zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Nonlinear vibrations of the Euler-Bernoulli beam subjected to transversal load and impact actions. (English) Zbl 1229.37103
Summary: In this work vibrations of a flexible nonlinear Euler-Bernoulli-type beam, driven by a dynamic load and with various boundary conditions at its edge, including an impact, are studied. The governing equations include damping terms, with damping coefficients $\varepsilon_1,\varepsilon_2$ associated with velocities of the vertical deflection wand horizontal displacement $u$, respectively. Damping coefficients $\varepsilon_1,\varepsilon_2$ and transversal loads $q_0$ and $\omega_p$ serve as the control parameters in the problem. The continuous problem is reduced to a finite-dimensional one by applying finite differences with respect to the spatial coordinates, and is solved via the fourth-order Runge-Kutta method. This approach enables the identification of damping coefficients, as well as the investigations of elastic waves generated by the impact of rigid mass moving at constant velocity $V$.

37N05Dynamical systems in classical and celestial mechanics
37N15Dynamical systems in solid mechanics
39A14Partial difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)