The vibration and instability of functionally graded material(FGM)sandwich cylindrical shells conveying fluid are investigated.The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwi...The vibration and instability of functionally graded material(FGM)sandwich cylindrical shells conveying fluid are investigated.The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells.Based on the third-order shear deformation shell theory,the governing equations of the system are derived by using the Hamilton’s principle.To check the validity of the present analysis,the results are compared with those in previous studies for the special cases.Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent,while decreases with the rise of fluid density,radius-to-thickness ratio and length-to-radius ratio.The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1-2.5,which should be avoided in engineering application.展开更多
The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t...The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t）x＇（t） ＋ q（t）x（t）=0where M〉 0, r（t） is positive continuous function. The conclusion is based also on building function where coefficients are involved in the equation and positive functions used by Philo H（t, s） and averaging techniques. Our results generalized, extend to some already known oscillation criteria in the literature. Also, here we give some applications of oscillation solution of. （1） and （2）, wherep（t） and q（t） are positive. The original purposes of differential equation are the mathematical formulation of the vibration frequency and the amplitude profile of a vibrating string with friction which the mass may have to encounter air resistance in its motion and in electric circuit containing an ac voltage source, an indicator, a capacitor, and a resistor in series is analyzed mathematically, the equation that results is a second order linear differential equation with oscillatory solution.展开更多
This paper, we discuss a class of second order nonlinear neutral differential equations with variable coefficients and variable deviations， Sharp conditions are established for all bounded solutions of the equations ...This paper, we discuss a class of second order nonlinear neutral differential equations with variable coefficients and variable deviations， Sharp conditions are established for all bounded solutions of the equations to be oscillatory， Linearized oscillation criteria of the equations are also given，展开更多
In this paper, some counterexamples are offered to illustrate that some results stated in a recent paper on the oscillatory behavior of solutions of second order nonlinear difference equation are incorrect.
基金supported by the National Natural Science Foundation of China(Nos.11922205,12072201)the Fundamental Research Fund for the Central Universities(No.N2005019)。
文摘The vibration and instability of functionally graded material(FGM)sandwich cylindrical shells conveying fluid are investigated.The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells.Based on the third-order shear deformation shell theory,the governing equations of the system are derived by using the Hamilton’s principle.To check the validity of the present analysis,the results are compared with those in previous studies for the special cases.Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent,while decreases with the rise of fluid density,radius-to-thickness ratio and length-to-radius ratio.The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1-2.5,which should be avoided in engineering application.
文摘The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t）x＇（t） ＋ q（t）x（t）=0where M〉 0, r（t） is positive continuous function. The conclusion is based also on building function where coefficients are involved in the equation and positive functions used by Philo H（t, s） and averaging techniques. Our results generalized, extend to some already known oscillation criteria in the literature. Also, here we give some applications of oscillation solution of. （1） and （2）, wherep（t） and q（t） are positive. The original purposes of differential equation are the mathematical formulation of the vibration frequency and the amplitude profile of a vibrating string with friction which the mass may have to encounter air resistance in its motion and in electric circuit containing an ac voltage source, an indicator, a capacitor, and a resistor in series is analyzed mathematically, the equation that results is a second order linear differential equation with oscillatory solution.
文摘This paper, we discuss a class of second order nonlinear neutral differential equations with variable coefficients and variable deviations， Sharp conditions are established for all bounded solutions of the equations to be oscillatory， Linearized oscillation criteria of the equations are also given，
文摘In this paper, some counterexamples are offered to illustrate that some results stated in a recent paper on the oscillatory behavior of solutions of second order nonlinear difference equation are incorrect.
