GENERALIZED SOLUTIONS FOR THE EULER–BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES
2013 ◽
Vol 11
(02)
◽
pp. 1350017
◽
Keyword(s):
We study the initial-boundary value problem for an Euler–Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is a fourth-order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener-type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.
2011 ◽
Vol 51
(12)
◽
pp. 2102-2114
◽
2020 ◽
Vol 2
(330)
◽
pp. 133-141
2007 ◽
Vol 147
(1)
◽
pp. 6470-6482
◽
1971 ◽
Vol 5
(3)
◽
pp. 305-314
2001 ◽
Vol 9
(ASAT CONFERENCE)
◽
pp. 1-9