Practice Mode Shapes (18.10.1) - Separation of Variables, Use of Fourier Series

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6 sample questions

Question 1.
What is a mode shape?
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Think about how a guitar string vibrates.
Question 2.
Define fundamental mode.
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It's the baseline shape.
3Question 3.
What is a mode shape?
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Think of it like the shape or form a structure takes when it vibrates.
4Question 4.
True or False: The fundamental mode is the simplest form of vibration.
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Consider other overtones in vibration.
Question 5.
Given a simply supported beam with length L, derive the expressions for the first three mode shapes using separation of variables. Consider boundary conditions.
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Use boundary conditions to solve the differential equations.
Question 6.
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.
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Consider thermal expansion and changes in Young's modulus.

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