On the sensitivities of multiple eigenvalues

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Isogeometric Shape Optimization of Vibrating Membranes (2011, background): “It can be shown [36] that the sensitivities of the functions λ k + λ k +1 and λ k λ k +1 are given as b b b b b From (9) and (15), it follows that if the partial derivative of a function f with respect to ρ has been calculated as above, its sensitivities with respect to the design variables ρ b are…”
Topology optimization of continuum structures under buckling constraints (2015, unknown): “[30] can be used.”