scholarly journals A Simpler Formulation for Effective Mass Calculated from Experimental Free Mode Shapes of a Test Article on a Fixture

2017 ◽  
pp. 275-283 ◽  
Author(s):  
Randall L. Mayes ◽  
Patrick S. Hunter
Keyword(s):  
Effective Mass ◽  
Mode Shapes ◽  
Test Article ◽  
Free Mode

scholarly journals Prediction of the Resonant Response of Frictionally Constrained Blade Systems Using Constrained Mode Shapes

1998 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Contact Point ◽  
Element Model ◽  
The Other ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Cyclic Symmetry ◽  
Resonant Response ◽  
Friction Contact ◽  
Blade System ◽  
Free Mode

In this paper, the concept of constrained mode shapes is employed to predict the resonant response of a frictionally constrained blade system. For a tuned blade system, the constrained mode shapes can be calculated using a finite element model of a single blade along with the cyclic symmetry constraint that simulates a fully stuck friction contact. The resulting constrained mode shapes are often complex and can be used to obtain the constrained receptance of the frictionally constrained blade. It is shown that by examining each mode’s contribution to the receptance at the friction contact point, the importance of each individual modes to the prediction of the resonant response of a frictionally constrained blade can be determined. Furthermore, by comparing the receptances calculated from free mode shapes and those from constrained mode shapes, it is found that in the neighborhood of the fully slipping region, the prediction of resonant response requires fewer number of modes when using free mode shapes compared to using constrained mode shapes. On the other hand, in the neighborhood of the fully stuck region, it requires fewer number of modes if constrained mode shapes are used. Therefore, when high preload at the friction contact is desirable, such as for shrouded blade systems, using the constrained mode shapes for the prediction of resonant response is preferred. Moreover, the concept of hybrid receptance is introduced so as to yield very accurate prediction of the resonant response based on only very few vibration modes.

Design Methods of Friction Damping at Blade-Disk Joints

2009 ◽  
Author(s):  
Jie Hong ◽  
Lulu Chen ◽  
Yanhong Ma ◽  
Xin Yang
Keyword(s):  
Low Frequency ◽  
Harmonic Balance Method ◽  
Large Error ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Tracking Motion ◽  
Nonlinear Force ◽  
Free Mode

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

2016 ◽  
Vol 16 (06) ◽  
pp. 1550013 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Material Anisotropy ◽  
Rotating Speed ◽  
Multipliers Method ◽  
Free Mode ◽  
The Difference ◽  
Laminated Composite Beams

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

Closed-Loop Behavior of a Feedback-Controlled Flexible Arm: A Comparative Study

1991 ◽  
Vol 10 (3) ◽  
pp. 263-275 ◽  
Author(s):  
Sabri Cetinkunt ◽  
Wen-Lung Yu
Keyword(s):  
Mode Shape ◽  
Closed Loop ◽  
Transfer Functions ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Dimensional Model ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Shape Models ◽  
Free Mode

The dynamics of mechanical systems with distributed flexi bility are described by infinite-dimensional mathematical models. In order to design afinite-dimensional controller, a finite-dimensional model of the system is needed. The con trol problem of a flexible beam is a typical example. The general practice in obtaining a finite-dimensional model is to use modal approximation for distributed flexibility, retain a finite number of modes, and truncate the rest. In this approx imation, the appropriate selection of the mode shape func tions and the number of modes is not clearly known. Mostly standard pinned-free and clamped-free mode shapes are used for the flexible beam model, retaining only two or three modes and truncating the rest. The actual system, on the other hand, is infinite-dimensional, and the modes describing its flexible behavior under feedback control would be neither pinned-free nor clamped-free boundary condition modes. Rather, the mode shapes themselves are a function of the feedback control. The infinite-dimensional transcendental transfer functions for a flexible beam are formulated without any modal ap proximation. Finite-dimensional transfer functions with different shapes and numbers of modes are formulated. The closed-loop performance predictions of different models under the same colocated and noncolocated controllers, which attempt to achieve high closed-loop bandwidth, are compared. Results are surprisingly consistent in all cases; the predictions of clamped-free mode shape models are much more accurate than the predictions of the pinned-free mode shape models.

