASN GUIDE
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
How to match a specified response spectrum ? I
Some guidelines are given in the following documents : • ASCE 4-98 • EUROCODE-8 • ASN GUIDE
I
We must have : • A time step less than 0.02s. Generally 0.01s and sometime
0.005s (EUROCODE 8) • For each frequency the spectral value mus be greater than
90% the target value • The mean value of the PGA must be greater than the PGA of
the target spectrum • The strong motion duration must be greater than a specified
value depending of the magnitude. • The Inter-correlation function must be lower than 0.3. • etc... Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
A good bibliography I
On random vibrations and simulation : • Random vibrations in structural systems : Crandal & Mark
(1973). • Vibrations al´ eatoires et analyse spectrale (1990). • Applications of randmo vibrations theory : Penzien (1965). • A program for artificial motion generation (SIMQKE) :
Vanmarke (1976).
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
The engineering problem
A good bibliography I
On random vibrations and simulation : • Random vibrations in structural systems : Crandal & Mark
(1973). • Vibrations al´ eatoires et analyse spectrale (1990). • Applications of randmo vibrations theory : Penzien (1965). • A program for artificial motion generation (SIMQKE) :
Vanmarke (1976). I
On structural response to random vibrations. • Structural response to stationary excitation : Der Kiureghian
(1980). • Structural response to earthquake : Vanmarke (1976). • Vibrations al´ eatoires des structures : Gibert (1988). • The power spectral density method for seismic response
analysis : Livolant (1987). Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random vibrations in seismic analysis
Response of structures (linear or nonlinear) : I
Spectral analysis (linear)
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random vibrations in seismic analysis
Response of structures (linear or nonlinear) : I
Spectral analysis (linear)
I
Transient using time histories (linear or nonlinear)
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random vibrations in seismic analysis
Response of structures (linear or nonlinear) : I
Spectral analysis (linear)
I
Transient using time histories (linear or nonlinear)
I
Random vibrations (direct prediction of probability distribution of response parameters) : use of power spectral density function.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random process I
Random process may be • • • • •
Non stationary (earthquake), Stationary, Ergodics (stationary, ensemble average=mean average) Gaussian, Markovian
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random process I
Random process may be • • • • •
I
Non stationary (earthquake), Stationary, Ergodics (stationary, ensemble average=mean average) Gaussian, Markovian
For seismic analysis, approximation are made by splitting the non stationary and stationary parts.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Random process I
Random process may be • • • • •
Non stationary (earthquake), Stationary, Ergodics (stationary, ensemble average=mean average) Gaussian, Markovian
I
For seismic analysis, approximation are made by splitting the non stationary and stationary parts.
I
In the next slides we resume some mathematical basis used to build artificial time histories.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Simulated earthquake : stationary part A typical accelerogram has the appearance of a transient stochastic function
z(t) = I (t)x(t) The stationary motion can be simulated by : P x(t) = ni=1 Ai sin(ωi t + Φi )
Figure: Stationary part
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
(1)
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Simulated earthquake : non stationary part
Figure: Non stationary part
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Spectral density function I
Power of the stady motion n X
A2i /2
(2)
i=1 I
Power density function G (ωi )∆ω =
A2i 2
with n → ∞
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
(3)
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Spectral density function I
Proposed form (Kanai’s study in 1961 with limited number of strong ground motions records h
i 1 + 4xig ( ωωg )2 G0 i G (ω) = h 1 − ( ωωg )2 + 4ξg ( ωωg )2
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
(4)
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Spectral density function I
Proposed form (Kanai’s study in 1961 with limited number of strong ground motions records h
i 1 + 4xig ( ωωg )2 G0 i G (ω) = h 1 − ( ωωg )2 + 4ξg ( ωωg )2 I
(4)
In this model, the strong motion of the seismic signal is idealized as the realisation of a stationary gaussian process obtained from filtered white noise in acceleration, through an oscillator of characteristics fg = 2.5Hz, ξg = 0.6 Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Autocorrelation function I
Using the autocorrelation function of a stationary process, it can be shown that the spectral density function is the statistical average of some kind of Fourier decomposition applied to individual samples of the process,
E [x1 , x2 ] = E [x(t), x(t + τ )]
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
(5)
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Autocorrelation function I
Using the autocorrelation function of a stationary process, it can be shown that the spectral density function is the statistical average of some kind of Fourier decomposition applied to individual samples of the process,
E [x1 , x2 ] = E [x(t), x(t + τ )] I
(5)
On an another hand, it can be shown that the undamped pseudo velocity response spectrum of an oscillator is close to the Fourier transform of the inpur signal
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Autocorrelation function I
