Excitation of Arbitrary Displacement/Velocity Conditions in Rotationally Periodic Structures

1995 ◽  
Author(s):  
P. Schmiechen ◽  
D. J. Ewins ◽  
I. Bucher
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Search Algorithm ◽  
Simulated Data ◽  
Travelling Wave ◽  
Modal Testing ◽  
Mode Shapes ◽  
Wave Form ◽  
Structure Interaction ◽  
Wave Patterns

Abstract For an investigation into the structural interaction between rotating and non-rotating rotationally periodic turbine components, it was required to be able to generate experimentally prescribed response conditions. In more descriptive terms, conditions were sought to excite wave-patterns such as travelling and standing waves, and to suppress certain modes. In the paper these conditions are derived from modal properties. Simulated data are presented to demonstrate some of the phenomena and to highlight the practical difficulties. For rotationally periodic structures, most natural frequencies are of multiplicity two, and are sometimes called ‘double modes’. Their associated mode shapes can rotate in the plane of symmetry. The responses due to the two modes can be combined and expressed in a wave form, which can be split into travelling and standing wave components. Theoretically, it is possible to excite a pure travelling wave in a perfectly rotationally periodic structure, but there are limits to this in practice as real structures will always exhibit some degree of imperfection. These structures are said to be mistuned, and the imperfection splits the double modes into pairs of close modes. Simulations show the predicted vibration phenomena. In particular, the case of discrete excitations relevant to modal testing is investigated. The simulations show clearly that in this case components of other modes will generally be present. In an experiment, the results for driving the excitations will not give the theoretically expected response due to non-linearities of the shaker-structure interaction. However, the effects can be reduced by employing a computerised search algorithm.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

A Damage Identification Method Using Vibration Modal Parameters Through Finite Element Discretization

2003 ◽  
Author(s):  
Xiaoping Zhou ◽  
Abhijit Gupta
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Least Squares Method ◽  
Modal Testing ◽  
Mode Shapes ◽  
Element Formulation ◽  
Element Discretization ◽  
Damage Indices ◽  
Actual Damage

Natural frequencies and mode shapes of a structure will change whenever the structure has any kind of damage. This paper introduces a technique to quantify and locate the damage when the natural frequencies and mode shapes of undamaged and damaged structure are known. Aluminum beams (with and without damage) are used for numerical simulation and experimental verification. To establish the theoretical basis of this method, finite element formulation is used. A set of undetermined equations involving damage indices and natural frequencies and mode shapes of undamaged and damaged structures are obtained. The damage indices are computed using non-negative least squares method. Impact modal testing was conducted with three aluminum beams and damage indices based on experimental data are compared with actual damage cases to establish the effectiveness of this method to identify the damage.

Hydroelastic Modal Analysis of the Perforated Cylindrical Shell in SMART

2011 ◽  
Author(s):  
Youngin Choi ◽  
Seungho Lim ◽  
Kyoung-Su Park ◽  
No-Cheol Park ◽  
Young-Pil Park ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Steam Generators ◽  
Structure Interaction ◽  
The Finite Element Model ◽  
Reactor Internals

The System-integrated Modular Advanced ReacTor (SMART) developed by KAERI includes components like a core, steam generators, coolant pumps, and a pressurizer inside the reactor vessel. Though the integrated structure improves the safety of the reactor, it can be excited by an earthquake and pump pulsations. It is important to identify dynamic characteristics of the reactor internals considering fluid-structure interaction caused by inner coolant for preventing damage from the excitations. Thus, the finite element model is constructed to identify dynamic characteristics and natural frequencies and mode shapes are extracted from this finite element model.

scholarly journals Modal Testing Using Impact Excitation and a Scanning LDV

2000 ◽  
Vol 7 (2) ◽  
pp. 91-100 ◽  
Author(s):  
A.B. Stanbridge ◽  
D.J. Ewins ◽  
A.Z. Khan
Keyword(s):  
Impact Test ◽  
Natural Frequencies ◽  
Laser Doppler Vibrometer ◽  
Modal Testing ◽  
Impact Excitation ◽  
Mode Shapes ◽  
Natural Mode ◽  
Output Spectrum ◽  
Angular Vibration ◽  
Scan Line

If a laser Doppler vibrometer is used in a continuously-scanning mode to measure the response of a vibrating structure, its output spectrum contains side-bands from which the response mode shape, as defined along the scan line, may be obtained. With impact excitation, the response is the summation of a set of exponentially-decaying sinusoids which, in the frequency domain, has peaks at the natural frequencies and at `sideband' pseudo-natural frequencies, spaced at multiples of the scan frequency. Techniques are described for deriving natural mode shapes from these, using standard modal analysis procedures. Some limitations as to the types of mode which can be analysed are described. The process is simple and speedy, even when compared with a normal point-by-point impact test survey. Information may also be derived, using a circular scan, on the direction of vibration, and angular vibration, at individual points.

