18.3.2 - Orthogonality of Modes
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Practice Questions
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What does orthogonality of modes mean in structural dynamics?
💡 Hint: Think of how vector pieces interact in coordinate systems.
Give an example of a multi-degree-of-freedom system.
💡 Hint: Consider structures with many interconnected components.
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Interactive Quizzes
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What is meant by the term orthogonality in the context of structural dynamics?
💡 Hint: Think about the independence of factors in analysis.
True or False: The orthogonality property applies only to linear systems.
💡 Hint: Recall what linear and nonlinear systems entail.
1 more question available
Challenge Problems
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Given a real-world structure with multiple vibrational modes, N, list the key steps to determine which modes retain their orthogonality and arrange them accordingly.
💡 Hint: Consider the mathematical principles that support establishing independence.
Analyze a coupled multi-degree-of-freedom system with three unknown mode shapes. Discuss how each mode's interaction can be translated into an equation of motion given their orthogonal properties.
💡 Hint: Think about how to express one mode's influence without impacting others.
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