### Stochastic Dynamics of Slender Structures of Composite Materials

#### Abstract

This article is concerned with the dynamic analysis of structures constructed with composite materials. There are many ways to manufacture a composite material for uses in structural constructions, for example filament winding and resin transfer molding, among others. Depending on the manufacturing

process composite materials may have deviations with respect to the calculated response (or deterministic response). These manufacturing aspects lead to a source of uncertainty in the structural response associated with constituent proportions or geometric parameters. Another source of uncertainty can be the mathematical model that represents the mechanics of the slender structure. In many structural models, the type of hypotheses invoked can reflect the most of the physics of a structure, however in some circumstances these hypotheses are not enough, and cannot represent properly the mechanics of the structure.

Uncertainties should be considered in a structural system in order to improve the predictability of a given modeling scheme. There are some strategies to face the uncertainties in the dynamics of structures.

The parametric probabilistic approach quantifies the uncertainty of given parameters such as variation of the angles of fiber reinforcement, material constituents, etc. In this study a shear deformable model of composite beams is employed as the mean model. The probabilistic model is constructed by adopting random variables for the uncertain parameters of the model. The probability density functions of the random variables are constructed appealing to the Maximum Entropy Principle. Then the probabilistic model is possed in the context of the finite element method and the Monte Carlo method is employed to perform the statistical simulations. Numerical studies are carried out to show the main advantages of the modeling strategies employed, as well as to quantify the propagation of the uncertainty in the dynamics of slender composite structures.

process composite materials may have deviations with respect to the calculated response (or deterministic response). These manufacturing aspects lead to a source of uncertainty in the structural response associated with constituent proportions or geometric parameters. Another source of uncertainty can be the mathematical model that represents the mechanics of the slender structure. In many structural models, the type of hypotheses invoked can reflect the most of the physics of a structure, however in some circumstances these hypotheses are not enough, and cannot represent properly the mechanics of the structure.

Uncertainties should be considered in a structural system in order to improve the predictability of a given modeling scheme. There are some strategies to face the uncertainties in the dynamics of structures.

The parametric probabilistic approach quantifies the uncertainty of given parameters such as variation of the angles of fiber reinforcement, material constituents, etc. In this study a shear deformable model of composite beams is employed as the mean model. The probabilistic model is constructed by adopting random variables for the uncertain parameters of the model. The probability density functions of the random variables are constructed appealing to the Maximum Entropy Principle. Then the probabilistic model is possed in the context of the finite element method and the Monte Carlo method is employed to perform the statistical simulations. Numerical studies are carried out to show the main advantages of the modeling strategies employed, as well as to quantify the propagation of the uncertainty in the dynamics of slender composite structures.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**