Numerical and computational modeling of the Timoshenko beam subject to point loads

• Autor: Acasiete Quispe, Frank Henry
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/15723
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/15723
• Nivel de acceso: acceso abierto
• Materia: Diferential partial equations; beam; semigroup; polinomial stability; Ecuación Diferencial Parcial; viga; semigrupo; estabilidad polinomial

We studied the uniform stabilization of a class of Timoshenko systems with tip load at the free end of the beam. Our main result is to prove that the semigroup associated to this model is not exponentially stable. Moreover, we prove that the semigroup decays polynomially to zero. When the damping mechanism is efective only on the boundary of the rotational angle, the solution also decays polynomially with rate depending on the coecients of the problem. The objective of this work is to present in a didactic way the results obtained in the article [9], using the theory of semigroups used in [10] and also contribute with the numerical part seen in [1]