A modified perturbation method for treating non-linear oscillation problems

✍ Scribed by G.L. Anderson

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 571 KB
• Volume: 38
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(75)80133-7

✦ Synopsis

In this investigation a method that uses multiple time scales for the purpose of obtaining uniform asymptotic solutions of non-linear ordinary differential equations is modified through the introduction of a new small parameter, p, defined by p = e/(l + e), where c denotes the non-linearity parameter given in the differential equation under consideration. Since the value 0fp is positive and less than unity forany positive value ofe, asymptotic expansions in terms ofp are attempted in the hope of enlarging the radius of convergence of these expansions. The technique is applied to a differential equation which arises in the nonlinear theory of transverse vibrations of hinged-hinged thin cylindrical shells. A series of numerical calculations reveal that the p-expansion proposed here yields an approximation for the frequency of free periodic motion of the shell which represents an improvement over the corresponding e-expansion for a significant range of the parameters studied.