Exact closed-form solution for the vibration modes of the Euler–Bernoulli beam with multiple open cracks
S Caddemi, I Calio - Journal of Sound and Vibration, 2009 - Elsevier
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 …
beam in the presence of multiple concentrated cracks are presented. The proposed …
[HTML][HTML] Multi-cracked Euler–Bernoulli beams: Mathematical modeling and exact solutions
S Caddemi, A Morassi - International journal of solids and structures, 2013 - Elsevier
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 …
the behavior of damaged beams and frames. Important applications, such as the …
An existence and uniqueness result about algebras of Schwartz distributions
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 …
satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur …
[HTML][HTML] One-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulation
Using an extension of the Hörmander product of distributions, we obtain an intrinsic
formulation of one-dimensional Schrödinger operators with singular potentials. This …
formulation of one-dimensional Schrödinger operators with singular potentials. This …
[HTML][HTML] Vibration modes of the Euler–Bernoulli beam equation with singularities
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 …
singular coefficients. Using an extension of the Hörmander product of distributions with non …
Square of the Dirac's delta distribution a new definition for engineering mechanics
A Ranjbaran - NED University Journal of Research, 2014 - go.gale.com
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 …
Aerospace engineering. The Dirac's delta distribution and its square are used for modelling …
Foundations of the calculus of variations in generalized function algebras
S Konjik, M Kunzinger… - Acta Applicandae …, 2008 - Springer
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 …
singular problems in the calculus of variations. After a general study of extremal problems on …
Generalized solutions for the Euler–Bernoulli model with distributional forces
G Hörmann, L Oparnica - Journal of mathematical analysis and …, 2009 - Elsevier
We establish existence and uniqueness of generalized solutions to the initial–boundary
value problem corresponding to an Euler–Bernoulli beam model from mechanics. The …
value problem corresponding to an Euler–Bernoulli beam model from mechanics. The …
Generalized solutions for the Euler–Bernoulli model with Zener viscoelastic foundations and distributional forces
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 …
discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial …
On application of theory of distributions to static and dynamic analysis of cracked beams
RO Grossi, JL Raffo - International Journal of Structural Stability and …, 2016 - World Scientific
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 …
by cracks. The theory of distributions developed by Laurent Schwartz is adopted as it is …