16.4.2 - Orthogonality of Mode Shapes
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Practice Questions
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What does the term 'mode shape' refer to?
💡 Hint: Think about how structures move.
Define orthogonality in terms of vectors.
💡 Hint: Consider how two vectors might not affect each other.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the orthogonality of mode shapes imply?
💡 Hint: Remember how each mode operates uniquely.
Is the following statement true or false? 'Orthogonality helps in simplifying dynamic analysis.'
💡 Hint: Consider the benefits of independent calculations.
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Challenge Problems
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You have two mode shapes with a given mass matrix. Calculate if they are orthogonal, using {ϕ}_1 and {ϕ}_2 with [M] given as a diagonal matrix. What does the result indicate?
💡 Hint: Perform matrix multiplication and check the outcome.
Explain how the lack of orthogonality would affect a skyscraper's response to an earthquake and propose a method to address this complication.
💡 Hint: Think about simulation tools used in structural analysis.
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