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

Table 2

Inverse problem for 2nd and 4th 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=1411.9003,𝜆4=20420.5236; (obtained with 𝑚=0.2𝜌𝐿; 𝑙=0.4𝐿 in the forward code)	𝑚=0.1516𝜌𝐿; 𝑙=0.0972𝐿; (this result was obtained via DirectSearch  and  fsolve  packages)	94.7851𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑6626.2231𝟐𝟎𝟒𝟐𝟎.𝟓𝟐𝟑𝟔51205.11501.11210×10^52.15698×10^53.82314×10^56.29638×10^59.73288×10^5
	𝑚=0.4695𝜌𝐿; 𝑙=0.4268𝐿; (this result was obtained via DirectSearch  package only)	51.2467𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑6082.1204𝟐𝟎𝟒𝟐𝟎.𝟓𝟐𝟑𝟓57662.48081.00203×10^52.33797×10^53.33408×10^56.17507×10^59.04206×10^5
	𝑚=0.2𝜌𝐿; 𝑙=0.4𝐿; (this result was obtained via  DirectSearch  package only)	71.3527𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑7164.6511𝟐𝟎𝟒𝟐𝟎.𝟓𝟐𝟑𝟔60880.68191.05946×10^52.21752×10^53.77388×10^55.73630×10^59.74091×10^5