Using the autocorrelation function of a stationary process, it can be shown that the spectral density function is the statistical average of some kind of Fourier decomposition applied to individual samples of the process,
E [x1 , x2 ] = E [x(t), x(t + τ )]
(5)
I
On an another hand, it can be shown that the undamped pseudo velocity response spectrum of an oscillator is close to the Fourier transform of the inpur signal
I
All these related mathematical informations are used to build artificial time histories. Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Artificial time histories The production of artificial time histories can be resumed to : • generate compatible spectral density function from smooth
site response spectrum,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Artificial time histories The production of artificial time histories can be resumed to : • generate compatible spectral density function from smooth
site response spectrum, • Obtain accelerograms compatible with earthquake duration
and site conditions,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Artificial time histories The production of artificial time histories can be resumed to : • generate compatible spectral density function from smooth
site response spectrum, • Obtain accelerograms compatible with earthquake duration
and site conditions, • Compute and validate the response spectrum,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Artificial time histories The production of artificial time histories can be resumed to : • generate compatible spectral density function from smooth
site response spectrum, • Obtain accelerograms compatible with earthquake duration
and site conditions, • Compute and validate the response spectrum, • Verify some statistical parameters,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Artificial time histories The production of artificial time histories can be resumed to : • generate compatible spectral density function from smooth
site response spectrum, • Obtain accelerograms compatible with earthquake duration
and site conditions, • Compute and validate the response spectrum, • Verify some statistical parameters, • verify inter-correlation when several accelerograms are used
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V, I The maximum of the absolute value of the displacement,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V, I The maximum of the absolute value of the displacement, I The ratio A of A and V aboce, V
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V, I The maximum of the absolute value of the displacement, I The ratio A of A and V aboce, V I The cumulated value of the absolute value of the velocity RT (CAV) : 0 | γ(t) | dt
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V, I The maximum of the absolute value of the displacement, I The ratio A of A and V aboce, V I The cumulated value of the absolute value of the velocity RT (CAV) : 0 | γ(t) | dt RT 2 I The Arias intensity (AI) : π 2g 0 γ(t) dt
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Statistical parameters We have studied the following parameters I The maximum of the absolute value of the acceleration A, I The maximum of the absolute value of the velocity V, I The maximum of the absolute value of the displacement, I The ratio A of A and V aboce, V I The cumulated value of the absolute value of the velocity RT (CAV) : 0 | γ(t) | dt RT 2 I The Arias intensity (AI) : π 2g 0 γ(t) dt I The strong motion duration computed from T = t2 − t1 : Z
t2
2
Z
γ(t) dt ≥ 0.9 t1 Ph.Maurel December 2008
T
γ(t)2 dt
0
Acc´ el´ erogram characteristics comparison
(6)
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Comparisons
We have made the following comparisons I
Statistical parameters obtained from artificial accelerograms for a specified site,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Comparisons
We have made the following comparisons I
Statistical parameters obtained from artificial accelerograms for a specified site,
I
Statistical parameters obtained from natural accelerograms used to establish the corresponding site response spectrum,
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Comparisons
We have made the following comparisons I
Statistical parameters obtained from artificial accelerograms for a specified site,
I
Statistical parameters obtained from natural accelerograms used to establish the corresponding site response spectrum,
I
On the next slides, we show a computed artificial accelerogram and associated response spectrum ant the statistical parameters as explained above.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Example of results Time history and computed response spectrum compared to target response spectrum
Figure: Simulated earthquake and response spectrum Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
Table of Paremeters Parameters compared to statistical values obtained from natural accelerograms, with similar magnitude, epicentral distance and soil. Accélérogramme - MA/SD1 A (accel max (m/s2)) 2.3623
Magnitude 7 OUI
Distance 26
valeurs statistiques (accel. naturels) Moyenne M-s M+s 1.7630 0.8655 3.5913
V (vit max (m/s)) 0.1489
OUI
0.1655
0.0757
0.3621
D (depl max(m)) 0.0489
OUI
0.0844
0.0286
0.2490
A/V 15.862
OUI
10.6339
6.7561
16.7376
CAV 7.764
OUI
5.9455
3.5010
10.0969
Intensité d'ARIAS (m/s) 0.878
OUI
0.4545
0.1712
1.2065
Durée de phase forte (s) 13.45
OUI
13.2877
8.3071
21.2545
Figure: Parameters and statistics Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison A natural accelerogram from the European database (EC8)
Figure: Natural accelerogram 000044xa EC8 database Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Response spectrum of the natural accelerogram
Figure: Response spectrum 5% damping 000044xa EC8 database Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Artificial accelerogram of the spectrum of the natural accelerogram
