15.3.1 - Orthogonality of Mode Shapes
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Practice Questions
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Define mode shape in your own words.
💡 Hint: Think about how structures move when disturbed.
What does it mean for two mode shapes to be orthogonal?
💡 Hint: Consider vectors that point in different directions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the orthogonality of mode shapes allow in structural analysis?
💡 Hint: Think about how vectors can behave in an analysis.
True or False: Mode shapes are orthogonal with respect to the mass matrix.
💡 Hint: Consider the definition of orthogonality.
1 more question available
Challenge Problems
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Using a 2-DOF system as an example, demonstrate how to establish the orthogonality of two mode shapes mathematically.
💡 Hint: Coordinate the analysis using the properties of eigenvectors.
In designing a building, how would you illustrate the importance of stiffness orthogonality when faced with uneven mass distribution?
💡 Hint: Think about how sway patterns might be altered with irregular mass distributions.
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