Importance of Enclosed Gas for Modal Analysis of Space Inflatable Structure

2014 ◽  
Vol 1016 ◽  
pp. 244-248
Author(s):  
Fei Liu ◽  
Wei Liang He
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Fluid Structure Interaction ◽  
Mode Shapes ◽  
Follower Load ◽  
Nonlinear Finite Element Method ◽  
Load Effect ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Structure Research

The stress distribution and modal characteristics of a space inflatable torus is investigated using the nonlinear finite element method. This paper focused on the effect of enclosed air on the modal analysis of the torus, including the effect of follower pressure load and the effect of the interaction between the enclosed air and the torus structure. Research shows that follower pressure stiffness significantly reduces the natural frequencies and changes mode shapes order. The fluid-structure interaction obviously reduces the natural frequencies, and the in-plane translation mode is observed. Follower pressure stiffness has no effect on the in-plane translation mode. Fluid-structure interaction decreases the natural frequencies of the modal considering the follower load effect, but it does not change mode shapes order. The effect of enclosed gas seriously reduces the natural frequencies, changes mode shapes order, and produces the in-plane translation mode.

Experimental Modal Analysis of a Half-Scale Model Twin-Engine Aircraft Rear Fuselage Engine Mount Support Frame

2017 ◽  
Author(s):  
Diego A. Chamberlain ◽  
Chris K. Mechefske
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Testing Procedure ◽  
Modal Testing ◽  
Scale Model ◽  
Mode Shapes ◽  
Component Testing ◽  
Fitting Procedures ◽  
Engine Mount ◽  
Set Up

Experimental modal testing using an impact hammer is a commonly used method for obtaining the modal parameters of any structure for which the vibrational behavior is of interest. Natural frequencies and associated mode shapes of the structure can be extracted directly from measured FRFs (Frequency Response Functions) through various curve fitting procedures. This paper provides an overview of the modal testing conducted on an aerospace component. Testing set-up, experimental equipment and the methodology employed are all described in detail. Further validation of the testing procedure was done by ensuring that the experimental results satisfy the requirements of repeatability, reciprocity and linearity. The relevant ISO standard has been referenced and important concepts to modal analysis are expanded upon. Recorded natural frequencies, coherence and a description of the observed mode shapes are presented along with notable trends.

scholarly journals High Frequency Modal Testing of the Multiblade Packets Using a Noncontact Measurement and Excitation System

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
C. H. Liu ◽  
C. Zang ◽  
F. Li ◽  
E. P. Petrov
Keyword(s):  
High Frequency ◽  
Measurement Method ◽  
Natural Frequencies ◽  
Spectral Lines ◽  
Modal Testing ◽  
Frequency Resolution ◽  
Mode Shapes ◽  
Finite Model ◽  
Frequency Range ◽  
Noncontact Measurement

High cycle failure of blades and vanes caused by the vibration is one of the major causes reducing the lifetime of turbomachines. For multiblade packets, the failure may occur at vibrations with high frequencies that can reach up to tens of kHz. The experimental modal testing of blades is crucial for the validation of numerical models and for the optimization of turbomachine design. In this paper, the test rig and procedure for measurements of dynamic characteristics of lightweight multiblade packets in wide and high frequency ranges are developed. The measurements are based on a noncontact excitation and noncontact measurement method, which allows the determination of the modal characteristics of the packets with high accuracy in wide frequency ranges. The responses of the multiblade packets are measured using a Scanning Laser Doppler Vibrometry (SLDV), while vibrations are excited by the acoustic excitation technique. Modal tests of the blade packet comprising 18 vane blades connected by shrouds are performed. The measurements are performed within the high frequency range of 0–30 kHz, and the natural frequencies and mode shapes are obtained for first 97 modes. To capture the complex high frequency blade mode shapes, each blade in the packet is scanned over 25 reference points uniformly distributed over the blade concave surface. In order to obtain the high frequency resolution, the frequency range used for the measurements is split into several frequency intervals accordingly to the number of spectral lines available in the used data acquisition system, and for each such interval, the test is performed separately. The finite model of the packet is created, and the numerical modal analysis is performed to compare the calculated natural frequencies and mode shapes with the experimental measurements. The comparison shows the satisfactory with those from finite element analysis. It illustrates the measurement method described in this work is effective and reliable.

