In a two-degree-of-freedom (2DOF) system, what is the primary purpose of solving for the system’s natural frequencies and mode shapes?
- ATo understand the dynamic behaviour and predict the response under dynamic loadingCorrect
- BTo optimize the damping in the system
- CTo determine the system’s failure points under dynamic loads
- DTo optimize the material usage in the system
Solution
Concept
Natural frequencies and mode shapes analysis
Formula
NONE
Step-by-step solution
1. Natural frequencies and mode shapes define the dynamic characteristics of a multi-degree-of-freedom system. 2. Solving for these parameters allows engineers to predict structural dynamic behaviour and responses under dynamic loads. Answer: A
Explanation
Natural frequencies and mode shapes characterize the inherent dynamic properties of a multi-degree-of-freedom structural system. Determining these parameters allows engineers to predict how the structure will deform and respond when subjected to arbitrary dynamic or seismic loads. Therefore, option A correctly states the fundamental purpose of solving for frequencies and mode shapes.
Why the other options are wrong
B) Optimizing damping is a control strategy, not the main purpose of solving for natural frequencies and mode shapes. C) Failure points are determined by structural strength limits and stress analysis rather than modal analysis alone. D) Material usage optimization is a structural design process not directly provided by modal analysis.
Shortcut
Natural frequencies and mode shapes predict dynamic behavior and system response.
Common mistake
Selecting option B or D by assuming natural frequencies and mode shapes are solved to optimize damping or material usage.
Correct answer: A) To understand the dynamic behaviour and predict the response under dynamic loading