Mochida, YusukeIlanko, SinniahKennedy, D.2018-05-032017-05-012018-05-032017Mochida, Y., Ilanko, S., & Kennedy, D. (2017). Attaching negative structures to model cut-outs in the vibration analysis of structures. Computers & Structures, 184, 14–24. https://doi.org/10.1016/j.compstruc.2017.02.0030045-7949https://hdl.handle.net/10289/11809The presence of a hole, cut-out or void in a structure makes it difficult to be modelled for calculating natural frequencies. A theoretical basis for simplifying the modelling of cut-outs in a structure by attaching a negative structure is presented. The Dynamic Stiffness Method has been used to prove that this method yields the required natural frequencies. The derivations also show the presence of additional natural frequencies which correspond to the vibration of the positive and negative parts vibrating together while the actual structure with the hole or cut-out usually remains stationary.application/pdfenThis is an author’s accepted version of an article published in the journal: Computers & Structures. © 2017 Elsevier.Science & TechnologyTechnologyComputer Science, Interdisciplinary ApplicationsEngineering, CivilComputer ScienceEngineeringNegative structureDynamic Stiffness MethodNatural frequenciesPlates with holesIndependent Coordinate Coupling MethodRayleigh-Ritz MethodEXACT STIFFNESS ANALYSISNATURAL FREQUENCIESCOMPOSITE PLATESRECTANGULAR-PLATESCIRCULAR HOLERITZ METHODDELAMINATIONSOPTIMIZATIONCONVERGENCESHELLSJournal Article10.1016/j.compstruc.2017.02.0031879-2243