Practice Orthogonality of Mode Shapes - 12.4 | 12. Two Degree of Freedom System | Earthquake Engineering - Vol 1
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Orthogonality of Mode Shapes

12.4 - Orthogonality of Mode Shapes

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does it mean for mode shapes to be normalized?

💡 Hint: Think about why scaling matters in analysis.

Question 2 Easy

State the mass-orthogonality condition.

💡 Hint: This should involve vectors and matrices.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the mass orthogonality condition?

The dot product of two modes equals one.
The dot product with the mass matrix equals zero for different modes.
Mass shapes depend on frequency.

💡 Hint: Think about how energy is distributed across modes.

Question 2

True or False: Stiffness orthogonality means that modes do not affect each other in terms of stiffness.

True
False

💡 Hint: Recall how modes interact with stiffness matrices.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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