Two approaches for studying the impact response of viscoelastic engineering systems: an overview. (English) Zbl 1381.74170
Summary: Two approaches for studying the impact response of viscoelastic engineering structures are considered by the example of the dynamic response of a viscoelastic Bernoulli-Euler beam transversely impacted by an elastic sphere. The Young’s modulus of the viscoelastic beam is the time-dependent operator, which is defined either via the Kelvin-Voigt fractional derivative model or via the standard linear solid fractional derivative model. The first approach assumes that Poisson’s ratio is not an operator but a constant, while under the second approach the bulk modulus is considered to be constant. The transverse impact of the elastic sphere upon the viscoelastic beam is investigated using both approaches. The comparison of the results obtained shows that the solution obtained at the constant Poisson’s ratio is much simpler than that at the constant bulk modulus.
MSC:
| 74M20 | Impact in solid mechanics |
| 74D05 | Linear constitutive equations for materials with memory |
| 26A33 | Fractional derivatives and integrals |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
fractional operators; fractional exponential function; resolvent kernels; Volterra correspondence principle; impact response; viscoelastic structuresReferences:
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