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.

Application of Lifting-Surface Theory to the Prediction of Hydroelastic Response of Hydrofoil Boats

1968 ◽  
Vol 12 (04) ◽  
pp. 286-301
Author(s):  
C. J. Henry
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Operator Technique ◽  
Elastic Mode ◽  
Surface Theory ◽  
Lifting Surface ◽  
Modes Of Vibration ◽  
Elastic Modes

In this report a theoretical procedure is developed for the prediction of the dynamic response elastic or rigid body, of a hydrofoil-supported vehicle in the flying condition— to any prescribed transient or periodic disturbance. The procedure also yields the stability indices of the response, so that dynamic instabilities such as flutter can also be predicted. The unsteady hydrodynamic forces are introduced in the equations of motion for the elastic vehicle in terms of the indicia I pressure-response functions, which are de rived herein from lifting-surface theory. Thus, the predicted vehicle-response includes the effects of three-dimensional unsteady flow conditions at specified forward speed. The natural frequencies and elastic modes of vibration of the vehicle and foil system in the absence of hydrodynamic effects are presumed known. A numerical procedure is presented for the solution of the downwash integral equations relating the unknown indicial pressure distributions to the specified elastic-mode shapes. The procedure is based on use of the generalized-lift-operator technique together with the collocation method.

Optimal configuration of shakers for phase resonance testing using modal parameters

2019 ◽  
Vol 233 (16) ◽  
pp. 5676-5690 ◽  
Author(s):  
Wei Chen ◽  
Mengshi Jin ◽  
Hanwen Song
Keyword(s):  
Amplitude Ratio ◽  
A Priori ◽  
Ground Vibration ◽  
Element Model ◽  
Optimal Configuration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Target Mode ◽  
Modal Force ◽  
Phase Resonance

The phase resonance testing is widely used in the ground vibration test for aircraft due to the advantages of distinguishing closely spaced modes and directly comparing normal mode shapes with those from finite element model. However, the process to configure the shakers is time-consuming. A method to configure the shakers, which calculates the appropriate force vector and estimates the optimal combination of excitation locations for phase resonance testing, is proposed in this paper. Compared with other configuration methods, where the frequency response function matrix is known a priori, the proposed method only requires a priori information of rough modal parameters. Therefore, less information is used in this method, which leads to the advantage of calculating the optimal configuration more efficiently. In this method, the modal force amplitude ratio of the target mode to all the modes, called the modal ratio indicator, is set up as the criterion to select the optimal configuration. Simulations of a discrete plate are performed to show the process of the method. An experiment of a steel beam is conducted to validate the effectiveness and reliability of this method.

Finite Element Model Tuning Using Measured Mass Properties and Ground Vibration Test Data

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Chan-gi Pak
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Ground Vibration ◽  
Element Model ◽  
Mode Shapes ◽  
Test Fixture ◽  
Mass Properties ◽  
Model Tuning ◽  
Final Optimization ◽  
Mother Ship

A simple and efficient approach for tuning finite element models to match computed frequencies, mode shapes, and mass properties to the experimental data is introduced in this study. The model tuning procedure proposed in this study is based on a series of optimizations. This approach has been successfully applied to create an equivalent beam finite element model for the X-37 drogue chute test fixture with the X-planes pylon. The goal was a simple model capable of being analyzed in a captive carry configuration with the B-52H mother ship. This study has shown that natural frequencies, corresponding mode shapes, and mass properties from the updated finite element model achieved at the final optimization iteration have excellent agreement with corresponding measured data.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

A new method for finite element model updating in structural dynamics

2010 ◽  
Vol 24 (7) ◽  
pp. 2137-2159 ◽  
Author(s):  
J.L. Zapico-Valle ◽  
R. Alonso-Camblor ◽  
M.P. González-Martínez ◽  
M. García-Diéguez
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Structural Dynamics ◽  
Model Updating ◽  
Element Model ◽  
New Method ◽  
Finite Element Model Updating

Selection of Component Modes for Craig-Bampton Substructure Representations

1996 ◽  
Vol 118 (2) ◽  
pp. 264-270 ◽  
Author(s):  
D. C. Kammer ◽  
M. J. Triller
Keyword(s):  
Efficient Method ◽  
Singular Values ◽  
General Purpose ◽  
Mode Shapes ◽  
Frequency Range ◽  
Reduced Representation ◽  
Absolute Measure ◽  
Fixed Interface ◽  
Interface Mode ◽  
Selection Of

Three measures of modal dynamic importance are studied for the purpose of ranking Craig-Bampton substructure fixed interface mode shapes based upon their contribution to forces at the substructure interface, modal velocity, or modal displacement. These measures can be employed to identify mode shapes which are dynamically important and thus should be retained in a reduced analytical representation, or identified during a modal survey of the substructure. The first method considered. Effective Interface Mass, has been studied previously. However, new results are presented showing the relation between Effective Interface Mass and a commonly used control dynamics measure of modal importance called approximate balanced singular values. In contrast to the general case of approximate balanced singular values, Effective Interface Mass always gives an absolute measure of the dynamic importance of mode shapes. The EIM method is extended to consider modal velocity and modal displacement outputs. All three measures are applied to a simple substructure called the General Purpose Spacecraft. It is shown that each of these measures provides an efficient method for ranking the dynamic importance of Craig-Bampton fixed interface modes such that a reduced representation will accurately reproduce the substructure’s response in the frequency range of interest.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Sign in / Sign up

Export Citation Format

Share Document