Quadratic Mode Shape Components From Ground Vibration Testing

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
L. H. van Zyl ◽  
E. H. Mathews
Keyword(s):  
Mode Shape ◽  
Ground Vibration ◽  
Axial Displacement ◽  
Vibration Test ◽  
Transverse Displacement ◽  
Vibration Testing ◽  
Linear Mode ◽  
Quadratic Mode ◽  
Acceleration Signals ◽  
Shape Component

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.

Comparison of flutter calculation methods based on ground vibration test result

2019 ◽  
Vol 91 (3) ◽  
pp. 466-476
Author(s):  
Wojciech Chajec
Keyword(s):  
Low Cost ◽  
Ground Vibration ◽  
Control Surface ◽  
Vibration Test ◽  
Problem Solution ◽  
Lattice Method ◽  
Mass Model ◽  
Content Type ◽  
Strip Theory ◽  
Flutter Analysis

PurposeA low-cost but credible method of low-subsonic flutter analysis based on ground vibration test (GVT) results is presented. The purpose of this paper is a comparison of two methods of immediate flutter problem solution: JG2 – low cost software based on the strip theory in aerodynamics (STA) and V-g method of the flutter problem solution and ZAERO I commercial software with doublet lattice method (DLM) aerodynamic model and G method of the flutter problem solution. In both cases, the same sets of measured normal modes are used. Design/methodology/approachBefore flutter computation, resonant modes are supplied by some non-measurable but existing modes and processed using the author’s own procedure. For flutter computation, the modes are normalized using the aircraft mass model. The measured mode orthogonalization is possible. The flutter calculation made by means of both methods are performed for the MP-02 Czajka UL aircraft and the Virus SW 121 aircraft of LSA category. FindingsIn most cases, both compared flutter computation results are similar, especially in the case of high aspect wing flutter. The Czajka T-tail flutter analysis using JG2 software is more conservative than the one made by ZAERO, especially in the case of rudder flutter. The differences can be reduced if the proposed rudder effectiveness coefficients are introduced. Practical implicationsThe low-cost methods are attractive for flutter analysis of UL and light aircraft. The paper presents the scope of the low-cost JG2 method and its limitations. Originality/valueIn comparison with other works, the measured generalized masses are not used. Additionally, the rudder effectiveness reduction was implemented into the STA. However, Niedbal (1997) introduced corrections of control surface hinge moments, but the present work contains results in comparison with the outcome obtained by means of the more credible software.

An integrated design technique of advanced linear-mode-shape method and serviceability drift optimization for tall buildings with lateral–torsional modes

2010 ◽  
Vol 32 (8) ◽  
pp. 2146-2156 ◽  
Author(s):  
M.F. Huang ◽  
K.T. Tse ◽  
C.M. Chan ◽  
K.C.S. Kwok ◽  
P.A. Hitchcock ◽  
...  
Keyword(s):  
Mode Shape ◽  
Integrated Design ◽  
Tall Buildings ◽  
Design Technique ◽  
Linear Mode

A Semi-Analytical Approach for the Geometrically Nonlinear Analysis of Skew Plates

2014 ◽  
Vol 704 ◽  
pp. 118-130
Author(s):  
Hanane Moulay Abdelali ◽  
Mounia El Kadiri ◽  
Rhali Benamar
Keyword(s):  
Mode Shape ◽  
Algebraic Equations ◽  
Skew Angle ◽  
Geometrically Nonlinear Analysis ◽  
Good Convergence ◽  
Linear Mode ◽  
Skew Plate ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Analytical Expressions

The present work concerns the nonlinear dynamic behaviour of fully clamped skew plates at large vibration amplitudes. A model based on Hamilton’s principle and spectral analysis has been used to study the large amplitude free vibration problem, reducing the non linear problem to solution of a set of non-linear algebraic equations. Two methods of solution have been adopted, the first method uses an improved version of the Newton-Raphson method, and the second leads to explicit analytical expressions for the higher mode contribution coefficients to the first non-linear mode shape of the skew plate examined. The amplitude dependent fundamental mode shape and the associated non-linear frequencies have been obtained by the two methods and a good convergence has been found. It was found that the non-linear frequencies increase with increasing the amplitude of vibration, which corresponds to the hardening type effect, expected in similar cases, due to the membrane forces induced by the large vibration amplitudes. The non-linear mode exhibits a higher bending stress near to the clamps at large deflections, compared with that predicted by linear theory. Numerical details are presented and the comparison made between the results obtained and previous ones available in the literature shows a satisfactory agreement. Tables of numerical results are given, corresponding to the linear and nonlinear cases for various values of the skew angle θ and various values of the vibration amplitude. These results, similar to those previously published for other plates, are expected to be useful to designers in the need of accurate estimates of the non-linear frequencies, the non linear strains and stresses induced by large vibration amplitudes of skew plates.

Spatial Fine Beam Model Based on Vector Form Intrinsic Finite Element Analysis

2014 ◽  
Vol 638-640 ◽  
pp. 238-243
Author(s):  
Chong Chen ◽  
Xing Fei Yuan ◽  
Ruo Jun Qian
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Axial Displacement ◽  
Shear Displacement ◽  
Transverse Displacement ◽  
Beam Model ◽  
Deep Beam ◽  
Vector Form ◽  
Euler Beam ◽  
Load Displacement

Different from the Euler beam and Timoshenko beam, the spatial fine beam model considers some effects such as shear displacement, the additional axial displacement produced by lateral bending and the additional transverse displacement induced by reduced stiffness due to transverse shear deformation. In this paper the internal force formula of the spatial fine beam model, applying to Vector Form Intrinsic Finite Element (VFIFE) analysis, are derived and corresponding programs are developed. A spatial cantilever beam and a space frame are analyzed and the load-displacement curves are compared using different beam element models. The results show that when the depth-span ratio is relatively small, the load-displacement curves nearly have no difference. When the depth-span ratio becomes larger, the yield load gotten by the fine beam model is significantly smaller than that obtained by the Euler beam and Timoshenko beam. Therefore, when the deep beam is analyzed, the shear displacement, the additional axial displacement and the additional transverse displacement caused by stiffness reduction can’t be ignored. The spatial fine beam model proposed in this paper has good accuracy in the analysis of deep beam.

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