# Finite Element Method Questions and Answers – Dynamic Considerations – Rigid Body Modes

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Dynamic Considerations – Rigid Body Modes”.

1. What are the two types of modes available for modal consideration of dynamic bodies?
a) Rigid body and deformation modes
b) Rigid body and translational modes
c) Rigid body and rotational modes
d) Linear and non linear modes

Explanation: For modal consideration of dynamic bodies, we have two modes available – rigid body modes and deformation modes. Usually these bodies contain 6 rigid body modes and 2 deformation modes. The deformation modes are expected to be found out using the eigenvalue analysis.

2. What do the rigid body modes of a structure correspond to?
a) Rotations and directions
b) Translations and rotations
c) Vectors and magnitudes
d) Shapes and sizes

Explanation: The rigid body modes of a structure correspond to the translations and rotations of the structure under consideration. They are usually six in number, three translations and three rotations – one along each of the co ordinate axes respectively.

3. Rigid body mode is defined as the free translation or rotation of a body with undergoing any significant internal deformation.
a) True
b) False

Explanation: The given statement is false. Rigid body modes correspond to the translational and rotational motions that a structure can undergo without having to succumb to any significant internal stresses or loads.

4. Which of the following corresponds to a rigid body mode?
a) It is a constrained mode
b) It cannot be translated easily
c) It is an unconstrained mode
d) It cannot be rotated easily

Explanation: A rigid body mode corresponds to an unconstrained mode which if free to have translational and rotational types of motion. In this entire process, the mode cannot be under the influence of external/internal loads and stresses or constraints.

5. Rigid body modes have zero natural frequency.
a) True
b) False

Explanation: Modal analysis of rigid body modes has proven that they have zero natural frequency. This means that, the body is capable of showing structural deformations without any flexible deformations. Zero frequency excitation corresponds to no vibration; and hence makes path for a rigid body mode.
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6. Which of the following is an example of a rigid body mode?
a) Beam with bending
b) Constrained spring mass system
d) Unconstrained spring mass system

Explanation: The unconstrained spring mass system corresponds to a system having rigid body modes. This body would have a natural frequency equal to zero. All the other examples do not correspond to rigid body modes as they are either under application of loads or are constrained in one manner or the other.

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