Resumo

GRANADOS M, Andrés. MECHANICS OF CONTINUOUS MATERIAL SYTEMS FROM NON-INERTIAL FRAMES OF REFERENCE. IMME [online]. 2002, vol.40, n.1, pp.59-94. ISSN 0376-723X.

ABSTRACT In this paper it has been developed a simplified mathematical model for the study of the mechanics of continuous deformable material systems (those dynamical continuous systems with an invariant mass), kinematically described from a non-inertial frame of reference. In the first part, basic definitions and some fundamental kinematical and dynamical concepts are stated, for their subsequent use in the second and in the third parts. Within these, the coordinate transformation and the relations of some dynamical integral quantities are of special attention. In the second part, it has been established the conservative equations of mass, linear momentum and angular momentum applied to general continuous deformable material systems flowing through a generalized translating control volume, which may rotate and deform in an arbitrary way. In order to obtain these conservative equations, the Reynolds Transport Theorems are applied. These same equations will be obtained in a substantially more simplified form, using a different analysis and adopting a condensed notation, taken from the integral point of view of the classical mechanics. In the third part the law of conservation for mechanical energy, the König and Steiner Theorems are deduced for the general case studied in the second part. Also, it is established a way to calculate the transportation of the tensor of inertia when the body (i.e. the material system) is deformable. In this part the objective is to extend to deformable bodies those results traditionally known for rigid bodies. At the end, it is found that this last dissertation (deduced from an integral dynamical analysis) is equivalent to that studied in the second pan (deduced from the Reynolds Transport Theorems). Additionally, in an attached appendice the Leibniz Rule is briefly deduced, and the Reynolds Transport Theorems are presented in a summarized way

Palavras-chave : Mechanics; continuum; material system.