Nonlinear reduced order modeling of isotropic and functionally graded plates

Estimation of time to stationarity in geometrically nonlinear structural responses

“…The material properties of the beam were selected as: Young's modulus of 204.7 GPa and mass density of 7.86 Â 10 3 kg/m 3 . A Nastran finite element model of this beam was constructed with 40 CBEAM elements and a reduced order model was obtained using the transverse and dual modes methodology of [5,6,7]. The beam was subjected to a uniform pressure along its length varying in time as a bandlimited white noise process of cut-off frequency equal to 2500 Hz.…”

“…Ever increasing computational capabilities and the successful development of reduced order modeling techniques of geometrically nonlinear structures [1][2][3][4][5][6][7] have led to a more routine inclusion of geometric nonlinearity in structural dynamic analyses. This trend is particularly noticeable in connection with supersonic/hypersonic aircraft where the combination of the expected thermal, acoustic, and aerodynamic loads will result in structural responses exceeding their linear limits.…”

Response of a Panel to Shock Impingement: Modeling and Comparison with Experiments

“…The static loads are selected to excite a structural response that is a scaled version of the free vibration mode shapes or their linear combinations. Previous studies by the authors [16][17][18] have shown that the combination of linear and dual modes facilitates an accurate and efficient treatment of geometric nonlinearities. The time dependent generalized coordinates, denoted by q, are determined using the following ordinary differential equation (ODE) [14]:…”

“…(p s ) plateau =p a p s p a plateau p s p a max (16) where, (p s /p a ) max is computed using oblique shock theory [34], and (p s /p a ) plateau is the ratio of the mean pressures in the attached and separated regions given by…”

Reduced Order Modeling for the Nonlinear Geometric Response of Some Joined Wings

“…A particularly convenient approach to resolve these difficulties while maintaining an accurate modeling of the nonlinear effects is to rely on a modal-like reduced order model of the structural response such as those reviewed recently in [5] which are derived from standard commercial finite element codes. The focus of the present paper is on demonstrating and validating the construction of such nonlinear ROMs, specifically those following [6][7][8], for several structural models including configurations of the PrandtlPlane as a first step toward the aeroelastic study of these wings.…”