12.4 - Orthogonality of Mode Shapes
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Practice Questions
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What does it mean for mode shapes to be normalized?
💡 Hint: Think about why scaling matters in analysis.
State the mass-orthogonality condition.
💡 Hint: This should involve vectors and matrices.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the mass orthogonality condition?
💡 Hint: Think about how energy is distributed across modes.
True or False: Stiffness orthogonality means that modes do not affect each other in terms of stiffness.
💡 Hint: Recall how modes interact with stiffness matrices.
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Challenge Problems
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Evaluate a 3-DOF system's eigenvalues and establish the orthogonality criteria across three mode shapes. Describe the implications of finding zero products in each case.
💡 Hint: Follow the standard procedure for eigenvalue problems in dynamic systems.
How would you apply the principle of orthogonality to a complex building structure with many floors and irregular shapes? Discuss the implications.
💡 Hint: Consider modeling methods that normalize and decouple systems effectively.
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