Define orthogonality principle in vibration?
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Orthogonal means that two things are at right angles to each other. When we say two vectors are orthogonal, it means they’re perpendicular, forming a 90-degree angle. This shows that these vectors are independent—they don’t affect each other’s movement. The vectors are completely unrelated or uncorrelated in terms of their direction. The motion of one vector does not interfere or interact with another vector. Hence, they can be evaluated or calculated independently since there is no relation between them.
Similarly, the modes or mode shapes in a vibrating body are said to be orthogonal because the shape and characteristics of one mode do not influence or interact with other modes. Hence, they can be evaluated independently and separately. This idea leads to what we call the mode superposition principle.
That’s why the off-diagonal elements of the decoupled equations of motion (decoupled using modal orthogonal property) are zero.