Modal testing

About: Modal testing is a research topic. Over the lifetime, 4047 publications have been published within this topic receiving 64772 citations.

Support Conditions for Experimental Modal Analysis

Abstract: When modal testing a structure for model validation, free boundary conditions are frequently approximated in the lab to compare with free boundary-condition analyses. Free conditions are used because they are normally easy to simulate analytically and easier to approximate experimentally than boundary conditions with fixed conditions. However, the free conditions can only be approximated in the lab, because the structure must be supported in some manner. This article investigates and quantifies the effects of the support conditions on both the measured modal frequencies and damping factors. The investigation has determined that the measured modal damping is significantly more sensitive to the support system (stiffness and damping) than the measured modal frequency. Included in the article are simple formulas that can be used to predict the effect on measured modal parameters given the support stiffness and damping. Modal testing is frequently used to validate the accuracy of structural dynamic models. Modal tests are performed on a structure to measure the modal frequencies, damping factors, and mode shapes. However during the modal test, a structure must be supported in some manner by the surrounding environment. Very frequently, free boundary conditions are the desired support conditions for comparison with computational results. Free conditions can only be approximated in the lab using soft supports, but the stiffness and damping of these added supports will affect the modal parameters of the combined structural system. A required part of pre-test planning is to design the support system to minimally affect the modal parameters. Obviously, one can include a model of the support system as part of the overall system model, and sometimes that is required due to compromises involved in the support system design. But one would like to be able to calculate the effects of the support system on the modal parameters to determine whether the effects are negligible or need to be accounted for. One of the primary objectives of this article is to derive fairly simple formulas and rules of thumb by which one can calculate the effect of the support conditions on the measured modal frequencies and damping factors so that appropriate support design can be performed before the test. The formulas and the effects of poor support conditions are also illustrated with results from two different modal tests. Historically, there has been concern for support stiffness and its effect on measured modal frequencies. Bisplinghoff, Ashley and Halfman 1 discuss the effects of support stiffness and mass on the modal frequencies, based on results of Rayleigh. 2 Wolf 3 discusses the effects of support stiffness with regard to modal testing of automotive bodies. He reports that the rule of thumb to simulate free boundary conditions is to design the support system so that the rigid-body modes, that is, the modes that would be at zero frequency except for the support conditions, are no more than one-tenth the frequency of the lowest elastic mode. But it is seldom possible to achieve this separation for vehicle tests. He states that test engineers frequently use a 1:3 to 1:5 separation ratio between the rigid-body modes and the lowest elastic mode. Wolf shows that such stiff supports can lead to significant errors in the measured modal frequencies. One of the current authors discussed support conditions in an earlier work, 4 and this article expands on that work with additional theoretical results and illustrates the theory with experiments and modeling. In his second edition of Modal Testing, 5 Ewins briefly discusses the issue of location of suspen sions for free boundary conditions in the test planning chapter. More recently, Brillhart and Hunt presented an exposition of many of the practical difficulties involved in designing good fixtures for a modal test, 6 and Avitabile briefly discussed this issue in a “Back to Basics” article. 7 In this article our primary emphasis here was to develop some quantitative measures of the effect of the support conditions on the modal frequencies and the modal damping ratios. Most finiteelement models could include the support stiffnesses and masses in the model, thus taking into account those effects. However, structural dynamic models often do not initially include damping, but use the measured modal damping ratios from a test to create a model, including damping. There is typically no validation of the damping model; it is taken directly from the test with the support conditions included. Consequently, one must be concerned with how the support conditions affect the measured damping. The remainder of this article is divided into four primary sections. In the first section, simple formulas are derived for a two degree-offreedom system. These formulas are simplistic, but can be used to derive rules of thumb and also easily illustrate the severity of the problem. The next section develops approximate formulas for the multi-degree-of-freedom problem that can be used for general structures. The last two sections further illustrate both the problem and the theory with some example modal tests, first from a very lightly damped uniform beam and second with a wind turbine blade that required a modal test for model validation and damping determination.

Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces

Abstract: A method for non-linear modal analysis of mechanical sys- tems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical system's equations of motion. The dissipative aspects of these non- linearities result in complex eigensolutions and the modal pa- rameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The gener- ality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, sta- bility analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dove- tail attachment are proposed. Finally, we propose a study of dy- namical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.

Reduction of Magnetically Induced Vibration of a Spoke-Type IPM Motor Using Magnetomechanical Coupled Analysis and Optimization

Abstract: We present an optimization methodology to reduce magnetically induced vibrations of a spoke-type interior permanent magnet (IPM) motor that we developed by performing magnetic and structural finite element analyses and optimization. The magnetic forces acting on the teeth of the stator were calculated by magnetic finite element analysis and the Maxwell stress tensor method. The natural frequencies and mode shapes of the stator were calculated by structural finite element analysis and verified by modal testing. The vibration of the motor due to the rotating magnetic force was calculated by the mode superposition method, and it was compared with the measured vibration. Finally, two optimization problems were formulated and solved to reduce magnetically induced vibration: minimization of magnetic force and minimization of acceleration. We showed that minimization of acceleration was more effective than minimization of magnetic force at reducing magnetically induced vibrations, because the former method effectively decreased the amplitudes of the excitation frequencies of magnetic force by considering the transfer function of the motor.

Modal Testing and Finite-Element Model Updating of a Lively Open-Plan Composite Building Floor

Abstract: This paper presents results of a combined experimental and analytical approach to investigate modal properties of a lively open-plan office floor. It is based on state-of-the-art finite-element (FE) modeling, FRF-based shaker modal testing, FE model correlation, manual model tuning, and sensitivity-based automatic model updating of a detailed FE model of this composite floor structure. The floor studied accommodates a fully furnished office. Such environments can be problematic regarding their vibration serviceability. However, there is a lack of reliable information about their as-built modal properties and the ability of designers to predict them. Therefore this paper has two aims: (1) to assess the ability to both predict and measure as accurately as possible the fundamental and higher modes of floor vibration, and (2) to correlate and update the initially developed FE model of the floor, so that its modes match as accurately as possible their measured counterparts. It was found that even a very detail...