Vibration Of Nanoplates Via Strain Gradient Meshless Method

Interesting on the dynamic characteristics of two-dimensional nanostructures kept increasing for their excellent properties for potential application.In this thesis,strain gradient plate model is used to calculate the vibration of the two-dimensional nanostructure.The influence of small scale parameter and boundary condition on the vibration characteristics are studied via meshless method.The main results of this thesis are as follows:1 A shifted and scaled basis function and a high-order weighting functions are proposed.The vibrational frequency of simply supported plate via the shifted and scaled basis functions is better than that of the polynomial function.2 The scale parameter has little influence on the lower order frequencies of Kirchhoff plate,but has a greater influence on the higher frequencies.The Kirchhoff plate based on strain gradient theory with the elastically supported conditions is studied.With the spring coefficient increasing,the frequency exist a lower bound and an upper bound.3 The natural frequency of strain gradient Mindlin plate model is slightly less than that of classical plate model with essential boundary condition.There exists a certain range of dimensionless spring coefficient where the dimensionless frequency increases significantly.The dimensionless frequency increases very little outside of the range.4 The vibrations of strain gradient Kirchhoff plate with Winkler foundation and the suspended plate are investigated.The boundary condition is the main factor which affect the vibration frequency of strain gradient Kirchhoff plate with Winkler foundation,when the Winkler coefficient is small.When the Winkler coefficient is large,the main factor that affect natural frequency turns to be the Winkler coefficient.With the increase of Winkler coefficient,the vibration modal of the suspended plate tends to fixed boundary case.