A Non-Probabilistic Strategy to Investigate Imprecisely Defined Nonlinear Eigenvalue for Structural Dynamic Problems

Structural dynamic problems are influenced by many parameters which are uncertain in nature. As such, for better estimation, the problems can be considered with epistemic-type uncertainties. Due to the epistemic type of uncertainties, the modeled system appears in the form of an imprecise nonlinear eigenvalue problem. Therefore, this paper proposes a novel nonprobabilistic approach to analyze nonlinear eigenvalue problems in structural dynamics, particularly when dealing with imprecisely defined parameters. In order to solve the fuzzy nonlinear eigenvalue models, the same is to be transformed into a fuzzy eigenvalue problem. Traditional methods often rely on probabilistic frameworks, which may not adequately capture uncertainties inherent in real-world structural systems. The proposed approach leverages concepts from fuzzy set theory to handle imprecise data, providing a more robust and realistic analysis. Then, the developed method is used to solve a case study of structural dynamic problem. Here, a spring-mass system is demonstrated through the developed technique to quantify the uncertain field variables. Based on the imprecise system parameters, different fuzzy models are discussed in various cases and results are reported here. This framework offers valuable insights for engineers and researchers working on dynamic analysis of complex structures, paving the way for more reliable and informed decision-making in structural engineering applications.