Nanoscale Inertial-Sensor Elements. Numerical and Analytical Modeling of Motion

A mathematical model of the motion of sensor's nanoscale elements as nanoscale rectangular plates under the action of a non-stationary distributed load is constructed. The principle of virtual displacements, the third-order shear deformation plate theory, and a new modified theory of coupled stresses were used for the construction of the model. For some boundary conditions, an analytical solution of the constructed mathematical model was obtained. The obtained relations are verified by numerical simulation using ANSYS and with zero values of the length scale parameters introduced by the new modified theory, which takes into account the discontinuity of the plate material. The difference in the results was less than 0.8%. To determine the degree of influence of the size-dependent parameters of the material on the deformation of the nanoplate, a series of computer experiments were conducted.