Volex Labs / Calculations / Seismic time-history analysis (Newmark method).

Seismic time-history analysis (Newmark method).

Enter the system mass, stiffness and damping and a ground-motion record, and Volex Anvil integrates the equation of motion by the Newmark-β method to give the response history — the peak displacement, velocity and acceleration — and the spectral acceleration for the system period.

The Newmark integration is checked against closed-form step-response and free- vibration solutions from Chopra, 'Dynamics of Structures', so the peak response matches the reference for a linear SDOF oscillator.

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What Volex Anvil checks

Validated against the published example

SDOF Newmark response — step response and spectral acceleration Newmark-β integration; Chopra 'Dynamics of Structures'
QuantityPublishedVolex AnvilError
Peak displacement u_max46.98 mm46.98 mm0.01%
Spectral acceleration Sa0.189 g0.189 g0.00%
This case is one of 359 published checks the platform passes — the full table, with every source and every error, is public at volexlabs.com/verification.

Frequently asked

Linear or nonlinear?
The current analysis is linear (elastic SDOF); it is the basis for response-history verification and for building elastic spectra from records.
What integration scheme?
Newmark-β with the average-acceleration (unconditionally stable) or linear-acceleration option.
Is it validated?
The peak response and spectral acceleration are checked against Chopra's closed-form solutions — within 0.01%.
Free tier?
Yes — 10 calculations a month free; Pro (£29/month) adds unlimited runs and PDF calc sheets.

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