Note on the small vibration of beams with varying Young's modulus carrying a concentrated mass distribution (Q1115673)

The problem of vibration of beams or rods with varying Young's modulus has been solved assuming that the beam or rod carries a concentrated mass distribution. The effect of concentrated mass has been described by introducing a Dirac \(\delta\)-function into the differential equation. The methods of separation of variables and the Laplace transform have been used. A forced vibration problem has been solved after deriving the orthogonlity relation for a variable density beam.