ucla-geotech-tools-response-spectrum 1.0.1

Python package for computing acceleration response spectra.

---

useMath: true

Welcome to response_spectrum

response_spectrum computes a psuedo-acceleration response spectrum from an input ground motion or set of ground motions sampled at a constant frequency. Calculates are performed in the frequency domain by

1. taking the Fourier transform of the input motion(s)
2. multiplying by the transfer function for computing the motion of a single-degree-of-freedom (SDOF) oscillator with natural period T and damping D

\begin{equation} H_u = \frac{1}{1+2j\cdot D \cdot f \cdot T-(f\cdot T)^2} /end{equation}

3. computing the peak acceleration amplitude for the SDOF oscillator 4. repeating steps 2 and 3 for a range of user-specified periods

Installation

pip install ucla_geotech_tools.response_spectrum

Command

get_response_spectrum(**kwargs)

Input parameters.

motion(s) = an M x N list or python array containing acceleration data, where M is the number of motions and N is the number of data points in each motion. All motions must have the same number of data points. (required)  
dt = time step (required)
D = damping (optional, default = 0.05)
T = array of natural periods (optional, default = array used for NGAwest2 project: 
T = [0.01, 0.02, 0.022, 0.025, 0.029, 0.030, 0.035, 0.036, 0.040, 0.042, 0.044, 0.045, 0.046, 0.048, 0.050, 0.055, 0.060, 0.065, 0.067, 0.070, 0.075, 0.080, 0.085, 0.090, 0.095, 0.100, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.22, 0.24, 0.25, 0.26, 0.28, 0.29, 0.30, 0.32, 0.34, 0.35, 0.36, 0.38, 0.40, 0.42, 0.44, 0.45, 0.46, 0.48, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.2, 2.4, 2.5, 2.6, 2.8, 3.0, 3.2, 3.4, 3.5, 3.6, 3.8, 4.0, 4.4, 4.6, 4.8, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 20.0])
zeropad = 1: apply zero padding to speed up FFT operation, 0: do not pad with zeros (optional, default = 1)
verbose = 1: print output message when default values are being used, 0: suppress output messages (optional, default = 1)

Example

Python script

import numpy as np
import ucla_geotech_tools.response_spectrum as ars
import matplotlib.pyplot as plt

N = 4000               # Number of time steps
M = 3                  # Number of motions
dt = 0.005             # Time step in seconds
D = 0.05               # Damping
freq = [1.0, 3.0, 5.0] # Frequencies for three different harmonic motions

motions = np.empty([M,N],dtype="float64")
for i in range(M):
    for j in range(N):
        motion[i][j] = np.sin(2*np.pi*freq[i]*j*dt)

Sa = ars.get_response_spectrum(motions=motions, dt=dt, D=D, zeropad=0, verbose=0) # returns Python array containing pseudo-spectral acceleration values 

for i in range(M):
    plt.loglog(T,Sa[i])

Output