Multimode Nonlinear Vibration Analysis of Stiffened Functionally Graded Double Curved Shells in a Thermal Environment

<p>The motivation of the current work is to develop a multi-modal analysis of the nonlinear response of stiffened double curved shells made of functionally graded materials under thermal loads. The formulation is based on the first order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain-displacement relationships. The nonlinear equations of motion of stiffened double curved shell based on the extended Sanders’s theory were derived using Galerkin’s method. The resulting system of infinite nonlinear ordinary differential equations, that includes both cubic and quadratic nonlinear terms, was solved using a nonlinear dynamic software XPPAUT to obtain the force-amplitude relationship. The effect of both, longitudinal and transverse stiffeners, was considered using the Lekhnitsky’s technique and the material properties are temperature dependent and vary in the thickness direction according to the linear rule of mixture. In order to obtain accurate natural frequency in thermal environments, critical buckling temperature differences are carried out, resulting in closed form solutions. The effect of temperature’s variation as well as power index, functionally graded stiffeners, geometrical parameters, temperature depended materials and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed. This dissertation showed that the nonlinear study of problems of thin-walled structures with even stiffeners is of paramount importance. It was also found that the difference between single-mode and multi-mode analyses could be very significant for nonlinear problems in a thermal environment. Hence, multimode vibration analysis is necessary for structures of this nature.</p>

Name thesis:degree_name

Doctor of Philosophy in Aerospace Engineering

Level thesis:degree_level

Dissertation - Open Access

Discipline thesis:degree_discipline

Aerospace Engineering

Year

2019

Author dc:creator

• Azizi, Boutros

• vibration analysis
• shells
• thermal
• nonlinear
• Aerospace Engineering

Repository record dc:identifier

https://commons.erau.edu/edt/469

OAI identifier oai:identifier

oai:commons.erau.edu:edt-1469