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Vibrations of the Euler–Bernoulli Beam Under a Moving Force Based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

Śniady Paweł, Misiurek Katarzyna, Szyłko-Bigus Olga, Idzikowski Rafał

Studia Geotechnica et Mechanica

2020

Vol. 42, nr 4

306--318

Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.