Practice Orthogonality of Mode Shapes - 16.4.2 | 16. Introduction to MDOF Systems | Earthquake Engineering - Vol 2
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Orthogonality of Mode Shapes

16.4.2 - Orthogonality of Mode Shapes

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the term 'mode shape' refer to?

💡 Hint: Think about how structures move.

Question 2 Easy

Define orthogonality in terms of vectors.

💡 Hint: Consider how two vectors might not affect each other.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the orthogonality of mode shapes imply?

They affect each other's energy
They do not interfere with each other
They are identical

💡 Hint: Remember how each mode operates uniquely.

Question 2

Is the following statement true or false? 'Orthogonality helps in simplifying dynamic analysis.'

True
False

💡 Hint: Consider the benefits of independent calculations.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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