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

Table 6

Inverse problem for 2nd, 4th, 6th, and 8th frequencies for a simply-supported beam with two mass attachments.

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=668.684,𝜆4=19864.9146, 𝜆6=1.08009×10^5,𝜆8=2.93825×10^5; The original masses used in the forward problem to obtain these frequencies are 𝑚1=0.2𝜌𝐿,𝑥1=0.2𝐿 and 𝑚2=0.8𝜌𝐿,𝑥2=0.7𝐿	𝑚1=0.1878𝜌𝐿, 𝑙1=0.3164𝐿; 𝑚2=0.5629𝜌𝐿,𝑙2=0.8001𝐿; (this result was obtained using  fsolve package)	58.6059𝟔𝟔𝟖.𝟔𝟖𝟒5460.7847𝟏𝟗𝟖𝟔𝟒.𝟗𝟏𝟒𝟕50993.9093𝟏.𝟎𝟖𝟎𝟎𝟗×𝟏𝟎^𝟓1.8551×10^5𝟐.𝟗𝟑𝟖𝟐𝟓×𝟏𝟎^𝟓
	𝑚1=0.8818𝜌𝐿, 𝑙1=0.6982𝐿; 𝑚2=0.1733𝜌𝐿,𝑙2=0.3026𝐿; (this result was obtained using DirectSearch package)	40.0684𝟔𝟓𝟎.𝟒𝟕𝟏𝟏7374.925𝟏𝟗𝟖𝟓𝟐.𝟗𝟖𝟗𝟔36398.8778𝟏.𝟎𝟖𝟎𝟎𝟗×𝟏𝟎^𝟓2.2392×10^5𝟐.𝟗𝟑𝟖𝟐𝟓×𝟏𝟎^𝟓
	𝑚1=0.1664𝜌𝐿, 𝑙1=0.3052𝐿; 𝑚2=0.992𝜌𝐿,𝑙2=0.7001𝐿; (this result was obtained using DirectSearch package)	37.9215𝟔𝟑𝟕.𝟕𝟎𝟓𝟖7355.9992𝟏𝟗𝟗𝟎𝟒.𝟒𝟖𝟒𝟑36200.0203𝟏.𝟎𝟖𝟎𝟎𝟗×𝟏𝟎^𝟓2.24118×10^5𝟐.𝟗𝟑𝟖𝟐𝟓×𝟏𝟎^𝟓
	𝑚1=0.3414𝜌𝐿, 𝑙1=0.3092𝐿; 𝑚2=0.2602𝜌𝐿,𝑙2=0.797𝐿; (this result was obtained using DirectSearch package)	58.8707𝟕𝟓𝟔.𝟖𝟓𝟓𝟗5907.6828𝟏𝟗𝟗𝟏𝟕.𝟔𝟑𝟓𝟖48021.3302𝟏.𝟎𝟖𝟎𝟎𝟗×𝟏𝟎^𝟓1.93859×10^5𝟐.𝟗𝟑𝟖𝟐𝟓×𝟏𝟎^𝟓