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 enforced displacement. It may also be used for base displacement excitation.
mdof_enforced_displacement_nm.zip
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Here is a Matlab script that performs this calculation for enforced displacement 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_enforced_displacement_nm.zip
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Here is modal damping version that also has an option for the mode acceleration method. mdof_modal_arbit_force_newmark_MA.zip
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See also:
Newmark-beta Method, Applied Force
Dynamic Response to Enforced Motion
Vibrationdata Matlab Newmark Page
– Tom Irvine