5. Structural Dynamics and Seismic

Modal Analysis — Quiz

Test your understanding of modal analysis with 5 practice questions.

Practice Questions

Question 1

In modal analysis, what is the physical interpretation of the generalized mass $M_n$ for a specific mode $n$?

Question 2

For a multi-degree-of-freedom system, if the damping matrix $[C]$ is not proportional to a linear combination of the mass matrix $[M]$ and stiffness matrix $[K]$, what is the consequence for classical modal analysis?

Question 3

Consider a multi-degree-of-freedom system. The potential energy of the system can be expressed as $\frac{1}{2} q^T [K] q$. If the system's response is expressed in terms of modal coordinates $p(t)$ such that $q(t) = [\Phi] p(t)$, where $[\Phi]$ is the modal matrix, what is the expression for the potential energy in modal coordinates?

Question 4

When applying modal superposition, the total dynamic response of a structure is obtained by summing the responses of individual modes. What is the underlying mathematical principle that allows this summation?

Question 5

In modal analysis, what is the primary implication of a structure having closely spaced natural frequencies?