The Newmark-beta method can be used to solve structural dynamics problems in the time domain, of the form:

M (d^2x/dt^2) + C dx/dt + K x = F

This method performs direct integration on the mass, damping and stiffness matrices which may be fully-coupled.

Here is a Matlab script that performs this calculation for an applied force or forces: Newmark.zip

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Here is a Matlab script that performs this calculation for an applied force or forces for the case of modal damping. The script converts the system to an uncoupled system via the normal modes for a modal transient analysis.

mdof_modal_arbit_force_newmark.zip

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Here is a Matlab script the performs the calculation for a subset of modes with an option for mode acceleration.

mdof_modal_arbit_force_newmark_MA.zip

Here is a paper: The Mode Acceleration Method

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Here is a hybrid method that allows for a subset of modes. The mode subset is used to reduce the order of the system. The full set of physical displacements is then recovered. Newmark_hybrid.m

Note that the script uses the supporting functions previously given in: Newmark.zip

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See also:

Newmark-beta, Enforced Acceleration

Vibrationdata Matlab Newmark Page

Python Newmark Page

– Tom Irvine

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