Question

The number of natural frequencies of an elastic beam with cantilever boundary conditions is

• A. 1
• B. 3
• C. 6
• D. infinite

Hint:

Only the first few natural frequencies are generally of practical interest.

Answer 1

The Correct Option is D

In the context of an elastic beam with cantilever boundary conditions, it's important to understand the concept of natural frequencies. Natural frequencies are the characteristic frequencies at which a system tends to oscillate in the absence of any driving force. For a beam, these frequencies are determined by its physical properties and boundary conditions.

A cantilever beam is fixed at one end and free at the other. This setup allows the beam to support various modes of vibration. Each mode corresponds to a natural frequency, and theoretically, a beam can vibrate in an infinite number of modes. These modes are harmonics, where each higher mode has a higher frequency.

Mathematically, the relation for natural frequencies of a cantilever beam involves solving a differential equation based on the beam’s material and geometric properties typically resulting in multiple eigenvalues representing these frequencies. Because there are an infinite number of possible modes (and hence, natural frequencies), the correct answer is infinite.