The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinea...The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching, the influence of volume fraction profile parameter and temperature change. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Taking the temperature-dependency of the effective material properties into consideration, the Voigt model is used to simulate the material properties of the FGMs （functionally graded materials）. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using DQM （differential quadrature method）. The natural frequencies of clamped-clamped micro-switches are obtained. The solutions are validated through direct comparisons with experimental results reported in previous studies. A parametric study is conducted to show the effects of geometric nonlinearity, material composition, temperature change and geometrical parameters for the natural frequencies.展开更多
Based on some assumptions,the dynamic governing equation of anchorage system is established.The calculation formula of natural frequency and the corresponding vibration mode are deduced.Besides,the feasibility of the ...Based on some assumptions,the dynamic governing equation of anchorage system is established.The calculation formula of natural frequency and the corresponding vibration mode are deduced.Besides,the feasibility of the theoretical method is verified by using a specific example combined with other methods.It is found that the low-order natural frequency corresponds to the first mode of vibration,and the high-order natural frequency corresponds to the second mode of vibration,while the third mode happens only when the physical and mechanical parameters of anchorage system meet certain conditions.With the increasing of the order of natural frequency,the influence on the dynamic mechanical response of anchorage system decreases gradually.Additionally,a calculating method,which can find the dangerous area of anchorage engineering in different construction sites and avoid the unreasonable design of anchor that may cause resonance,is proposed to meet the seismic precautionary requirements.This method is verified to be feasible and effective by being applied to an actual project.The study of basic dynamic features of anchorage system can provide a theoretical guidance for anchor seismic design and fast evaluation of anchor design scheme.展开更多
基金Acknowledgments The research was financially supported by the National Natural Science Foundation of China （Grant No. 11402309） and the Science Foundation of China University of Petroleum, Beijing （No. YJRC-2013-32）.
文摘The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching, the influence of volume fraction profile parameter and temperature change. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Taking the temperature-dependency of the effective material properties into consideration, the Voigt model is used to simulate the material properties of the FGMs （functionally graded materials）. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using DQM （differential quadrature method）. The natural frequencies of clamped-clamped micro-switches are obtained. The solutions are validated through direct comparisons with experimental results reported in previous studies. A parametric study is conducted to show the effects of geometric nonlinearity, material composition, temperature change and geometrical parameters for the natural frequencies.
基金Projects(51308273,41372307,41272326)supported by the National Natural Science Foundation of ChinaProject(20090211110016)supported by Specialized Research Fund for the Doctoral Program of Higher Education of ChinaProject(2010(A)06-b)supported by Science and Technology Fund of Yunan Provincial Communication Department,China
文摘Based on some assumptions,the dynamic governing equation of anchorage system is established.The calculation formula of natural frequency and the corresponding vibration mode are deduced.Besides,the feasibility of the theoretical method is verified by using a specific example combined with other methods.It is found that the low-order natural frequency corresponds to the first mode of vibration,and the high-order natural frequency corresponds to the second mode of vibration,while the third mode happens only when the physical and mechanical parameters of anchorage system meet certain conditions.With the increasing of the order of natural frequency,the influence on the dynamic mechanical response of anchorage system decreases gradually.Additionally,a calculating method,which can find the dangerous area of anchorage engineering in different construction sites and avoid the unreasonable design of anchor that may cause resonance,is proposed to meet the seismic precautionary requirements.This method is verified to be feasible and effective by being applied to an actual project.The study of basic dynamic features of anchorage system can provide a theoretical guidance for anchor seismic design and fast evaluation of anchor design scheme.
