Structural Dynamics MCQ with answer and solution

Concept

Estimating fundamental natural frequencies using energy

Formula

ω² = (g × Σ W_i × y_i) / (Σ W_i × y_i²)

Step-by-step solution

1. Rayleigh's principle states that for an undamped conservative vibrating system, maximum kinetic energy equals maximum potential (strain) energy. 2. By assuming a realistic deflected dynamic mode shape, Rayleigh's quotient provides an upper bound approximation of the fundamental circular frequency ω. 3. Therefore, Rayleigh's method is widely utilized to estimate natural frequencies of structures. Answer: B

Explanation

Rayleigh's method is an energy-based technique that equates the maximum kinetic energy of a vibrating system during motion to its maximum strain energy, providing an accurate estimate of the fundamental natural frequency.

Why the other options are wrong

A) Support reactions are found using static equilibrium equations. C) Deflections can be calculated using Macaulay's or conjugate beam methods. D) Buckling loads are calculated using Euler's formula or Southwell plots.

Shortcut

Rayleigh's quotient equates T_max = U_max to estimate fundamental natural frequency.

Common mistake

Believing Rayleigh's method is for finding static reactions or static deflections.