The “Smeared” Property Technique for the FE Vibration Analysis of Printed Circuit Cards

1991 ◽  
Vol 113 (3) ◽  
pp. 250-257 ◽  
Author(s):  
J. M. Pitarresi ◽  
D. V. Caletka ◽  
R. Caldwell ◽  
D. E. Smith
Keyword(s):  
Natural Frequencies ◽  
Primary Objective ◽  
Mode Shapes ◽  
Fe Model ◽  
Printed Wiring Board ◽  
Modal Assurance Criterion ◽  
Printed Circuit ◽  
Wiring Board

The primary objective of this paper is to investigate the accuracy of the finite element (FE) smeared properties approach for the determination of the mode shapes and frequencies of a printed wiring board (PWB) populated with electronic modules. Smearing of the material and/or structural properties is a recognized means of reducing a complicated structure to a less complicated approximation. Comparisons of both the natural frequencies and mode shapes are made between the smeared FE model and those obtained from vibration testing. The extent of correlation between the mode shapes is characterized by the modal assurance criterion (MAC). Since the intent of this study is to examine the effectiveness of the smearing technique, free boundary conditions are assumed. It is shown that the smearing technique can produce good correlation of both natural frequencies and mode shapes of PWBs populated with modules. A case study of a PWB with both surface mount technology (SMT) and pin-in-hole (PIH) components is presented.

scholarly journals Linear Finite Element Modeling of Joined Structures With Riveted Connections

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
J. S. Kim ◽  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Modeling Method ◽  
Test Structure ◽  
Mode Shapes ◽  
Fe Model ◽  
Fe Modeling ◽  
Engineering Structures ◽  
Modal Assurance Criterion ◽  
Linear Finite Element

Abstract Riveted connections are widely used to join basic components, such as beams and panels, for engineering structures. However, accurately modeling joined structures with riveted connections can be a challenging task. In this work, an accurate linear finite element (FE) modeling method is proposed for joined structures with riveted connections to estimate modal parameters in a predictive manner. The proposed FE modeling method consists of two steps. The first step is to develop nonlinear FE models that simulate riveting processes of solid rivets. The second step is to develop a linear FE model of a joined structure with the riveted connections simulated in the first step. The riveted connections are modeled using solid cylinders with dimensions and material properties obtained from the nonlinear FE models in the first step. An experimental investigation was conducted to study accuracy of the proposed linear FE modeling method. A joined structure with six riveted connections was prepared and tested. A linearity investigation was conducted to validate that the test structure could be considered to be linear. A linear FE model of the test structure was constructed using the proposed method. Natural frequencies and corresponding mode shapes of the test structure were measured and compared with those from the linear FE model. The maximum difference of the natural frequencies was 1.63% for the first 23 out-of-plane elastic modes, and modal assurance criterion values for the corresponding mode shapes were all over 95%, which indicates high accuracy of the proposed linear FE modeling method.

scholarly journals Assessment of human-induced vibrations of a cable-stayed footbridge

2018 ◽  
Vol 211 ◽  
pp. 09001 ◽  
Author(s):  
Izabela Drygała ◽  
Joanna M. Dulinska ◽  
Marek Wazowski
Keyword(s):  
Natural Frequencies ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Fe Model ◽  
In Situ Tests ◽  
Modal Assurance Criterion ◽  
Comfort Criteria ◽  
Abaqus Software

The primary purpose of this research is the evaluation of human-induced vibrations of a cable-stayed footbridge. The cable-stayed pedestrian bridge with total length of the span equal to 46.90 m located in Czestochowa (Southern Poland) was chosen as a case study. The footbridge consists of two spans (21.10 m and 25.80 m). A three-dimensional (3D) finite element (FE) model of the footbridge was prepared with the ABAQUS software program. The dynamic properties of the structure, i.e. its natural frequencies, modes shapes and damping ratios, were estimated on the basis of the in situ tests results as well as numerical analysis. For the validation of the modal models the modal assurance criterion (MAC) theory was applied. In the next stage of the investigation the dynamic response of the structure to human-induced loading was evaluated. Finally, the vibration comfort criteria for the footbridge were checked.

Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
K. He ◽  
W. D. Zhu
Keyword(s):  
Natural Frequencies ◽  
Beam Element ◽  
Mode Shapes ◽  
Beam Specimen ◽  
Fe Model ◽  
Modal Assurance Criterion ◽  
Solid Element ◽  
Out Of Plane ◽  
Thin Walled ◽  
Shell Plate

Fillets are commonly found in thin-walled beams. Ignoring the presence of a fillet in a finite element (FE) model of a thin-walled beam can significantly change the natural frequencies and mode shapes of the structure. A large number of solid elements are required to accurately represent the shape and the stiffness of a fillet in a FE model, which makes the size of the FE model unnecessarily large for global dynamic and static analyses. In this work the equivalent stiffness effects of a fillet in a thin-walled beam are decomposed into in-plane and out-of-plane effects. The in-plane effects of a fillet are analyzed using the wide-beam and curved-beam theories, and the out-of-plane effects of the fillet are analyzed by modeling the whole fillet section as a slender bar with an irregular cross section. A simple shell/plate and beam element model is developed to capture the in-plane and out-of-plane effects of a fillet on a thin-walled beam. The natural frequencies and mode shapes of a thin-walled L-shaped beam specimen calculated using the new methodology are compared with its experimental results for 28 modes. The maximum error between the calculated and measured natural frequencies for all the modes is less than 2%, and the associated modal assurance criterion values are all over 95%. The methodology is also applied to other thin-walled beams, and excellent agreement is achieved between the natural frequencies from the shell/plate and beam element models and those from the solid element models. While the shell/plate and beam element models provide the same level of accuracy as the intensive solid element models, the degrees of freedom of the shell/plate and beam element models of the thin-walled beams are only about 10% or less of those of the solid element models.

scholarly journals Dynamic Modal Correlation of an Automotive Rear Subframe, with Particular Reference to the Modelling of Welded Joints

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Vincenzo Rotondella ◽  
Andrea Merulla ◽  
Andrea Baldini ◽  
Sara Mantovani
Keyword(s):  
Welded Joints ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Structural Performance ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Assurance Criterion ◽  
Structural Dynamic ◽  
Actual Structure ◽  
Modal Response

This paper presents a comparison between the experimental investigation and the Finite Element (FE) modal analysis of an automotive rear subframe. A modal correlation between the experimental data and the forecasts is performed. The present numerical model constitutes a predictive methodology able to forecast the experimental dynamic behaviour of the structure. The actual structure is excited with impact hammers and the modal response of the subframe is collected and evaluated by the PolyMAX algorithm. Both the FE model and the structural performance of the subframe are defined according to the Ferrari S.p.A. internal regulations. In addition, a novel modelling technique for welded joints is proposed that represents an extension of ACM2 approach, formulated for spot weld joints in dynamic analysis. Therefore, the Modal Assurance Criterion (MAC) is considered the optimal comparison index for the numerical-experimental correlation. In conclusion, a good numerical-experimental agreement from 50 Hz up to 500 Hz has been achieved by monitoring various dynamic parameters such as the natural frequencies, the mode shapes, and frequency response functions (FRFs) of the structure that represent a validation of this FE model for structural dynamic applications.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

The Use of Interference Diagrams to Avoid Impeller Resonance: An Application to IGV Design

2009 ◽  
Author(s):  
Marco Ferioli
Keyword(s):  
Centrifugal Compressor ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Common Source ◽  
Operating Speed ◽  
Element Analysis ◽  
Exciting Frequency ◽  
Combine Information ◽  
The Impact

Interference diagrams can be used to avoid the potential excitation of a particular mode of vibration for centrifugal compressor impellers, thus reducing the risk of fatigue failures. Such diagrams are an excellent tool to combine information on impeller natural frequencies and mode shapes, excitation sources and operating speed of the machine on the same graph. Once the impeller design has been finalized in terms of aerodynamic performance, structural assessments and therefore geometry, Finite Element Analysis can be used to predict its natural frequencies and mode shapes (i.e. nodal diameters). Results can therefore be shown on a chart, together with the operating speed range of the machine. The need to plot on a single diagram this whole set of data arises from the mathematical evidence to consider the frequency of vibration together with the mode shape and the shape of the exciting force, while analyzing resonances. Typical Campbell diagrams are unable to provide this information at a glance. A common source of excitation for the first impeller of centrifugal compressors is the IGV set. Inlet Guide Vanes produce an exciting frequency that is directly proportional to the number of vanes N, where N represents also the shape of the excitation. The interference diagram can therefore be used: • to design and optimize the IGV for a new machine; • to choose between two different designs; • to evaluate the impact of a new IGV for the impeller of an existing compressor. A case study will be introduced, in order to show the application of interference diagrams to avoid potentially dangerous resonances between an IGV set and the first impeller during the re-design phase for a centrifugal compressor already in operation.

An Extension of the Holzer Method for Redundant Drive Trains

1974 ◽  
Vol 96 (2) ◽  
pp. 697-698 ◽  
Author(s):  
M. S. Hundal
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
System Of Equations ◽  
Redundant System ◽  
Drive Trains ◽  
Redundant Drive

A method is described for the determination of natural frequencies and mode shapes of closed drive trains. It is an extension of the Holzer method to a redundant system. The “error” for a given value of frequency is computed by the solution of a tridiagonal system of equations.

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