Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams

摘要: In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The beams account for rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach show, that certain polynomial variations mass per unit length and flexural stiffness, there exists a fundamental closed form solution to fourth order governing differential equation derived property variation can serve as test functions numerical methods. For rotating case, results have been compared with those using