Moving load

Quantum mechanics

Galerkin method

Discretization

Beam (structure)

Engineering

Materials science

Boundary value problem

Vibration

Classical mechanics

Thermodynamics

Deflection (physics)

Physics

Finite element method

Nonlinear system

Timoshenko beam theory

Mathematics

Optics

Added mass

Mathematical analysis

Structural engineering

Kinematics

Mechanics

Cantilever

Applied Acoustics

In this article, it is proposed to comprehend the coupled nonlinear analysis of beam under three different boundary conditions, such as (1) cantilever, (2) fixed-fixed and (3) simply supported having moving mass. Due to the beam and mass interaction, coupling term arises and it results kinematic nonlinearities in the system. A fundamental geometric model is developed by considering nonlinearities of the system. Euler-Bernoulli beam assumptions are considered. By applying Hamilton’s principle a coupled mathematical formulation of the desired system is derived. Further Galerkin discretization method is used in the mathematical system to analyse dynamic behaviour by converting it from continuous to discrete problem. The resulting equations are solved using perturbation method. Then MATLAB ODE solver is used to plot various graphs for variation of amplitude and deflection with respect to time in case of both beam and mass. Under the internal resonance condition the time response curves are plotted to analyze the beating phenomenon for the beam and mass. Due to small time steps and very high frequency variation, mass position and tip deflection plots appear dark. Finally, a comparative study is also made for various detuning parameter to show the modal behavior of beam-mass system.

Coupled nonlinear behavior of beam with a moving mass