Figure: Artificial accelerogram Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison
spectrum of the artificial accelerogram Response
Figure: Response spectrum (5% damping) of the artificial accelerogram Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Parameters comparison
Statistical parameters for 000044xa.cof Artificial Real A(m/s2) 2.768 2.69 V(m/s) 0.107 0.1 D(m) 0.02 0.01 A/V 25.75 26.85 CAV 7.91 2.66 IA 0.96 0.27 tsm(s) 11.75 4.86 dominant fréquency 7.74 7.67
Figure: Parameters artificial/natural Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison
We can see that : • Main differences appears for parameters CAV,IA,tsm(strong
motion duration). This seems to show the conservatism of artificial accelerograms, but this parameter has no influence for linear response.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison
We can see that : • Main differences appears for parameters CAV,IA,tsm(strong
motion duration). This seems to show the conservatism of artificial accelerograms, but this parameter has no influence for linear response. • When studying the response of a non linear spring with each
acceleregrom, we get two times more excursion in the plastic range with the artificial accelerogram.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Conclusion for this nice example I
We can obtain artificial accelerograms that match well the target response spectrum
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Conclusion for this nice example I
We can obtain artificial accelerograms that match well the target response spectrum
I
The statistical parameters are in good agreement
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Conclusion for this nice example I
We can obtain artificial accelerograms that match well the target response spectrum
I
The statistical parameters are in good agreement
I
The artificial accelerograms seems unfavorable if appreciated with these statistical parameters.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Conclusion for this nice example I
We can obtain artificial accelerograms that match well the target response spectrum
I
The statistical parameters are in good agreement
I
The artificial accelerograms seems unfavorable if appreciated with these statistical parameters.
I
The transient response of the same non linear spring gives two times more excursions in the plastic range with the artificial accelerogram
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Simplification for simulated time histories Numerical examples and comparisons
A nice comparison Conclusion for this nice example I
We can obtain artificial accelerograms that match well the target response spectrum
I
The statistical parameters are in good agreement
I
The artificial accelerograms seems unfavorable if appreciated with these statistical parameters.
I
The transient response of the same non linear spring gives two times more excursions in the plastic range with the artificial accelerogram
I
The statistical parameters seems insufficient to qualify artificial accelerograms, especially for non linear analysis
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions I
Many publications have been produced on the subject of random vibrations in earthquake engineering, but they are not easy to understand for practicing engineers : examples are missing !
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions I
Many publications have been produced on the subject of random vibrations in earthquake engineering, but they are not easy to understand for practicing engineers : examples are missing !
I
Simulation of non stationary signals representative of earthquake is an iterative process.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions I
Many publications have been produced on the subject of random vibrations in earthquake engineering, but they are not easy to understand for practicing engineers : examples are missing !
I
Simulation of non stationary signals representative of earthquake is an iterative process.
I
New parameters have to be discovered to qualify artificial time histories, especially for the response analysis of non linear structures.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions I
Many publications have been produced on the subject of random vibrations in earthquake engineering, but they are not easy to understand for practicing engineers : examples are missing !
I
Simulation of non stationary signals representative of earthquake is an iterative process.
I
New parameters have to be discovered to qualify artificial time histories, especially for the response analysis of non linear structures.
I
Artificial time histories should not be used for nonlinear analysis.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions
I
Natural or synthetic (obtained from natural) time histories do not produce response spectrum that match very well a specified response spectrum.
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions
I
Natural or synthetic (obtained from natural) time histories do not produce response spectrum that match very well a specified response spectrum.
I
Artificial time histories should not be produced from floor response spectra (the mathematical process uses hypothesis that concern ground accelerograms).
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
Objet Introduction Random vibrations and earthquakes Conclusions
Conclusions
I
Natural or synthetic (obtained from natural) time histories do not produce response spectrum that match very well a specified response spectrum.
I
Artificial time histories should not be produced from floor response spectra (the mathematical process uses hypothesis that concern ground accelerograms).
I
Eurocode 8 specifies ground elastic response spectra with hight frequencies content. This conduct to establish artificial time histories with low time step (0.005s or lower).
Ph.Maurel December 2008
Acc´ el´ erogram characteristics comparison
