It is of importance to study and predict the possible buckling of submarine pipeline under thermal stress in pipeline design.Since soil resistance is not strong enough to restrain the large deformation of pipeline,hig...It is of importance to study and predict the possible buckling of submarine pipeline under thermal stress in pipeline design.Since soil resistance is not strong enough to restrain the large deformation of pipeline,high-order buckling modes occur very easily.Analytical solutions to high-order buckling modes were obtained in this paper.The relationships between buckling temperature and the amplitude or the wavelength of buckling modes were established.Analytical solutions were obtained to predict the occurrence and consequence of in-service buckling of a heated pipeline in an oil field.The effects of temperature difference and properties of subsoil on buckling modes were investigated.The results show that buckling will occur once temperature difference exceeds safe temperature;high-order pipeline buckling occurs very easily;the larger the friction coefficients are,the safer the submarine pipeline will be.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
Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then trans...Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.展开更多
基金Supported by Innovative Research Groups of the National Natural Science Foundation of China(No.51021004)National Natural Science Foundation of China(No.40776055)+1 种基金Program for New Century Excellent Talents in University(NCET-11-0370)State Key Laboratory of Ocean Engineering Foundation(1002)
文摘It is of importance to study and predict the possible buckling of submarine pipeline under thermal stress in pipeline design.Since soil resistance is not strong enough to restrain the large deformation of pipeline,high-order buckling modes occur very easily.Analytical solutions to high-order buckling modes were obtained in this paper.The relationships between buckling temperature and the amplitude or the wavelength of buckling modes were established.Analytical solutions were obtained to predict the occurrence and consequence of in-service buckling of a heated pipeline in an oil field.The effects of temperature difference and properties of subsoil on buckling modes were investigated.The results show that buckling will occur once temperature difference exceeds safe temperature;high-order pipeline buckling occurs very easily;the larger the friction coefficients are,the safer the submarine pipeline will be.
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Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
