Mounting Stiffness Effects in “Free-Free” Modal Tests

1997 ◽  
Author(s):  
Joseph A. Wolf
Keyword(s):  
Support System ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
A Priori ◽  
Mode Shapes ◽  
Vibration Test ◽  
Complex Structures ◽  
Fundamental Issue ◽  
Test Results ◽  
Modal Test

Abstract The fundamental issue confronting a vibration test engineer is how to obtain the best representation for the natural frequencies and corresponding mode shapes of a mechanical system. In the case of a structure such as a vehicle that has rigid body degrees of freedom, a vibration test requires some sort of artificial support system. The purpose of this work is to quantify the influence of this support system using two example structures: a one-degree-of-freedom oscillator, and a uniform beam on two types of supports. In all cases, the actual influence of the supports on the modal test results is greater than one would estimate a priori. It is hoped that these results, which have been derived from exact solutions, will provide insight for designing test supports for more complex structures.

Dynamic Characteristics Analysis for the Headstock of a Vertical Machining Center

2016 ◽  
Vol 836-837 ◽  
pp. 348-358
Author(s):  
Zhe Li ◽  
Song Zhang ◽  
Yan Chen ◽  
Peng Wang ◽  
Ai Rong Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Control ◽  
Vibration Test ◽  
Machining Accuracy ◽  
Modal Test ◽  
Machining Center ◽  
Characteristics Analysis ◽  
Nc Machine

Dynamic characteristics of numerical control (NC) machine tools, such as natural frequency and vibration property, directly affect machining efficiency and finished surface quality. In general, low-order natural frequencies of critical components have significant influences on machine tool’s performances. The headstock is the most important component of the machine tool. The reliability, cutting stability, and machining accuracy of a machining center largely depend on the structure and dynamic characteristics of the headstock. First, in order to obtain the natural frequencies and vibration characteristics of the headstock of a vertical machining center, modal test and vibration test in free running and cutting conditions were carried out by means of the dynamic signal collection and analysis system. According to the modal test, the first six natural frequencies of the headstock were obtained, which can not only guide the working speed, but also act as the reference of structural optimization aiming at frequency-shift. Secondly, by means of the vibration test, the vibration characteristics of the headstock were obtained and the main vibration sources were found out. Finally the corresponding vibration reduction plans were proposed in this paper. That provides the reference for improving the performance of the overall unit.

scholarly journals Characteristic Constraint Modes for Component Mode Synthesis

1999 ◽  
Author(s):  
Matthew P. Castanier ◽  
Yung-Chang Tan ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Cantilever Plate ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Physical Insight ◽  
Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

An effective method for damage assessment based on limited measured locations in skeletal structures

2020 ◽  
Vol 24 (1) ◽  
pp. 183-195 ◽  
Author(s):  
Parsa Ghannadi ◽  
Seyed Sina Kourehli
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Damage Detection ◽  
Degrees Of Freedom ◽  
Truss Structures ◽  
Mode Shapes ◽  
Analysis Model ◽  
Test Analysis ◽  
Modal Test ◽  
Artificial Neural

This article proposes a new damage detection method using Modal Test Analysis Model and artificial neural networks. A challenge in damage detection problems is lack of measured degrees of freedom, as well as limitations of attached sensors. Modal Test Analysis Model has been used in order to estimate unmeasured degrees of freedom. An experimental cantilever beam was used to show Modal Test Analysis Model’s efficiency in estimation of unmeasured mode shapes. To solve the inverse problem of damage detection, mode shapes estimated by Modal Test Analysis Model were used as inputs, and characteristics of the damage served as outputs of the artificial neural network. The sensitivity analysis carried out for each example showing the performance of artificial neural network after mode shape expansion was efficiently improved. Three numerical examples for plane and space truss structures are considered, in order to verify effectiveness of the proposed method. Results demonstrate a high accuracy of Modal Test Analysis Model and artificial neural network for structural damage detection.

Modeling and Free Vibration of Flex Circuits in Hard Disk Drives

2003 ◽  
Author(s):  
Jonathan Wickert
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equilibrium Shape ◽  
Local Equilibrium ◽  
Hard Disk Drives ◽  
Laser Interferometry ◽  
Hard Disk ◽  
System Level ◽  
Mode Shapes ◽  
Free Length

A flex circuit connects the stationary electronic components in a hard disk drive to the rotating arm that carries the read/write heads and positions them above data tracks on the disk. Flex circuits are conventionally formed as a laminate of polyimide substrate, adhesive, and copper conductors. Deformation of a flex circuit is discussed in the context of the following stages: the initial unstressed shape, configurations in which stresses set and relax in response to elevated temperature, equilibrium, and small amplitude vibration. The model involves displacements of the flex circuit in the directions tangent and normal to the local equilibrium shape, and those motions couple with the arm’s dynamics. Nonlinearity associated with finite curvature, partial elastic springback, and the arm’s geometry and inertia properties are incorporated within the vibration model to predict system-level natural frequencies, mode shapes, and coupling factors between the circuit and the arm. Laboratory measurements using noncontact laser interferometry validate the model with respect to the circuit’s shape, stiffness, restoring moment, and natural frequencies. The primary degrees of freedom for optimizing flex circuit design are the thicknesses of the individual layers within the circuit, free length, and the locations and slopes of the circuit’s attachment points to the arm and electronics block. The model’s predictions and trends developed from a case study in free length are discussed with a view toward reducing coupling between the circuit and arm in certain vibration modes.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

