The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and mo...The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.展开更多
The velocity dispersion and attenuation of shear horizontal（SH） waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the（1- x）Pb（Mg（1/3）Nb（2/3））O（3-x）PbTiO3[PMN-xPT]single...The velocity dispersion and attenuation of shear horizontal（SH） waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the（1- x）Pb（Mg（1/3）Nb（2/3））O（3-x）PbTiO3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]c and[001]c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]c polarized PMN-0.29 PT is much smaller than that for the[001]c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]c case are stronger than that for the[001]c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.展开更多
文摘The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.
基金supported by the National Natural Science Foundation of China(No.11272221)the National Key Basic Research Program of China(No.2012CB723300)the support from the Natural Science Foundation of Hebei Province of China(No.A2013210106)
文摘The velocity dispersion and attenuation of shear horizontal（SH） waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the（1- x）Pb（Mg（1/3）Nb（2/3））O（3-x）PbTiO3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]c and[001]c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]c polarized PMN-0.29 PT is much smaller than that for the[001]c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]c case are stronger than that for the[001]c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.
