We intend to conduct a fairly complete study onTimoshenko beams with pointwise feedback controls and seek to obtain informationabout the eigenvalues, eigenfunctions, Riesz-Basis-Property,spectrum-determined-growth-condition, energy decay rate and various stabilitiesfor the beams. One major difficulty of the present problem is the non-simplicityof the eigenvalues.In fact, we shall indicate in this paper situations where the multiplicity ofthe eigenvalues is at least two. We build all the above-mentioned results from an effectiveasymptotic analysis on both the eigenvalues and the eigenfunctions, and concludewith the Riesz-Basis-Property and thespectrum-determined-growth-condition. Finally, these results are used to examinethe stability effects on the system by the location of the pointwise controlrelative to the length of the whole beam.
