Chapter 10: Problem 7
Consider free torsional vibrations of a uniform circular elastic rod of length \(L\), torsional stiffiness \(G J\) and mass per unit length \(m\), that is free at its left end and embedded in an elastic wall of stiffness \(k_{\theta}=G J / L\) at its right end, as shown. (a) Establish the modal boundary conditions for the structure. (Hint: See Problem 9.8). (b) Derive the frequency equation for the rod. (c) Determine the first three natural frequencies and modal functions. Plot the first three modes.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.