application of newmark average acceleration and ritz methods on dynamical analysis of composite beams under a moving load

In this paper, dynamic results of carbon nanotube (cnt)-reinforced composite beams under a moving load are presented. the constitutive equations in motion are obtained by the lagrange procedure according to timoshenko beam theory and then solved by using the ritz method. in the solution of the moving load problem, the newmark average acceleration method is used in the time history. in the numerical results, the effects of cnts’ volume fraction, patterns of cnts, and the velocity of moving load on the dynamic responses of cnt-reinforced composite beam are investigated in detail. it is observed that the reinforcement patterns and volume fraction of cnts are very effective on the behavior of the moving load. also, it is found that x-beam and obeam have the biggest and lowest rigidities in all models, respectively.