Xinyun Guo

Finite Element Multiple-Mode Approach to Nonlinear Free Vibrations of Shallow Shells

Two finite element (FE) modal formulations for large-amplitude free vibration of isotropic and arbitrary laminated composite shallow shells are presented. The system equation of motion is formulated first in the physical structural node degrees of freedom (DOF). Then the system is transformed into two distinctly different sets of general Duffing-type modal equations based on 1) modal amplitudes of coupled linear bending and in-plane modes, where in-plane inertia is included in the formulation, and 2) modal amplitudes of linear bending modes only, where the in-plane inertia is neglected. Multiple modes and the first-order transverse shear deformation are considered in the formulations. A shallow-shell finite element is developed as an extension from the triangular Mindlin (MIN3) plate element with the improved shear correction factor by Tessler. Time numerical integration is employed to determine the nonlinear periodic frequency characteristics. The inaccuracy in characterizing a shallow-shell response with coupled linear bending and in-plane modes is demonstrated and discussed by comparing with the FE solution in structural node DOF. Study cases include isotropic and composite panels of different shallow-shell geometries.

Supersonic Nonlinear Panel Flutter Suppression Using Shape Memory Alloys

An efficient finite element procedure is developed to predict large-amplitude nonlinear flutter response of shape memory alloy hybrid composite plates at an arbitrary supersonic yawed angle and an elevated temperature. The temperature-dependent material properties of shape memory alloy and traditional composites, as well as the von Karman large deflections, are considered in the formulation. Finite element system equations of motion are transferred to aeroelastic modal coordinates to reduce the large number of structural-node degrees of freedom. Time-domain numerical integration is employed to analyze flutter behaviors of the shape memory alloy hybrid composite panel under thermal loads. The flutter stability regions under the combined aerodynamic and thermal loads are studied. All of the possible behaviors, including the two types of static behavior and four types of dynamic motion of flutter, can be predicted for shape memory alloy hybrid composite plates. The static behaviors are 1) flat and stable and 2) aerothermally buckled but dynamically stable. The four types of dynamic motion are nearly simple harmonic limit-cycle oscillation, periodic limit-cycle oscillation, quasi-periodic oscillation, and chaotic oscillation. The flutter response of shape memory alloy hybrid composite plates are compared with those of traditional composite plates without a shape memory alloy. Results show that the desired flat and stable region can be greatly enlarged by using a shape memory alloy.

Thermal Buckling Suppression of Supersonic Vehicle Surface Panels Using Shape Memory Alloy

An efficient finite element method for the prediction of critical temperature, postbuckling deflection, and vibration characteristics is presented for traditional composite plates embedded with prestrained shape memory alloy (SMA) wires. The temperature-dependent material properties of SMA and composites and the large deflections are considered in the formulation. An iterative eigensolution is presented to determine the critical temperature, the Newton-Raphson method is employed to obtain postbuckling large deflection, and the eigensolver is used to predict free vibration frequencies about the thermally buckled equilibrium positions. Results show that the critical buckling temperature can be raised high enough and that the postbuckling deflection can be completely suppressed for surface panels of supersonic vehicle applications by the proper selection of SMA volume fraction, prestrain, and alloy composition. Weight savings based on critical temperature in the use of SMA as compared with the traditional composite and titanium plates are demonstrated.

Nonlinear Flutter of Cylindrical Shell Panels Under Yawed Supersonic Flow Using FE

In the extensive published literature about panel flutter, a large number of papers were dedicated to investigate flat plates with supersonic or hypersonic flow regimes. Very few authors have extended their work to flutter of shallow shell panels. The curved geometry generates a pre-flutter behavior due to a static aerodynamic pressure load over the panel, and resulting in the presence of a static deflection. The purpose of this paper is to provide additional insights in the area of flutter of stream-wise shallow shell panels. A finite element frequency domain method, and a multi-modal finite element time domain method are developed and presented to predict the flutter onset and the non-linear flutter response of shallow shell panels. The principle of virtual work is applied to develop the equations of motion of the fluttering system. The von Karman non-linear strain-displacement relations are used to account for large deflections, and the quasisteady first-order piston theory appended with a static aerodynamic load due to the panel geometry is employed. System equations of motion in structural degrees of freedom are obtained and reduced into the modal coordinates. The reduced non-linear finite element multi-modal equations account for pre-flutter and flutter behavior with curvature effect. In the frequency domain procedure, the Newton-Raphson method coupled with and eigen-value problem is used to determine the flutter critical dynamic pressure for different shallow shell panel height-rises. Through the time domain procedure, non-linear flutter bifurcation diagrams, time responses, phase plots and power spectrum densities were investigated for various shallow shell panel height-rises. The results showed that the flutter response of the shallow shell panel is quite similar to the one associated with flat plates for very low panel’s height-rises. As the panel’s height-rises increase, the shallow shell panel flutter response reveals a new variety of dynamic behaviors.

