An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and rev- olution shells was given in the turning-point frequency range in Chapter 1.It shows that some problems con-...An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and rev- olution shells was given in the turning-point frequency range in Chapter 1.It shows that some problems con- cerning vibrations of shells in the turning-point range have to be further studied.The linear vibrations展开更多
The turning-point problem in free vibration of revolution shells has the coupling property between the bending and membrane solutions. The uniformly valid solutions for this coupling turning-point problem are obtained...The turning-point problem in free vibration of revolution shells has the coupling property between the bending and membrane solutions. The uniformly valid solutions for this coupling turning-point problem are obtained based on three categories of generalized functions. Furthermore, they are verified to be uniformly valid in the low, turning-point and high frequency ranges. The obtained solutions exhibit a symmetric coupling structure between the bending and membrane solutions.展开更多
This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal...This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method. By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.展开更多
A second order linear ordinary differential equation has been studied,and thecomplete expression.of the formal uniformly valid asymptotic solutions to the equationnear turning point is obtained by using extended Airy ...A second order linear ordinary differential equation has been studied,and thecomplete expression.of the formal uniformly valid asymptotic solutions to the equationnear turning point is obtained by using extended Airy function.展开更多
文摘An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and rev- olution shells was given in the turning-point frequency range in Chapter 1.It shows that some problems con- cerning vibrations of shells in the turning-point range have to be further studied.The linear vibrations
基金Supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. 100039)the Shanghai Leading Academic Discipline Project (Grant No. S30106)
文摘The turning-point problem in free vibration of revolution shells has the coupling property between the bending and membrane solutions. The uniformly valid solutions for this coupling turning-point problem are obtained based on three categories of generalized functions. Furthermore, they are verified to be uniformly valid in the low, turning-point and high frequency ranges. The obtained solutions exhibit a symmetric coupling structure between the bending and membrane solutions.
文摘This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method. By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.
文摘A second order linear ordinary differential equation has been studied,and thecomplete expression.of the formal uniformly valid asymptotic solutions to the equationnear turning point is obtained by using extended Airy function.
