11.6 - Modal Analysis of Undamped MDOF Systems
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Practice Questions
Test your understanding with targeted questions
What does MDOF stand for?
💡 Hint: Think about degrees of freedom in mechanical systems.
Define mode shapes in the context of dynamic analysis.
💡 Hint: Consider how systems move when they vibrate.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary purpose of modal analysis in MDOF systems?
💡 Hint: Think about what modal analysis reveals about structures.
True or False: Each mode shape corresponds to a unique natural frequency.
💡 Hint: Consider how vibrations are characterized.
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Challenge Problems
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Given an MDOF structure with three modes, derive the basic form of the equations of motion when no damping is present. Assume mass and stiffness are known.
💡 Hint: Use the natural frequency definitions and moment balance.
Analyze how the modal responses would change if one of the mode shapes has a significantly higher natural frequency. What impact does this have on the total dynamic response?
💡 Hint: Consider the principle of resonance and mass participation.
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