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

12.4 - Orthogonality of Mode Shapes

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

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.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

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.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation