A vector unsymmetric eigenequation solver for nonlinear flutter analysis on high-performance computers

Qin, Jiangning; Mei, Chuh; Gray, C. E.

doi:10.2514/6.1991-1169

Cited by 7 publications

(1 citation statement)

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“…The limit-cycle oscillations are determined in the second step using the LUM/NTF method. 5 ' 9 ' 12 The FE-FD method, 5 ' 10 -12 which has been used successfully to study nonlinear panel flutter, requires less computational time 15 …”

Section: Finite Element Equations Of Motionmentioning

confidence: 99%

Finite element time domain - Modal formulation for nonlinear flutter of composite panels

1994

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A finite element time domain modal approach is presented for determining the nonlinear flutter characteristics of composite panels at elevated temperatures. The von Karman large-deflection strain-displacement relations, quasisteady first-order piston theory aerodynamics, and quasisteady thermal stress theory are used to formulate the nonlinear panel flutter finite element equations of motion in nodal displacements. A set of nonlinear modal equations of motion of much smaller degrees of freedom for the facilitation in time numerical integration is then obtained through a modal transformation and reduction. All five types of panel behavior-flat, buckled, limitcycle, periodic, and chaotic motions-can be determined. Examples show the accuracy, convergence, and versatility of the present approach. Nomenclature[A], [B], [D] = extension, coupling, and bending laminate stiffness matrices a, b = panel length and width [C] = modal aerodynamic damping matrix E b E 2 = Young's moduli in major and minor axes G 12 = shear modulus h = panel thickness [K], [k] = system and element linear stiffness matrices [Kl], [kl] = first-order nonlinear stiffness matrices [K2], [k2] = second-order nonlinear stiffness matrices [M], [m] = mass matrices M^ = Mach number p a = aerodynamic pressure {q} -modal amplitude vector u, v = in-plane displacements w = panel deflection a l9 ot 2 = major and minor coefficients of thermal expansion AJ = temperature change {e} = total strain vector 0 = lamination angle {K} = curvature vector X = nondimensional aerodynamic pressure ji = air-panel mass ratio v = Poisson's ratio p = mass density {a} = stress vector i = nondimensional time [O] = modal matrix {(j)} = normal modes co 0 = reference frequency Subscripts a = air b = bending

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Section: Finite Element Equations Of Motionmentioning

confidence: 99%