Altering structures to clear vibration frequencies from a band

Structures vibrate, and sometimes with frequencies that are not wanted. Structures are commonly required to be resonance-free within certain frequency ranges, and if they do have undesirable frequencies, these can be moved by changing the structure sti€ness, or mass, or both. A mixed sti€ness/¯exibility formulation of the vibration problem presents alternative condensations to sti€ness and ¯exibility eigenvalue equations for an altered structure. The ¯exibility form gives more compact equations, and this is developed to solve a parent problem where a structure has a single frequency in a nominated band, to be removed by adjusting the sti€ness of a brace stressing the structure in a single way. Interestingly, if the original eigenvalue problem has a Sturm sequence, the frequency exclusion problem can be solved without determining any frequency or mode of the original structure