Abstract. In this paper, free vibration analysis of rotating annular disc made of Functionally Graded Material (FGM) with variable thickness is presented. Elasticity modulus, density, and thickness of the disc are assumed to vary radially according to a power low function. The natural frequencies and critical speeds of the rotating FG annular disc of variable thickness with two types of boundary conditions are obtained employing the numerical Generalized Di erential Quadrature Method (GDQM). The boundary conditions considered in the analysis are both edges clamped (C-C): the inner edge clamped and outer edge free (C-F). The in uence of the graded index, thickness variation, geometric parameters, and angular velocity on the dimensionless natural frequencies and critical speeds is demonstrated. It is shown that we have higher critical speed and natural frequency using a plate with a convergent thickness pro le, and lower critical speed using a divergent thickness pro le. It is found that the increase in the ratio of inner-outer radii could increase the critical speed of the FG annular disk. The results of the present work could improve the design of the rotating FG annular disk in order to avoid resonance condition.
Conceptual modelling is known as a well suited alternative approach for Computer-Aided Engineering (CAE) analysis in automotive industry. In this paper, an improved conceptual modelling method in which beams and panels of the structure are modelled as simplified beam elements has been proposed. To explore the advantage of conceptual modeling in determining the resonant frequencies/mode-shapes, a case study for wheelhouse was performed. Firstly, an experimental test and advanced CAE analysis were carried out to measure the wheelhouse dynamic characteristics. The advanced CAE model was then validated by means of Modal Assurance Criterion and natural frequencies by associated experimental measurements. The results of wheelhouse concept model compared to the advanced CAE and experimental model in low frequency range, showed that the error percent of natural frequency is lower than 10% and the Modal Assurance Criterion is above 0.75 for the first four mode shapes of wheelhouse structure. Finally, the conceptual model is used as a baseline for optimization. The genetic algorithm was implemented to maximize the first natural frequency to 41.74 Hz. So The genetic algorithm successfully provided new possibility for optimization by attempting to influence the first mode shape by means of the cross section characteristics. Due to the accuracy and reliability of developed conceptual model, this modelling approach can be a crucial tool in CAE and vibration analysis of vehicle in the early design phase. The proposed method allows the designer to give the results of design changes very quickly by neglecting details. Therefore, for the analysis of the vehicle performance in NVH domain, the proposed method could be considered in the conceptual design phase.
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