Solvability of a hybrid model for a vertical slender structure

We consider the solvability of a hybrid model for the vibration of a vertical slender structure mounted on an elastic seating. The slender structure is modeled as a Rayleigh beam and gravity is taken into account. The seating and foundation block are modeled as rigid bodies connected by elastic springs with damping mechanisms. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system

Solvability of a hybrid model for a vertical slender structure

Labuschagne, A., Van Rensburg, N. F. J., & Van Der Merwe, A. J. (2009). "Solvability of a Hybrid Model for a Vertical Slender Structure". - The definitive, peer-reviewed and edited version of this article is published in Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM), International Conference of Numerical Analysis and Applied Mathematics (Vol. 936, No. 1, pp. 328-331). ISSN 1790–8140.We consider the solvability of a hybrid model for the vibration of a vertical slender structure mounted on an elastic seating. The slender structure is modeled as a Rayleigh beam and gravity is taken into account. The seating and foundation block are modeled as rigid bodies connected by elastic springs with damping mechanisms. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system

Solvability of a hybrid model for a vertical slender structure

We consider the solvability of a hybrid model for the vibration of a vertical slender structure mounted on an elastic seating. The slender structure is modeled as a Rayleigh beam and gravity is taken into account. The seating and foundation block are modeled as rigid bodies connected by elastic springs with damping mechanisms. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system

Comparison of linear beam theories

Labuschagne, A., van Rensburg, N. J., & Van der Merwe, A. J. (2009). Comparison of linear beam theories. Mathematical and Computer Modelling, 49(1), 20-30. DOI: http://dx.doi.org/10.1016/j.mcm.2008.06.006In this paper we consider three models for a cantilever beam based on three different linear theories: Euler–Bernoulli, Timoshenko and two-dimensional elasticity. Using the natural frequencies and modes as a yardstick, we conclude that the Timoshenko theory is close to the two-dimensional theory for modes of practical importance, but that the applicability of the Euler–Bernoulli theory is limited