Reference:

Analytical solution.

Problem description:

The accelerogram is considered in the form of a sinusoid, that is, the acceleration at time t is equal to sin(t). The response spectrum calculated by the program and obtained analytically is analyzed. The case is considered when the oscillation damping coefficient is equal to 15% of the critical value (the logarithmic damping decrement is equal to 0.953263).

Initial data:

Damping: β = 0.15;

Amplitude value of accelerogram acceleration: a₀ = 1 m/sec²;

Seismic exposure time: t_d = 19.9 sec;

Circular frequency: θ = 30 rad/sec.

Files with initial data:

8_5.ar1 — input accelerogram;

8_5.txt — obtained response spectrum;

8_5_result.txt — comparison of spectra.

Analytical solution:

Calculation results:

Graphical comparison of the response spectra of accelerations obtained in the SP LIRA 10 and analytically: