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 command-line Matlab script that performs this calculation for enforced acceleration. It may also be used for base acceleration excitation.
Here is a GUI version:
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Here is a Matlab script that performs this calculation for enforced acceleration for the case of modal damping. The script converts the system to an uncoupled system via the normal modes for a modal transient analysis.
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– Tom Irvine