Modal Analysis Response of Mdof
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MODAL ANALYSIS RESPONSE OF MDOF’S MODELS (uncoupled models ) to arbtrar! loads "e consder t#at t#e e$ternal %orces act a%ter t#e de&ree o% %reedom (transla 'no n • M* '* +, • - (normal.ed modal matr$), One uses t#e modal trans%ormaton (/) E0uaton o% moton (1) 2sn& (/) determne (3) "#ere
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Modal Analysis Response of Mdof
Transcript of Modal Analysis Response of Mdof
MODAL ANALYSIS RESPONSE OF MDOFS MODELS(uncoupled models ) to arbitrary loadsWe consider that the external forces act after the degree of freedom (translation)
Known: M, K, C;
(normalized modal matrix);
One uses the modal transformation :
(1)
Equation of motion:
(2)
Using (1) determine : (3)
Where :
=[]
The system equation is:
Or for i mode of vibration:
Where
Sollution is:
The value of displacement is :
Particular case: harmonical external forces
The sollution of displacements is:
Where:
The displacement will be:
Taken into account the unnormalized forms of vibration we have: