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.

mdof_enforced_acceleration_nm.zip

Here is a GUI version:

mdof_enforced_acceleration_newmark.zip

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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.

mdof_modal_enforced_acceleration_nm.zip

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See also:

Newmark-beta Method, Applied Force

Dynamic Response to Enforced Motion

Vibrationdata Matlab Newmark Page

Python Newmark Page

– Tom Irvine

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