This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Dynamic Considerations – Shaft Critical Speeds and Guyan Reduction”.

1. Guyan Reduction helps increase the degrees of freedom.

a) True

b) False

View Answer

Explanation: The given statement is false. Guyan reduction is a type of dynamic reduction technique. It helps us to decrease the degrees of freedom in order to improve computation capabilities of the system. In this method, the degrees of freedom are divided into active and deleted degrees of freedom.

2. What type of degrees of freedom are preferred to be retained?

a) Degrees of freedom corresponding to large concentrated masses

b) Degrees of freedom corresponding to small concentrated masses

c) Degrees of freedom corresponding to parallel masses

d) Degrees of freedom corresponding to perpendicular masses

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Explanation: The retained set of degrees of freedom constitutes of about 20% of the total degrees of freedom. It is preferred to retain the degrees of freedom with large concentrated masses associated with them. This helps us to easily describe the modal shapes and nodes.

3. Which of the following is not a dynamic reduction technique?

a) Guyan reduction

b) Dynamic condensation

c) Euler’s reduction

d) Kammer’s conduction

View Answer

Explanation: Dynamic reduction techniques are utilized to reduce the degrees of freedom of large structures. This is done in order to improve solvability and reduce computation time of solving the problem under consideration. Euler’s reduction is not a dynamic reduction technique.

4. Forces on the deleted degrees of freedom are assumed to be zero.

a) True

b) False

View Answer

Explanation: Upon partitioning the degrees of freedom into retainable and deleted types, the retained degrees of freedom are utilized for solving the given dynamic finite element model. In order to aid this method, the deleted degrees of freedom are assumed to have no forces associated with them. This helps us to omit the complexity of the given dynamic consideration.

5. “Guyan method is not accurate for stiffness reduction.” Why is this so?

a) It is a dynamic condensation method

b) It is a non linear condensation method

c) It is a linear condensation method

d) It is a static condensation method

View Answer

Explanation: Guyan reduction method is the simplest of all dynamic reduction techniques. It makes use of static condensation procedures in order to decrease the degrees of freedom. Because of this reason, the inertial forces are not preserved upon reduction; making it inaccurate for stiffness reduction.

6. Which of the following is a property of the Guyan reduction technique?

a) Quality of eigenvalue approximation decreases with increase in the number of modes

b) Quality of eigenvalue approximation increases with increase in the number of modes

c) Quality of eigenvalue approximation decreases with decrease in the number of modes

d) Quality of eigenvalue approximation decreases with increase in the number of vectors

View Answer

Explanation: It is true that the quality of eigenvalue approximation decreases with the increase in number of modes. In fact, the quality of this approximation is also dependent highly on the location of points reserved in the reduced model.

7. What are the outputs of the BEAMKM program?

a) Mass and stiffness matrices

b) Stiffness matrix only

c) Mass matrix only

d) Eigenvalue vectors

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Explanation: The outputs of the BEAMKM program are the mass and stiffness matrices respectively. These outputs are then fed as inputs to the INVITR program in order to arrive at desired results. The BEAMKM program is a simplified computer program that performs all the necessary calculations that help arrive at the respective matrices.

8. What are the outputs of the INVITR program?

a) Eigen values only

b) Eigen values and vectors

c) Eigen vectors only

d) Stiffness and mass matrices

View Answer

Explanation: The outputs of the INVITR program are the Eigen values and vectors respectively. These help in the determination of modal shapes of the given finite element model. INVITR makes use of inverse iteration methodology to arrive at the required solutions. It also helps in calculating the natural frequencies of the model under consideration.

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