A Generalization of Effective Mass for Selecting Free–Free Target Modes

2006 ◽  
Vol 129 (1) ◽  
pp. 121-127
Author(s):  
Daniel C. Kammer ◽  
Joseph Cessna ◽  
Andrew Kostuch
Keyword(s):  
Effective Mass ◽  
Equations Of Motion ◽  
Ground Vibration ◽  
Singular Values ◽  
Element Model ◽  
New Method ◽  
Mode Shapes ◽  
Vibration Test ◽  
Aerospace Applications ◽  
Elastic Modes

One of the most important tasks in pretest analysis and modal survey planning is the selection of target modes. The target modes are those mode shapes that are determined to be dynamically important using some definition. While there are many measures of dynamic importance, one of the measures that has been of greatest interest to structural dynamicists, is the contribution of each mode to the dynamic loads at an interface. Dynamically important modes contribute significantly to the interface loads and must be retained in any reduced analytical representation. These modes must be identified during a ground vibration test to validate the corresponding finite element model. Structural dynamicists have used interface load based effective mass measures to efficiently identify target modes for constrained structures. The advantage of these measures of dynamic importance is that they are absolute, in contrast to other measures that only indicate the importance of one mode shape relative to another. However, in many situations, especially in aerospace applications, structures must be tested in a free–free configuration. In the case of free–free elastic modes, the effective mass values are zero, making them useless measures of dynamic importance. This paper presents a new effective mass like measure of absolute dynamic importance that can be applied to free–free structures. The new method is derived based upon the free–free modal equations of motion. The approach is shown to be directly related to ranking mode shapes based on approximate balanced singular values. But, unlike the approximate balanced singular value approach, it is an absolute measure of importance. A numerical example of a general spacecraft system is presented to illustrate the application of the new technique. Dynamically important mode shapes were easily identified for modal acceleration, velocity, and displacement output. The new method provides an efficient technique for selecting target modes for a modal vibration test, or the reduction of a modal based analytical model to the dynamically important mode shapes.

scholarly journals An investigation into the free vibration analysis of intact and defective laminated coposite beams subjected to combined axial force and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb T. Kashani
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Axial Force ◽  
Free Vibration Analysis ◽  
Numerical Data ◽  
Mode Shapes ◽  
Future Research ◽  
Frequency Dependent ◽  
Advantages And Disadvantages ◽  
Free Mode

This research is focusing on the bending-torsion coupled free vibration modeling as well as the analysis of intact and defective pre-stressed beams subjected to combined axial force and end moment. In the recent years, many studies have been conducted in an attempt to investigate the free vibration of pre-stressed beams using numerical and analytical techniques. However, despite their numerous applications, there is limited research done on pre-stressed beams subjected to both axial force and end moment in addition to the coupled behavior caused by the latter one. In the present study, current trends in the literature are critically examined, new models are proposed, and numerical and semi-analytical formulations are developed to find the natural frequencies and mode shapes of different pre-stressed slender beam configurations. The proposed methods are compared in terms of accuracy and convergence. Furthermore, the effects of axial force, end moment and delamination defect on the vibrational behavior of each model are also investigated. Four different general types of thin beams, including isotropic, layered, composite and delaminated beams, are modeled using traditional Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) technique. The DFE formulation is distinct from the conventional FEM by the fact that the former exploits frequency-dependent basis and shape functions of approximation space, whereas the polynomial ones are used in the latter method. With regard to layered beams, a novel layer-wise method is introduced for both DFE and FEM. Delaminated beam is also modeled using both ‘free mode’ and ‘constrained mode’ models showing that the continuity (both kinematic and force) conditions at delamination tips, in particular, play a large role in formulation of ‘free mode’ model. In this case, the defect is assumed to be a single-symmetric through the thickness delamination. However, the presented models and formulations could be readily extended to more general cases. Where available, the results were validated against existing limited experimental, analytical, and numerical data in literature. In addition, the investigated cases are modeled in the commercial finite element suite ANSYS® for further validation. Finally, general concluding remarks are made on the performance of the presented models and solution techniques, where the advantages and disadvantages of the proposed formulations as well as possible future research works are highlighted.

Dynamic Modeling and Updating of a Stacked Plate Dynamic System

2013 ◽  
Author(s):  
Troy Lundstrom ◽  
Charlie Sidoti ◽  
Nader Jalili
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Technical Problem ◽  
Laser Doppler Vibrometer ◽  
Element Model ◽  
Circuit Board ◽  
Mode Shapes ◽  
Test Article ◽  
Modal Test ◽  
Flexible Mode

The dynamic control of stacked-plate mechanical systems such as circuit board assemblies is a common technical problem that often requires a complete description of the open loop system dynamics prior to controller development. Often, a preliminary finite element model (FEM) of the test article is developed to understand the dynamics of the system to perform a modal test. The results of this modal test must then be used to update the stiffness, mass and damping matrices to yield correct FEM frequencies mode shapes and damping. This work describes the mathematical development of a finite element model of a multi-plate test article and proceeds with a model update using differentiated velocity data collected at discrete points on the structure with a laser Doppler vibrometer (LDV) and drive point measurements collected at the excitation location with an impedance head. Using these data, accelerance FRFs were computed and the first three flexible mode shapes were estimated and these shapes were compared to the corresponding FEM shapes using both percent frequency difference and modal assurance criterion (MAC). Several parameters of the system model were modified yielding improved correlation with the experimental results.