Experimental and Numerical Modal Analysis of Gearbox Casing in a Polishing Machinery

2009 ◽  
Vol 69-70 ◽  
pp. 560-564
Author(s):  
Yang Yu Wang ◽  
Shi Ming Ji ◽  
Dong Hui Wen ◽  
Xian Zhang
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Test System ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Vibration Test ◽  
3D Fem ◽  
Fem Model

Vibrations in polishing machinery may affect the manual or automatic controls and reduce the efficiency of the operations to be carried out. In this article, an experimental and numerical analysis on the dynamic characteristic of a gearbox casing in polishing machinery have been carried out. The numerical investigation was achieved with NASTRAN based on a 3D FEM model and the experimental modal analysis for the determination of the natural frequencies and the associated eigenmodes of the gearbox casing with LMS structural vibration test system was performed. The fundamental modal parameters including the first 10-order natural frequencies, damping ratios and mode shapes were estimated and identified. Analytical and experimental results have been compared and discussed. Agreement between measurements and calculations is satisfactory and the results can be used as reliable reference for improving the dynamic behavior of the gearbox casing.

The Vibration Characteristics of a Large Flexible Vibration Isolation Structure with Finite Element Analysis and Modal Test

2011 ◽  
Vol 199-200 ◽  
pp. 858-864 ◽  
Author(s):  
Liu Bin Zhou ◽  
Tie Jun Yang ◽  
Wan Peng Yuan ◽  
Hui Shi ◽  
Zhi Gang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Vibration Isolation ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Test ◽  
The Finite Element Analysis

A large flexible vibration isolation structure is presented in this thesis, and experimental modal test based on the finite element analysis is carried out in order to find out the vibration characteristics of it. Results show that the natural frequencies and mode shapes calculated by finite element method basically conform to those measured from experimental modal test. Some suggestion to vibration active control in further research is also provided.

scholarly journals Free Modal Analysis for Spiral Bevel Gear Wheel Based on the Lanczos Method

2015 ◽  
Vol 9 (1) ◽  
pp. 637-645 ◽  
Author(s):  
Xiang Tieming ◽  
Zhou Shuiting ◽  
Yi Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Gear Wheel ◽  
Lanczos Method ◽  
Bevel Gear ◽  
Mode Shapes ◽  
Spiral Bevel Gear ◽  
Modal Test ◽  
Spiral Bevel

In order to obtain the spiral bevel gear wheel natural frequencies and mode shapes in the unconstrained state for the purpose of dynamic characteristics study, the spiral bevel gear wheel three-dimensional solid model of a mini-bus main reducer is established in this paper. The finite element model of spiral bevel gear wheel which consists of 32351 nodes, 18436 solid187 tetrahedrons finite element method elements is established by using free grid meshing method in this paper. Extract the first 6 orders modals parameters such as natural frequencies and main vibration mode shapes by using the Lanczos method. The new 1st to 4th orders modals are formed by comparing and merging 2 orders repeated modals. In order to verify the effectiveness of the finite element analysis results, the experiment modal test based on the impulse force hammer percussion transient single-point excitation and multi-point response analysis method has been done. The maximum difference value of natural frequency between experimental modal test result and finite element modal analysis results is 29.86 Hz, the maximum error rate is 0.41%, which confirmed the result of finite element method is effective and reliable. The conclusions reflect the vibration response characteristics of spiral bevel gear wheel, and provide theoretical basis for dynamic response, structure design and optimization of spiral bevel gear wheel.

scholarly journals An analytical formulation to evaluate natural frequencies and mode shapes of high-rise buildings

2021 ◽  
Vol 8 (1) ◽  
pp. 307-318
Author(s):  
Giuseppe Nitti ◽  
Giuseppe Lacidogna ◽  
Alberto Carpinteri
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Shear Walls ◽  
Vertical Axis ◽  
Mode Shapes ◽  
Analytical Formulation ◽  
High Rise ◽  
Open Section ◽  
Stiffness Matrices ◽  
Thin Walled

Abstract In this paper, an original analytical formulation to evaluate the natural frequencies and mode shapes of high-rise buildings is proposed. The methodology is intended to be used by engineers in the preliminary design phases as it allows the evaluation of the dynamic response of high-rise buildings consisting of thin-walled closed- or open-section shear walls, frames, framed tubes, and dia-grid systems. If thin-walled open-section shear walls are present, the stiffness matrix of the element is evaluated considering Vlasov’s theory. Using the procedure called General Algorithm, which allows to assemble the stiffness matrices of the individual vertical bracing elements, it is possible to model the structure as a single equivalent cantilever beam. Furthermore, the degrees of freedom of the structural system are reduced to only three per floor: two translations in the x and y directions and a rigid rotation of the floor around the vertical axis of the building. This results in a drastic reduction in calculation times compared to those necessary to carry out the same analysis using commercial software that implements Finite Element models. The potential of the proposed method is confirmed by a numerical example, which demonstrates the benefits of this procedure.

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