Nonlinear Free Vibration Analysis of SMA Laminated Beam Based on Two-step Perturbation Method
The nonlinear free vibration of SMA(shape memory alloy)laminated beams is analyzed.The mechanical properties of the SMA are described by the Brison one-dimensional constitutive model.Based on different shear functions and Von Karman's large deformation theory,the relationship between beam mass displacement and strain is established.Using Hamilton's variational principle,the dynamic equations of the simply supported SMA laminated beams at both ends on elastic foundations are obtained,and dimensionless processing is carried out.The nonlinear free vibration equation of the SMA laminated beam is obtained by the two-step perturbation method.The effects of different SMA volume fraction,pre-strain,SMA laying angle and temperature change on nonlinear vibration are studied.
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