Nonlinear vibration analysis of double-layered nanoplates with different boundary conditions

• Nonlinear vibrations of DLNP for four boundary conditions are investigated.
• Nonlocal effect and boundary condition highly affect the nonlinearity of DLNP.
• The point P where the nonlinearity is weakest can be found for lower mode.
• Point P only exists for clamped movable edges when ignoring nonlocal effect.

By the nonlocal theory, the nonlinear equations for double-layered nanoplates (DLNP) with different boundary conditions are established. The relation between aspect ratio and nonlinear frequencies with fixed mode amplitude is discussed. This relation for two vibration modes presents completely distinct trends. The novel fact is observed that there exists a point P where nonlinearity is weakest for the fundamental mode. Furthermore, we notice that P only appears for clamped movable edge when neglecting the nonlocal effect, which is substantially different from the other boundary conditions. It should distinguish whether the edge is movable or immovable for studying nonlinear dynamics of DLNP.