A Structured Approach to Solve the Inverse Eigenvalue Problem for a Beam with Added Mass

The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem). A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem). In this paper, a method to impose two natural frequencies on a dynamical system consisting of an Euler-Bernoulli beam and carrying a single mass attachment is evaluated.

Kratzer Potential for Vibrational Levels in Molecular Hydrogen

The vibrational part of the dihydrogen Hamiltonian obeys a quantized Sommerfeld-Kratzer potential, which takes into account internal H2 symmetries. All constants ωe, ke, and re needed for the H2 vibrational system derive from hydrogen mass. Ionic Kratzer bond theory gives covalent bond energy within 0.08% and all levels within 0.02%, which is 30 times better than with a Dunham oscillator and as accurate as early ab initio quantum mechanics