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

Table 3

Inverse problem for 2nd and 8th frequencies for a simply-supported beam.

Input given to the inverse problem	Solution via inverse determinant method	Full span of frequency squared spectrum obtained via the solution of forward problem
𝜆2=1411.900275,𝜆8=3.773881670×10^5; (obtained with 𝑚=0.2𝜌𝐿; 𝑙=0.4𝐿 in the forward code)	𝑚=0.2𝜌𝐿; 𝑙=0.6𝐿	71.3527𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑7164.6511120420.5236360880.68191.05946×10^52.21752×10^5𝟑.𝟕𝟕𝟑𝟖𝟖×𝟏𝟎^𝟓5.73630×10^59.74091×10^5
	𝑚=0.0807𝜌𝐿; 𝑙=0.6615𝐿	86.6441𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑7887.552322430.048556495.17321.26101×10^52.13015×10^5𝟑.𝟕𝟕𝟑𝟖𝟖×𝟏𝟎^𝟓6.37810×10^59.05601×10^5
	𝑚=0.0752𝜌𝐿; 𝑙=0.8447𝐿	94.2653𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑6953.808522707.079258428.84531.25669×10^52.31928×10^5𝟑.𝟕𝟕𝟑𝟖𝟖×𝟏𝟎^𝟓5.86872×10^59.10470×10^5
	𝑚=0.0585𝜌𝐿; 𝑙=0.7133𝐿	90.83562𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑7750.632324432.234855584.56851.20289×10^52.33870×10^5𝟑.𝟕𝟕𝟑𝟖𝟖×𝟏𝟎^𝟓5.98869×10^59.64184×10^5
	𝑚=0.0573𝜌𝐿; 𝑙=0.7944𝐿	93.4974𝟏𝟒𝟏𝟏.𝟗𝟎𝟎𝟑7262.291424320.898460836.87051.20776×10^52.15464×10^5𝟑.𝟕𝟕𝟑𝟖𝟖×𝟏𝟎^𝟓6.30690×10^59.72121×10^5