Tension-Leg Platform (TLP) is a vertically moored floating structure. The platform is permanently mooredby tendons. Surge equation of motion of TLP is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. This paper compare the dynamic motion responses of a TLP in regular sea waves obtained by applying three method in time domain usin...

In this paper, the nonlinear vibrations analysis of functionally graded (FG) rectangular plate in contact with fluid are investigated analytically using first order shear deformation theory (FSDT). The pressure exerted on the free surface of the plate by the fluid is calculated using the velocity potential function and the Bernoulli equation. With the aid of von Karman nonlinearity strain-displ...

A numerical order verification technique is applied to demonstrate that the asymptotic expansions of solutions of the Duffing equation obtained respectively by the Lindstedt-Poincaré(LP) method and the modified Lindstedt-Poincaré(MLP) method are uniformly valid for small parameter values. A numerical comparison of error shows that the MLP method is valid whereas the LP method is invalid for lar...

Weakly nonlinear oscillatory problems in engineering dynamics are frequently presented by nonlinear ordinary differential equations. Very few of such equations have exact solutions, thus the need for approximation techniques. In this study, the classical perturbation method, namely the Lindstedt-Poincare method (L-P method) is discussed. In most work, the L-P method is used to obtain uniformly ...

Doubly periodic solutions for the Lagrange{Euler equation of the (1+1)-dimensional scalar ' 4 theory are studied. Provided that nonlin-ear term is small, the Poincare{Lindstedt asymptotic method is used to nd asymptotic solutions in the standing wave form. It is proved that using the Jacobi elliptic function cn as a zero approximation one can solve the problem of the main resonance, appearing i...

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic...