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

Table 1

Inverse problem for 2nd and 3rd frequencies for a simply-supported beam.

Input given to inverse determinant method	Solution via inverse determinant method	Full span of frequency squared spectrum obtained via the solution of forward problem
𝜆2=1210.7430,𝜆3=7703.7093; (obtained with 𝑚=0.2𝜌𝐿; 𝑙=0.3𝐿  in the forward code)	𝑚=0.2𝜌𝐿; 𝑙=0.3𝐿; (this result was obtained via both  DirectSearch  and  fsolve  methods)	76.8682𝟏𝟐𝟏𝟎.𝟕𝟒𝟑𝟎𝟕𝟕𝟎𝟑.𝟕𝟎𝟗𝟑22705.248149733.61431.19385×10^52.29571×10^53.45310×10^55.95631×10^59.74091×10^5
	𝑚=0.3895𝜌𝐿; 𝑙=0.3587𝐿; (this result was obtained via both  DirectSearch  and  fsolve  packages)	59.0673𝟏𝟐𝟏𝟎.𝟕𝟒𝟑𝟎𝟕𝟕𝟎𝟑.𝟕𝟎𝟗𝟑18122.302255694.12921.18846×10^51.91164×10^53.88304×10^55.89699×10^58.69163×10^5