We present a comparative study between the energy balance method and amplitude-frequency formulation with exact solution.
To illustrate the accuracy of the energy balance method and amplitude-frequency formulation, we presented a comparative study between the analytical approximate techniques with exact solution.
Open image in new window Figure 3 Comparison of energy balance method and amplitude-frequency formulation with exact solution when A = 1, λ = 0.5.
In this paper, we investigated and applied two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, for solving the strongly nonlinear differential equation of a mass attached to the center of a stretched elastic wire.
To illustrate the accuracy of the energy balance method and amplitude-frequency formulation, we present the comparison results of analytical approximate techniques with exact solution in Tables 1, 2, 3 and 4 and Figures 2, 3, 4 and 5 for different values of λ.
In this paper, we investigate two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, and these approximate techniques are applied to solve the strongly nonlinear differential equation of a mass attached to the center of a stretched elastic wire (Figure 1).
This system oscillates between symmetric bounds [−A, A], and its angular frequency and corresponding periodic solution are dependent on the amplitude A. In this paper, our main purpose is to present a comparative study between the energy balance method and amplitude-frequency formulation with exact solution.
In this paper, we investigate two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, and these approximate techniques are applied to solve the strongly nonlinear differential equation of a mass attached to the center of a stretched elastic wire.
The proposal is a compromise between the measure of the equivalent shear stress amplitude, obtained from a prismatic convex hull method, and the amplitude of the first stress invariant.
Then, A ^ m + 1, 0, f ^ m + 1, 0, and φ ^ m + 1, 0 are set to A ^ m, q, f ^ m, p, and φ ^ m, p, and q and p are reset to 1. Next, the steepest descent method and the amplitude converging algorithm are recursed until the cost function becomes partially converged.
