Question 19.P.5: The uniform bar shown in Figure P19.5 is fixed at both ends ...
The uniform bar shown in Figure P19.5 is fixed at both ends and is undergoing vibrations in an axial direction. It is divided into three components and each component is further subdivided into 2 finite elements. Model each of components 1 and 3 by one normal mode and one residual flexibility attachment mode, the latter corresponding to the interface d.o.f. 2. Model component 2 by the one rigid body mode and two inertia relief attachment modes corresponding to d.o.f. 2 and 3. Obtain the transformed stiffness and mass matrices for each component. Next couple the component matrices by enforcing compatibility of displacements at the interfaces. Calculate the frequencies of the coupled system. Compare these with the frequencies calculated by assuming that the bar is represented by just one component with five d.o.f. Compare also with the exact frequencies of a uniform bar of length L=6 l vibrating in the axial direction. The axial rigidity of the bar is E A, the mass is m per unit length, and the length of each element is l.
