How to compute response to single node impulse in structural model from modal eigenvectors directly

According to https://www.mathworks.com/matlabcentral/answers/1968759-scaled-mode-shapes-in-modal-analysis-of-a-simulated-system-and-a-wind-turbine-blade?s_tid=ta_ans_results , in a modal analysis, for each mode shape vector, the component with the largest absolute value is scaled to 1, and the rest of the components in the vector are scaled accordingly for ease of visual comparison of the shapes. I have a structural model (femodel(AnalysisType="structuralModal")with displacement vector results u=[u_x, u_y,u_z ] for various frequencies. I would like to compute the amplitudes of all of the frequencies (found in a limited range of course) for a unit impact vector n ( a delta function in time) at any node directly from the components of u and think it is something like just the inner product of n with u at that node were u not arbitrarily normalized, and by that I take the answer to mean there is one scale factor for the entire u for any node. I'd like to do that for two cases: 1) any node/mass element within the volume as if it were struck by a dark matter particle (assuming assumptons of elastic continuum mechanics remain valid) and 2) for any surface node as if it were struck by a BB or similar - I mean the impulse could have normal and traction components. Perhaps this is just what a transient analysis does . I don't want to perform a transient analysis as found in examples like the tuning fork for every node and go some analysis of the resulting motions to derive what I'm after, just compute the amplitudes of the normal modes. ANy way to do this?

[Walter Roberson]

It would be easier to read if you were to break that up into paragraphs.

[Duncan Carlsmith]

According to https://www.mathworks.com/matlabcentral/answers/1968759-scaled-mode-shapes-in-modal-analysis-of-a-simulated-system-and-a-wind-turbine-blade?s_tid=ta_ans_results , in a modal analysis, for each mode shape vector, the component with the largest absolute value is scaled to 1, and the rest of the components in the vector are scaled accordingly for ease of visual comparison of the shapes. I take the answer to mean there is one scale factor for the entire u for any node.

I have a structural model (femodel(AnalysisType="structuralModal")with displacement vector results u=[u_x, u_y,u_z ] for various frequencies. I would like to compute the amplitudes of all of the frequencies (found in a limited range of course) for a unit impact vector n ( a delta function in time) at any node directly from the components of u and think it is something like just the inner product of n with u at that node, were u not arbitrarily normalized, and

I'd like to do that for two cases: 1) any node/mass element within the volume as if it were struck by a dark matter particle (assuming assumptons of elastic continuum mechanics remain valid) and 2) for any surface node as if it were struck by a BB or similar - I mean the impulse could have normal and traction components. Perhaps this is just what a transient analysis does . I don't want to perform a transient analysis as found in examples like the tuning fork for every node and go some analysis of the resulting motions to derive what I'm after, just compute the amplitudes of the normal modes. Any way to do this, or am I off-base?

Answer 1

[Duncan Carlsmith]

I think I found the answer. I need to extract the various matrices with assembleFEMatrices and renormalize the modal solutions.