Freno, Brian Andrew (2010-05). An Efficient Nonlinear Structural Dynamics Solver for Use in Computational Aeroelastic Analysis. Master's Thesis.
Thesis
Aerospace structures with large aspect ratio, such as airplane wings, rotorcraft blades, wind turbine blades, and jet engine fan and compressor blades, are particularly susceptible to aeroelastic phenomena. Finite element analysis provides an effective and generalized method to model these structures; however, it is computationally expensive. Fortunately, these structures have a length appreciably larger than the largest cross-sectional diameter. This characteristic is exploitable as these potential aeroelastically unstable structures can be modeled as cantilevered beams, drastically reducing computational time. In this thesis, the nonlinear equations of motion are derived for an inextensional, non-uniform cantilevered beam with a straight elastic axis. Along the elastic axis, the cross-sectional center of mass can be o set in both dimensions, and the principal bending and centroidal axes can each be rotated uniquely. The Galerkin method is used, permitting arbitrary and abrupt variations along the length that require no knowledge of the spatial derivatives of the beam properties. Additionally, these equations consistently retain all third-order nonlinearities that account for flexural-flexural-torsional coupling and extend the validity of the equations for large deformations. Furthermore, linearly independent shape functions are substituted into these equations, providing an efficient method to determine the natural frequencies and mode shapes of the beam and to solve for time-varying deformation. This method is validated using finite element analysis and is extended to swept wings. The importance of retaining cubic terms, in addition to quadratic terms, for nonlinear analysis is demonstrated for several examples. Ultimately, these equations are coupled with a fluid dynamics solver to provide a structurally efficient aeroelastic program.
Aerospace structures with large aspect ratio, such as airplane wings, rotorcraft blades, wind turbine blades, and jet engine fan and compressor blades, are particularly
susceptible to aeroelastic phenomena. Finite element analysis provides an effective and generalized method to model these structures; however, it is computationally
expensive. Fortunately, these structures have a length appreciably larger than the largest cross-sectional diameter. This characteristic is exploitable as these potential aeroelastically unstable structures can be modeled as cantilevered beams, drastically
reducing computational time.
In this thesis, the nonlinear equations of motion are derived for an inextensional, non-uniform cantilevered beam with a straight elastic axis. Along the elastic axis, the cross-sectional center of mass can be o set in both dimensions, and the principal bending and centroidal axes can each be rotated uniquely. The Galerkin method is used, permitting arbitrary and abrupt variations along the length that require no knowledge of the spatial derivatives of the beam properties. Additionally, these equations consistently retain all third-order nonlinearities that account for flexural-flexural-torsional coupling and extend the validity of the equations for large deformations.
Furthermore, linearly independent shape functions are substituted into these equations, providing an efficient method to determine the natural frequencies and mode shapes of the beam and to solve for time-varying deformation.
This method is validated using finite element analysis and is extended to swept wings. The importance of retaining cubic terms, in addition to quadratic terms, for
nonlinear analysis is demonstrated for several examples. Ultimately, these equations are coupled with a fluid dynamics solver to provide a structurally efficient aeroelastic program.