Vibrations of a double-beam complex system subjected to a moving force

Vibrations of a beam‐string complex system under a moving force

“…means the Heaviside or the unit step function. More examples of closed-form solutions can be found in [5][6][7][8].…”

“…One of the most important issues in the dynamics of structures is moving load problems witch modeling is very difficult in its complications and generates many mathematical problems [1][2][3][4][5][6][7][8]. Even simply models give very complex and unpredicted solutions of structural in dynamical and stability meaning [1,3].…”

Flexible Complex System of a Double-String Under Extreme Moving Loads

“…And Figure 6 shows graphs in a period of time i η ≤ T ≤ (i+1) η ≤ 1, where i = 1, 3, 5,…, 2n-1. More examples of closed-form solutions can be found [8,[18][19][20][21].…”

“…The presented solutions can be also used in axial and torsional vibration of the rod. Using this method, the closed solutions for undamped vibration of string and beam due to moving force have been obtained in the papers [18][19][20][21]. The solution for the dynamic response of the composite strings under moving force is important because it can be used also in order to find the solution for other types of moving loads.…”

“…The analogies between a string and the beams have been considered in papers [5,6,11]. Various aspects of the dynamics response of a string under a moving load have been considered, among others, in the papers [2,4,8,10,[12][13][14][15][18][19][20]22]. The classical solution of the response of complex systems subjected to forces moving with a constant velocity has a form of an infinite series.…”