T-tail flutter simulations with regard to quadratic mode shape components

It is known that the dynamic aeroelastic stability of T-tails is dependent on the steady aerodynamic forces at aircraft trim condition. Accounting for this dependency in the flutter solution process involves correction methods for doublet lattice method (DLM) unsteady aerodynamics, enhanced DLM algorithms, unsteady vortex lattice methods (UVLM), or the use of CFD. However, the aerodynamic improvements along with a commonly applied modal approach with linear displacements results in spurious stiffness terms, which distort the flutter velocity prediction. Hence, a higher order structural approach with quadratic mode shape components is required for accurate flutter velocity prediction of T-tails. For the study of the effects of quadratic mode shape components on T-tail flutter, a generic tail configuration without sweep and taper is used. Euler based CFD simulations are applied involving a linearized frequency domain (LFD) approach to determine the generalized aerodynamic forces. These forces are obtained based on steady CFD computations at varying horizontal tail plane (HTP) incidence angles. The quadratic mode shape components of the fundamental structural modes for the vertical tail plane (VTP), i.e., out-of-plane bending and torsion, are received from nonlinear as well as linear finite element analyses. Modal coupling resulting solely from the extended modal representation of the structure and its influence on T-tail flutter is studied. The g-method is applied to solve for the flutter velocities and corresponding flutter mode shapes. The impact of the quadratic mode shape components is visualized in terms of flutter velocities in dependency of the HTP incidence angle and the static aerodynamic HTP loading.

Seismic Analysis for Axial Fan Used in Nuclear Power Plant

The seismic performance of the axial fan used in nuclear power plants (NPP) is investigated by using the commercial FEM software ANSYS. In the modal analysis, the first five orders of the natural frequencies of the axial fan is obtained, as well as the corresponding vibration modes. And in the spectrum analysis, the complete quadratic mode combination method is applied to determine the dynamic response of the axial fan under a random seismic excitation. The simulation results show that the seismic performance of the axial fan satisfies the requirement of the RCC-M 2007 design codes.

Quadratic Mode Shape Components From Ground Vibration Testing

Points on a vibrating structure generally move along curved paths rather than straight lines. For example, the tip of a cantilever beam vibrating in a bending mode experiences axial displacement as well as transverse displacement. The axial displacement is governed by the inextensibility of the neutral axis of the beam and is proportional to the square of the transverse displacement; hence the name “quadratic mode shape component.” Quadratic mode shape components are largely ignored in modal analysis, but there are some applications in the field of modal-basis structural analysis where the curved path of motion cannot be ignored. Examples include vibrations of rotating structures and buckling. Methods employing finite element analysis have been developed to calculate quadratic mode shape components. Ground vibration testing typically only yields the linear mode shape components. This paper explores the possibility of measuring the quadratic mode shape components in a sine-dwell ground vibration test. This is purely an additional measurement and does not affect the measured linear mode shape components or the modal parameters, i.e., modal mass, frequency, and damping ratio. The accelerometer output was modeled in detail taking into account its linear acceleration, its rotation, and gravitational acceleration. The response was correlated with the Fourier series representation of the output signal. The result was a simple expression for the quadratic mode shape component. The method was tested on a simple test piece and satisfactory results were obtained. The method requires that the accelerometers measure down to steady state and that up to the second Fourier coefficients of the output signals are calculated. The proposed method for measuring quadratic mode shape components in a sine-dwell ground vibration test seems feasible. One drawback of the method is that it is based on the measurement and processing of second harmonics in the acceleration signals and is therefore sensitive to any form of structural nonlinearity that may also cause higher harmonics in the acceleration signals. Another drawback is that only the quadratic components of individual modes can be measured, whereas coupled quadratic terms are generally also required to fully describe the motion of a point on a vibrating structure.

Quadratic Mode Shape Components From Linear Finite Element Analysis

Points on a vibrating structure move along curved paths rather than straight lines; however, this is largely ignored in modal analysis. Applications where the curved path of motion cannot be ignored include beamlike structures in rotating systems, e.g., helicopter rotor blades, compressor and turbine blades, and even robot arms. In most aeroelastic applications the curvature of the motion is of no consequence. The flutter analysis of T-tails is one notable exception due to the steady-state trim load on the horizontal stabilizer. Modal basis buckling analyses can also be performed when taking the curved path of motion into account. The effective application of quadratic mode shape components to capture the essential kinematics has been shown by several researchers. The usual method of computing the quadratic mode shape components for general structures employs multiple nonlinear static analyses for each component. It is shown here how the quadratic mode shape components for general structures can be obtained using linear static analysis. The derivation is based on energy principles. Only one linear static load case is required for each quadratic component. The method is illustrated for truss structures and applied to nonlinear static analyses of a linear and a geometrically nonlinear structure. The modal method results are compared to finite element nonlinear static analysis results. The proposed method for calculating quadratic mode shape components produces credible results and offers several advantages over the earlier method, viz., the use of linear analysis instead of nonlinear analysis, fewer load cases per quadratic mode shape component, and user-independence.