This set of Earthquake Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Model Order Reduction in Structural Dynamics”.

1. How to minimize the time spent in the eigen solution phase?

a) Making use of generalized coordinates

b) Making use of specific coordinates

c) Making use of constant coordinates

d) Making use of Cartesian coordinates

View Answer

Explanation: It is not necessary to compute all eigenvalues and eigenvectors for a system. To minimize the time spent in the eigen solution phase which directly results in reduced solution times, the concept of generalized coordinates is used. It reduces the problem size itself.

2. Which of the following equation represents the generalized mass matrix?

a) Ḿ = Ψ^{T}KΨ

b) Ḿ = Ψ^{T}MΨ

c) Ḿ = ΨZ

d) Ḿ = Ψφ_{z}

View Answer

Explanation: The generalized mass matrix is given by the equation Ḿ = Ψ

^{T}MΨ. Ψ

^{T}KΨ represents the generalized stiffness matrix. ΨZ gives the N-dimensional vector v. Ψφ

_{z}denotes the mode shapes required for lower modes of actual structure.

3. What is the apparent change in the natural period of vibration known as?

a) Artificial damping

b) Artificial elongation

c) Period elongation

d) Algorithmic damping

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Explanation: Period elongation is the apparent change in the natural period of vibration. It is caused due to the finite approximation of the integration operator. A direct consequence of this error is the distortion in the computed response waveforms.

4. What is the other name of Artificial damping?

a) Semi logarithmic damping

b) Linear damping

c) Exponential damping

d) Algorithmic damping

View Answer

Explanation: Artificial damping is also known as algorithmic damping. This is caused by the deviation from unity of modulus of the complex eigenvalues of the integration operator. It leads to either artificial decay or build-up of response amplitudes depending on whether the eigenvalue modulus is less than 1 or greater than 1, respectively.

5. Artificial decay occurs when the eigenvalue modulus is less than unity.

a) False

b) True

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Explanation: Artificial decay occurs when the modulus of eigenvalue is less than 1. Whereas, build-up of response amplitudes occurs when the modulus of eigenvalue is more than 1. These two types of error are dependent on the modulus of eigenvalue.

6. Which method is used to estimate the frequencies and mode shapes of lower modes?

a) Lagrangian approach

b) Eularian approach

c) Rayleigh-Ritz method

d) Newtonian approach

View Answer

Explanation: Rayleigh-Ritz method of model reduction is a very powerful tool to quickly estimate the frequencies and mode shapes of lower modes. This method is used in all commercial structural analysis softwares. The Ritz vectors are determined and using that the matrices are generated.

**Sanfoundry Global Education & Learning Series – Earthquake Engineering.**

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