Estudo do comportamento dinâmico de membranas retangulares hiperelásticas
Carregando...
Data
2015-06-12
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
Structural elements with large deformation capacity as hyperelastic membranes are gaining
prominence in several engineering branches and have applications in biomechanics, thus the
study of the dynamic behavior of hyperelastic structures is very important to minimize effects
as the loss of the stability and undesirable vibrations. In this paper the elasticity theory for
large deformations in the development of membrane theory, in order to investigate the linear
and nonlinear dynamic behavior of hyperelastic membrane is used. A rectangular membrane
composed of an elastomeric material, isotropic, homogeneous, incompressible and consisting
of neo-Hookeano, Mooney-Rivlin and Yeoh models is considered. To model the membrane,
the energy and work of external forces are used together with the application of the Hamilton
on the Lagrange function. The Galerkin method is applied to obtain a discretized system of
nonlinear Partial Differential Equations (PDE) and the Runge-Kutta method of 4th order is
used to obtain its time response. Finally, the Brute Force and Continuation methods are
applied to investigate the nonlinear dynamic behavior of the membrane. A parametric analysis
is carried out looking to evaluate the influence of the material, geometry and initial tensions
on the natural frequencies of the membrane. It is noted that increasing the size of a tensioned
membrane, it is also increased the natural frequency for a given amplitude, and increasing the
strength of a pre-tensioned membrane, the smaller the value of the frequency in relation to a
range. Small differences are perceived in the behavior of the membrane for the three
constitutive models of material, which are calibrated to represent the same material.
Moreover, the main bifurcations of the analyzed membranes are of cyclic bending type,
known as saddle-node bifurcation.
Descrição
Citação
SILVA, R. S. Estudo do comportamento dinâmico de membranas retangulares hiperelásticas. 2015. 92 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2015.