Mode Evolution of Cyclic Symmetric Rotors Assembled to Flexible Bearings and Housing

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Hyunchul Kim ◽  
Nick Theodore Khalid Colonnese ◽  
I. Y. Shen
Keyword(s):  
Vibration Mode ◽  
Fluid Dynamic ◽  
Travelling Wave ◽  
Modal Testing ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Phase Index ◽  
Symmetric Rotor ◽  
Cyclic Symmetric ◽  
Inertia Forces

This paper is to study how the vibration modes of a cyclic symmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to assembly, the vibration modes of the rotor are classified as “balanced modes” and “unbalanced modes.” Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as unbalanced modes. By applying fundamental theorems of continuum mechanics, we conclude that balanced modes will present vanishing inertia forces and moments as they vibrate. Since each vibration mode of a cyclic symmetric rotor can be characterized in terms of a phase index (Chang and Wickert, “Response of Modulated Doublet Modes to Travelling Wave Excitation,” J. Sound Vib., 242, pp. 69–83; Chang and Wickert, 2002, “Measurement and Analysis of Modulated Doublet Mode Response in Mock Bladed Disks,” J. Sound Vib., 250, pp. 379–400; Kim and Shen, 2009, “Ground-Based Vibration Response of a Spinning Cyclic Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects,” ASME J. Vibr. Acoust. (in press)), the criterion of vanishing inertia forces and moments implies that the phase index by itself can uniquely determine whether or not a vibration mode is a balanced mode as follows. Let N be the order of cyclic symmetry of the rotor and n be the phase index of a vibration mode. Vanishing inertia forces and moments indicate that a vibration mode will be a balanced mode if n≠1,N−1,N. When n=N, the vibration mode will be balanced if its leading Fourier coefficient vanishes. To validate the mathematical predictions, modal testing was conducted on a disk with four pairs of brackets mounted on an air-bearing spindle and a fluid-dynamic bearing spindle at various spin speeds. Measured Campbell diagrams agree well with the theoretical predictions.

Modal Testing and Finite Element Calculations for Lightweight Aluminum Panels in Car Carriers

2006 ◽  
Vol 43 (01) ◽  
pp. 11-21
Author(s):  
Junbo Jia ◽  
Anders Ulfvarson
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Element Model ◽  
Modal Testing ◽  
Structural Behavior ◽  
Mode Shapes ◽  
Maintenance Cost ◽  
Car Suspension ◽  
Aluminum Panels

Due to their characteristics and lower maintenance cost, lightweight aluminum structures have been widely used for manufacturing deck structures. When this type of structure is developed, the natural frequencies for the unloaded deck may increase, while the natural frequencies for loaded decks are most likely to decrease and new problems of vibration and damping may appear. In addition, it has already been shown by the authors that compared to the load effects of normal cargo, the dynamic structural behavior of a vehicle-loaded deck is different due to the participation of vehicle vibrations. The current paper presents a modal analysis by both testing and finite element (FE) calculation for a lightweight deck using aluminum panels. By comparing the results between the unloaded and car-loaded cases, it is shown how vehicle loading influences the dynamic structural behavior of the deck structures. The authors report that an aluminum panel mechanically connected to a steel frame may participate in some mode shapes of vibrations that significantly increase the corresponding damping ratio. The reasonably good agreement between modal testing results and FE calculations validates the finite element model, which may then be used for further dynamic analysis. The authors found that the spring-damping systems of car suspension and tires can interfere in the dynamic transmission of the vehicle mass into the deck structure. The study enables structural engineers interested in the design of car carriers to have a better understanding of how the vehicles parked on decks can influence the dynamic characteristics of the vehicle deck systems.

Verification of a Finite Element Model of an Unmanned Aerial Vehicle Wing Torque Box via Experimental Modal Testing

2012 ◽  
Author(s):  
Levent Unlusoy ◽  
Melin Sahin ◽  
Yavuz Yaman
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Unmanned Aerial Vehicle ◽  
Natural Frequencies ◽  
Element Model ◽  
Modal Testing ◽  
Mode Shapes ◽  
Resonance Frequencies ◽  
Aerial Vehicle ◽  
Experimental Modal Testing

In this study, the detailed finite element model (FEM) of an unmanned aerial vehicle wing torque box was verified by the experimental modal testing. During the computational studies the free-free boundary conditions were used and the natural frequencies and mode-shapes of the structure were obtained by using the MSC® Software. The results were then compared with the experimentally obtained resonance frequencies and mode-shapes. It was observed that the frequencies were in close agreement having an error within the range of 1.5–3.6%.

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