Nonlinear Random Response of Cylindrical Panels to Acoustic Excitations Using Finite Element Modal Method

This paper investigates large amplitude multi-mode free vibration andrandom response of thin cylindrical panels of rectangular planform usinga finite element modal formulation. A thin laminated composite doublycurved element is developed. The system equation in structural nodal DOFis transformed into the modal coordinates by the using the modes of theunderlying linear system. The nonlinear stiffness matrices are alsotransformed into nonlinear modal stiffness matrices. Numericalintegration is employed to determine free vibration and random response.Single-mode free vibration results are compared with existing classicalanalytical solutions to validate the nonlinear modal formulation.Nonlinear random analysis results for cylindrical panels have shown thatthe root mean square of panel deflections could be larger than thoseobtained using the linear structure theory. Time histories, probabilitydistribution functions, power spectral densities, and phase plane plotsare also presented.

Reduction of Random Response of Composite Plates Using Shape Memory Alloy in Thermal Environments

An efficient finite element procedure is developed to predict large amplitude nonlinear random response of shape memory alloy hybrid composite (SMAHC) plates subjected to the combined thermal load and acoustic excitation. The temperature-dependent material properties of shape memory alloy (SMA) and traditional composites, and the von Karman large deflections are considered in the formulation. Finite element system equations of motion are developed and transferred to modal coordinates to reduce the large number of physical structural node degree of freedom (DOF). All three types of motion can be predicted for SMAHC plates, and they are (i) linear random vibration about one of the two thermally buckled equilibrium positions (BEPs), (ii) intermittent snap-through motion between the two BEPs, and (iii) large amplitude random vibration over the two BEPs. The random responses of SMAHC plates are compared with those of traditional composite plates without SMA. Results show that the random response in using SMA can be reduced greatly within a certain temperature range at low and moderate sound pressure levels (SPLs), but only slightly at high SPLs for the plates studied.

Nonlinear Response and Fatigue Life of Shallow Shells to Acoustic Excitation Using Finite Element

A finite element modal formulation for large amplitude random response of shallow shell panels to acoustic excitation and temperature is presented. A shallow shell triangular finite element is developed as an extension of MIN3 plate element with improved shear correction factor. A numerical integration is applied to solve the resulting system of Duffing equations. Barlow points are used to determine strains. S-N curves and rainflow counting method are combined by means of damage accumulation theory to predict panel fatigue life. Factors contributing the softening effect, namely unsymmetrical lamination and curvature are investigated along with their impact on the fatigue life. Two types of excitation inputs are considered. Responses and fatigue life estimations to simulated band-limited Gaussian white noise and in-flight recorded microphone data are presented and compared.

Nonlinear Stiffness Estimation for Modal Finite Element Approach to Free Vibrations of Shallow Shells

A finite element (FE) modal formulation for large amplitude free vibration of isotropic and arbitrary laminated composite shallow shells is presented. The system equations of motion are formulated first in the physical structural node degrees of freedom (DOF). Then the system is transformed into two distinctly different sets of general Duffing-type modal equations based on: (1) modal amplitudes of coupled linear bending and in-plane modes, where in-plane inertia is included in the formulation, and (2) modal amplitudes of linear bending modes only, where the in-plane inertia is neglected. Multiple modes and the first-order transverse shear deformation are considered in the formulation. A shallow shell finite element is developed as an extension from the triangular Mindlin (MIN3) plate element with the improved shear correction factor by Tessler. Time numerical integration is employed to determine the nonlinear periodic frequency characteristics. The inaccuracy in characterizing a shallow shell response with coupled linear bending and in-plane modes is demonstrated and discussed by comparing with the FE solution in structural node DOF. Study cases include isotropic and