The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing...The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.展开更多
The formula of the vibration response and power flow in beam-stiffened plate with force excitation applied on.the plate, have been obtained by using the Steepest Descent Integral method. The characteristics of the pow...The formula of the vibration response and power flow in beam-stiffened plate with force excitation applied on.the plate, have been obtained by using the Steepest Descent Integral method. The characteristics of the power flow have been studied through computer simulation.It is shown that the stiffener acts as an extra lineal excitation applied on the plate and changes the characteristics of the power flow of the infinite plate greatly The greater the stiffness and the smaller the distance between the exciting point and the stiffener is, the greater the induence is. Lastly, experiments have been carried out by using the dualaccelerometer measurement technique that based on cross spectrum, and the test data agree well with the theoretical results展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 60927005)the 2012 Innovation Foundation of BUAA for PhD Graduatesthe Fundamental Research Funds for the Central Universities,China (Grant No. YWF-10-01-A17)
文摘The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.
文摘The formula of the vibration response and power flow in beam-stiffened plate with force excitation applied on.the plate, have been obtained by using the Steepest Descent Integral method. The characteristics of the power flow have been studied through computer simulation.It is shown that the stiffener acts as an extra lineal excitation applied on the plate and changes the characteristics of the power flow of the infinite plate greatly The greater the stiffness and the smaller the distance between the exciting point and the stiffener is, the greater the induence is. Lastly, experiments have been carried out by using the dualaccelerometer measurement technique that based on cross spectrum, and the test data agree well with the theoretical results
