Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-st...Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.展开更多
Character of contract pressure distribution between the outside surface of the sealing material and rigid cylinder wall depending on geometrical sizes and mechanical properties of a sealer under its unilateral compres...Character of contract pressure distribution between the outside surface of the sealing material and rigid cylinder wall depending on geometrical sizes and mechanical properties of a sealer under its unilateral compression, is defined. The magnitude of the axial load for achieving tightness is determined. The dependence between the magnitude of the axial load necessary for achieving tightness and geometrical sizes is determined. It is shown that with a decrease in the height of the sealing element, the axial load necessary for achieving tightness greatly increases. Threshold height of the sealer, above which contact pressure depends little on the magnitude of the axial load, is defined. The stress-strain state of the sealing element is defined with regard to viscous-elastic properties of its material. It is shown that this greatly influences its sealing ability.展开更多
基金Supported by the National Outstanding Young Scientists Fund of China (Grant No. 10725209)the Shanghai Leading Academic Discipline Project (Grant No. S30106)Shandong Jiaotong University Science Foundation (Grant No. Z200812)
文摘Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
文摘Character of contract pressure distribution between the outside surface of the sealing material and rigid cylinder wall depending on geometrical sizes and mechanical properties of a sealer under its unilateral compression, is defined. The magnitude of the axial load for achieving tightness is determined. The dependence between the magnitude of the axial load necessary for achieving tightness and geometrical sizes is determined. It is shown that with a decrease in the height of the sealing element, the axial load necessary for achieving tightness greatly increases. Threshold height of the sealer, above which contact pressure depends little on the magnitude of the axial load, is defined. The stress-strain state of the sealing element is defined with regard to viscous-elastic properties of its material. It is shown that this greatly influences its sealing ability.
