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This work focuses on the detection of the buckling phenomena and bifurcationanalysis of the parametric Von K\'arm\'an plate equations based on reducedorder methods and spectral analysis. The computational complexity - due to thefourth order derivative terms, the non-linearity and the parameter dependence -provides an interesting benchmark to test the importance of the computationalreduction strategies, during the construction of the bifurcation diagram byvarying the parameter(s). To this end, together the state equations, we carryout also an analysis of the linearized eigenvalue problem, that allows us tobetter understand the physical behaviour near the bifurcation points, where welose the uniqueness of solution.

Reduced basis approaches for parametrized bifurcation problems held by non-linear Von K\'arm\'an equations