234 C. Martinelli et al. Fig. 30.5 Experimental linear TFs between the input base velocity and the acceleration of the tip masses for the three considered configurations: complete system (primary . +secondary structure), primary structure, and secondary structure. TFs of the complete system, i.e. .T1,3 and .T2,3, consider, respectively, the acceleration of the tip mass of the primary and the secondary structure as an output signal Finally, the efficacy of the compliant mechanism as a nonlinear vibration absorber is experimentally tested. The linear TF between the velocity of the base and the absolute acceleration of the tip masses is recorded again with random excitation and the unit DataPhysics Abacus 901 for the primary structure, the secondary structure, and the complete system with primary and secondary structure. The results are reported in Fig.30.5 and demonstrate that the compliant nonlinear mechanism is able to reduce the response amplitude of the beam around the resonance frequency of the primary structure, hence acting as a nonlinear vibration absorber. 30.5 Conclusion In this paper, the experimental analysis and the nonlinear characterisation of a compliant mechanism with a complex hexagonal shape which acts as a nonlinear vibration absorber of a simple cantilever beam are performed. Firstly, the linear properties of the primary and secondary structures are identified by using the averaged linear TF. Then, the RFSM is implemented to identify the nonlinear stiffness and damping characteristics of an equivalent SDOF oscillator, representing the compliant mechanism. These properties are fitted with a third-degree polynomial and the resulting quadratic and cubic coefficients of damping and stiffness are adopted in the validation process. Finally, the identified nonlinear SDOF oscillator is validated by comparing the numerical and experimental results in terms of amplitude response at different frequencies and excitation amplitudes. The RFS of the compliant mechanism shows interesting stiffness and damping nonlinear properties. Surprisingly, the system offers a softening stiffness characteristic which reduces the resonance frequency of the system when the excitation amplitude is increased. On the other hand, the damping shows an asymmetric quadratic behaviour with respect to the relative velocity. ˙z which could be due to small imperfections in the compliant mechanism. Such imperfections could be generated by the 3D-printing process, resulting in an asymmetric deformation of the mechanism which is responsible for the associated asymmetric damping characteristic. Moreover, the outlined identification process is shown to be effective in identifying an equivalent nonlinear SDOF oscillator, as demonstrated by the experimental validation. Finally, the system is experimentally tested in the three proposed configurations and the compliant mechanism capabilities to dampen the dynamic response of a simple steel beam are successfully demonstrated. Acknowledgments The authors would like to acknowledge the Institution of Engineering and Technology (IET) and the following NERC and EPSRC grants: GALLANT, Glasgow as a Living Lab Accelerating Novel Transformation (No. NE/W005042/1), RELIANT, Risk EvaLuatIon fAst iNtelligent Tool for COVID19 (No. EP/V036777/1).
RkJQdWJsaXNoZXIy MTMzNzEzMQ==