Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces

• Nonlinear dynamics of a nanobeam with piezoelectricity viscoelasticity coupling.
• Model establishment for a nanobeam subjected to van der Waals forces.
• Numerical simulations of the nanobeam with incremental harmonic balance method.
• Effects of system parameters on nanobeam buckling, post-buckling and instability.

A study on the buckling and dynamic stability of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces is performed in this research. The static and dynamic governing equations of the nanobeam are established with Galerkin method and under Euler–Bernoulli hypothesis. The buckling, post-buckling and nonlinear dynamic stability character of the nanobeam is presented. The quasi-elastic method, Leibnitz’s rule, Runge–Kutta method and the incremental harmonic balanced method are employed for obtaining the buckling voltage, post-buckling characteristics and the boundaries of the principal instability region of the dynamic system. Effects of the electrostatic load, van der Waals force, creep quantity, inner damping, geometric nonlinearity and other factors on the post-buckling and the principal region of instability are investigated.