Nonlinear Vibration and Instability Analysis of a PVDF Cylindrical Shell Reinforced with BNNTs Conveying Viscose Fluid Using HDQ Method

Using harmonic differential quadrature (HDQ) method, nonlinear vibrations and instability of a smart composite cylindrical shell made from piezoelectric polymer of polyvinylidene fluoride (PVDF) reinforced with boron nitride nanotubes (BNNTs) are investigated while clamped at both ends and subjected to combined electro-thermo-mechanical loads and conveying a viscous-fluid. The mathematical modeling of the cylindrical shell and the resulting nonlinear coupling governing equations between mechanical and electrical fields are derived using Hamilton’s principle based on the first-order shear deformation theory (FSDT) in conjunction with the Donnell's non-linear shallow shell theory. The governing equations are discretized via HDQ method, and solved to obtain the resonant frequencies and critical flow velocities associated with divergence and flutter instabilities as well as re-stabilization of the system. Results indicate that the internal moving fluid plays an important role in the instability of the cylindrical shell. Application of a smart material such as PVDF improves significantly the stability and vibration of the system.