The fuzzy variational principle of complex natural frequency

The fuzzy variational principle (FVP) is one of the important theoretic bases of the fuzzy finite element method (FFEM). Research works on fuzzy finite element method are relatively mature, however, research works on fuzzy variational principle are few. In order to study the fuzzy variational principle of complex natural frequency, firstly, some concepts of the fuzzy mathematics are introduced. And then, the quasi-Hamilton variational principle of non-conservative system is established. The fuzzy variational principle of complex natural frequency is derived by introducing fuzzy parameters into the quasi-Hamilton variational principle. After that, the fuzzy finite element method is presented as the application of the fuzzy variational principle. The presented method can obtain the fuzzy result directly. Compared with conventional fuzzy finite element methods, it avoids the case that the fuzzy parameters are transformed into interval parameters before calculation and then the fuzzy result is constructed by interval results. Therefore, the presented method can reduce the computational cost significantly. Finally, numerical examples are considered to illustrate the practicability of the presented method.