18.10.1 - Mode Shapes
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Practice Questions
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What is a mode shape?
💡 Hint: Think about how a guitar string vibrates.
Define fundamental mode.
💡 Hint: It's the baseline shape.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a mode shape?
💡 Hint: Think of it like the shape or form a structure takes when it vibrates.
True or False: The fundamental mode is the simplest form of vibration.
💡 Hint: Consider other overtones in vibration.
1 more question available
Challenge Problems
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Given a simply supported beam with length L, derive the expressions for the first three mode shapes using separation of variables. Consider boundary conditions.
💡 Hint: Use boundary conditions to solve the differential equations.
Discuss how varying material properties can affect mode shapes of a concrete slab subjected to heating. Provide examples of what kind of changes may occur.
💡 Hint: Consider thermal expansion and changes in Young's modulus.
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