{'fraction_non_alphanumeric': 0.015828677839851025, 'fraction_numerical': 0.0, 'mean_word_length': 5.554878048780488, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamic Behavior of a Functionally Graded Beam Under a Moving Load on Nonlinear Viscoelastic Foundation Considering Moving Mass

In this paper, linear dynamic analysis of a functionally graded materials (FGMs) beams on nonlinear viscoelastic foundation under to moving load considering moving mass has been investigated. The nonlinear behavior of viscoelastic foundation is represented by the third order relationship. The governing equation of motion of the beams is derived based on Hamilton principle expressed as Lagrange’s equations with specific boundary conditions satisfied with Lagrange’s multiplier and sporadic by high order polynomial. The computer program using Newmark- time integration and Newton Raphson procedure is written by MATLAB language. Material properties of the beam vary continuously in thickness direction according to a power law form. The effects of the material distribution, velocity of the moving load, mass of load, parameters of foundation as linear, shear and nonlinear layer on the displacement of the beam have been examined in detail.