Exact solutions of Euler–Bernoulli beams

• DOI: 10.1142/s0217984923501610
• Publication Date: 2023-07-13T13:48:56Z
• Authors: Jamil Abbas Haider; F. D. Zaman; Showkat Ahmad Lone; Sadia Anwar; Salmeh A. Almutlak; Ibrahim E. Elseesy
• Keywords: 0103 physical sciences; 01 natural sciences

In numerous real-world applications, transverse vibrations of beams are nonlinear in nature. It is a task to solve beam systems due their substantial dependence on the 4 variables system and boundary conditions. To comprehend vibration characteristics, it essential do precise parametric analysis. This research demonstrates an approximation solution for odd even vibrating using Laplace-based variation iteration method, formulation depends Galerkin approximation. For differential equation, this method efficient as compared existing methods literature because solutions exactly match with numerical solutions. The has been used first time obtain important problem. demonstrate applicability precision several initial conditions applied governing equation nonlinearly beams. natural frequencies periodic response curves computed VIM Runge–Kutta RK4 method. contrast RK4, results that proposed yields excellent consensus. Lagrange multiplier widely regarded one most concepts variational theory. result obtained displayed table form. Highlights highlights Euler–Bernoulli quintic nonlinearity are: 1. Introducing constraint into multipliers. 2. Formulating equations multipliers deflection beam. 3. Solving resulting algebraic methods. 4. Obtaining function its length load. 5. Analyzing behavior under different loads