A Holographic and BEM/FEM Analysis of a Fluid-Loaded Propeller

1993 ◽  
Author(s):  
John M. Rice ◽  
William G. Fennell
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Effective Mass ◽  
Dynamic Characteristics ◽  
Mass Matrix ◽  
Mode Shapes ◽  
Infinite Domain ◽  
Finite Element Program ◽  
Numerical Predictions ◽  
Element Method

Abstract The modal dynamic characteristics of an underwater propeller are investigated using a coupling of the Finite Element Method (FEM) to model the propeller and the Boundary Element Method (BEM) to model the fluid. Results of this numerical model are presented for a fluid-loaded propeller and are compared with experimental holographic results. The FEM is known to yield very reliable solutions in the analysis of the modal dynamic characteristics of solid structures such as a propeller and the BEM is very attractive in dealing with infinite domain problems and the radiation condition, such as the infinite fluid field. Combining the two methods exploits the best attributes of both. The fluid/structural coupling is achieved by discretizing Kirchhoff’s integral with boundary elements and isolating the effective mass of the fluid. This effective mass is in the form of a mass matrix which is coupled by the degrees of freedom of the propeller. The effective mass is then input into a finite element program in the form of user elements along with the propeller’s geometry, material properties, and boundary conditions to simulate an underwater propeller in a hub. An experiment using time averaged holographic interferometry was performed to identify the resonant modes of the propeller, identical in geometry to that used in the FEM model. In order to simulate the boundary conditions of the model the propeller was rigidly clamped in a vise at it’s root and submerged in water. Excitation of the propeller was provided by means of a mechanical shaker mounted to the vise. Both the resonant frequencies and their respective mode shapes agreed favorably with numerical predictions.

scholarly journals An investigation into the free vibration analysis of intact and defective laminated coposite beams subjected to combined axial force and end moment

2021 ◽  
Author(s):  
Mir Tahmaseb T. Kashani
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Axial Force ◽  
Free Vibration Analysis ◽  
Numerical Data ◽  
Mode Shapes ◽  
Future Research ◽  
Frequency Dependent ◽  
Advantages And Disadvantages ◽  
Free Mode

This research is focusing on the bending-torsion coupled free vibration modeling as well as the analysis of intact and defective pre-stressed beams subjected to combined axial force and end moment. In the recent years, many studies have been conducted in an attempt to investigate the free vibration of pre-stressed beams using numerical and analytical techniques. However, despite their numerous applications, there is limited research done on pre-stressed beams subjected to both axial force and end moment in addition to the coupled behavior caused by the latter one. In the present study, current trends in the literature are critically examined, new models are proposed, and numerical and semi-analytical formulations are developed to find the natural frequencies and mode shapes of different pre-stressed slender beam configurations. The proposed methods are compared in terms of accuracy and convergence. Furthermore, the effects of axial force, end moment and delamination defect on the vibrational behavior of each model are also investigated. Four different general types of thin beams, including isotropic, layered, composite and delaminated beams, are modeled using traditional Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) technique. The DFE formulation is distinct from the conventional FEM by the fact that the former exploits frequency-dependent basis and shape functions of approximation space, whereas the polynomial ones are used in the latter method. With regard to layered beams, a novel layer-wise method is introduced for both DFE and FEM. Delaminated beam is also modeled using both ‘free mode’ and ‘constrained mode’ models showing that the continuity (both kinematic and force) conditions at delamination tips, in particular, play a large role in formulation of ‘free mode’ model. In this case, the defect is assumed to be a single-symmetric through the thickness delamination. However, the presented models and formulations could be readily extended to more general cases. Where available, the results were validated against existing limited experimental, analytical, and numerical data in literature. In addition, the investigated cases are modeled in the commercial finite element suite ANSYS® for further validation. Finally, general concluding remarks are made on the performance of the presented models and solution techniques, where the advantages and disadvantages of the proposed formulations as well as possible future research works are highlighted.

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