In this study, exact closed-form expressions for the vibration modes of the Euler–Bernoulli
beam in the presence of multiple concentrated cracks are presented. The proposed …

Localized flexibility models of cracks enable one for simple and effective representation of
the behavior of damaged beams and frames. Important applications, such as the …

We prove that there exists essentially one minimal differential algebra of distributions A,
satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur …

Using an extension of the Hörmander product of distributions, we obtain an intrinsic
formulation of one-dimensional Schrödinger operators with singular potentials. This …

We consider the time dependent Euler–Bernoulli beam equation with discontinuous and
singular coefficients. Using an extension of the Hörmander product of distributions with non …

The analysis of cracked members is a paramount research interest in Civil, Mechanical and
Aerospace engineering. The Dirac's delta distribution and its square are used for modelling …

We propose the use of algebras of generalized functions for the analysis of certain highly
singular problems in the calculus of variations. After a general study of extremal problems on …

We establish existence and uniqueness of generalized solutions to the initial–boundary
value problem corresponding to an Euler–Bernoulli beam model from mechanics. The …

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 …

This paper presents a rigorous study on the static and dynamic behavior of beams affected
by cracks. The theory of distributions developed by Laurent Schwartz is adopted as it is …