Vibrations Analysis of Cable-Harnessed Plates: Continuum Modeling and Experimental Validation

2020 ◽  
pp. 1-34
Author(s):  
Pranav Agrawal ◽  
Armaghan Salehian
Keyword(s):  
Dynamic Modelling ◽  
Dry Mass ◽  
Linear Displacement ◽  
Modal Testing ◽  
Analytical Models ◽  
Mode Shapes ◽  
Power Cables ◽  
Dynamic Effects ◽  
Lumped Mass ◽  
Modal Assurance Criterion

Abstract Dynamic modelling of spacecraft structures is imperative to their successful design for flight missions. A large number of these structures' dry mass consists of signal and power cables, dynamics of which is not well-predicted using ad hoc cable lumped mass models. Hence, accurate modeling techniques are required to understand these cable dynamics effects. In the past, efforts towards developing analytical models for cable-harnessed structures have been primarily focused on beam-like host structures. The presented paper is aimed to fill this gap by obtaining analytical solutions through an energy equivalent homogenization approach for cable harnessed plate-like structures and to ultimately help with understanding the dynamic effects of signal and power cables on two-dimensional plate-like structures. As a first step, systems of periodic geometries with parallel cable configurations are considered. The strain and kinetic energy expressions for the fundamental repeated elements are found using linear displacement fields and Green-Lagrange strain tensors. The governing partial differential equation (PDE) for the out-of-plane motion of the cable-harnessed system is then found using Hamilton's principle. Experimental modal testing is performed for the purpose of validations of the frequency response functions (FRFs) obtained from the model for the cable-harnessed plates under clamped-free-free-free boundary conditions. The results clearly show the dynamic effects of the cables which are also well-predicted by the model. Finally, Modal Assurance Criterion (MAC) analysis has been used for further validations of the mode shapes obtained from the model.

A Lumped Inertia Force Method for Vibration Problems

1966 ◽  
Vol 17 (2) ◽  
pp. 127-140 ◽  
Author(s):  
A. V. Krishna Murty
Keyword(s):  
Distribution Function ◽  
Natural Frequency ◽  
Linear Displacement ◽  
Mode Shapes ◽  
Fourth Power ◽  
Inertia Force ◽  
Lumped Mass ◽  
Displacement Distribution ◽  
Transverse Vibrations ◽  
Cantilever Shaft

SummaryA rational method of lumping inertia forces by considering the equilibrium of the vibrating element has been developed. This method requires the selection of a suitable displacement distribution function over each element. The closer it is to the true mode shape, the better the result.Considering a linear displacement distribution function over each element, the natural frequencies and mode shapes are obtained for transverse vibrations of a stretched string, torsional vibrations of a cantilever shaft (fixed at one end and free at the other) and transverse vibrations of a uniform cantilever beam. It is found that, even with a few elements, a reasonable accuracy can be obtained in the natural frequency, while the mode shapes are exact in the first two cases and almost exact in the third at the points considered.In Appendix A, it is shown that, for the torsional vibration of a uniform cantilever shaft and with a linear displacement function over each element, this method gives exact mode shapes at the points considered, while the natural frequency is always an upper bound and the error follows an inverse square law when the number of elements considered is large.In Appendix B, it is shown that a combination of this method with the conventional lumped mass method reduces the error in the natural frequency. The error follows an inverse fourth-power law when the number of elements considered is large and the mode shapes are exact at the points considered.This method can incorporate better displacement distribution functions, to obtain better results and convergence, and can easily be adapted to the buckling of columns, the vibration of beam columns and forced vibrations, as well as more complicated problems such as the vibration or buckling of plates and shells.

Modal Parameter Identification of Jacket-Type Platforms Using Vibration Testing Data

2012 ◽  
Vol 170-173 ◽  
pp. 2243-2247
Author(s):  
Yu Jing Chen ◽  
Min Zhang ◽  
Yuan Dong Meng ◽  
Qiang Zhao ◽  
Jie Wen Nie
Keyword(s):  
Natural Frequencies ◽  
Measured Data ◽  
Offshore Platform ◽  
Modal Testing ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Parameter ◽  
Modal Assurance Criterion ◽  
Modal Parameter Identification ◽  
Testing Data

How to estimate the modal parameters (including natural frequencies and mode shapes) of an offshore platform accurately is crucial for the health monitoring problems. The purpose of this paper is to identify the modal parameters of a physical jacket-type platform model from measured modal testing data using Prony’s method. In the modal testing, the identified false modes are unavoidable and bring much difficulty to determine the accurate modal parameters. To solve these problems, in this paper, the Modal Phase Collinearity (MPC) and Modal Assurance Criterion (MAC) are applied to distinguish the true and false modal. The measured data are extracted from a physical model of a realistic offshore platform. And the results demonstrate that the modal parameters of the first two modes of each direction can be accurately estimated by using the proposed method.

scholarly journals Comparison Between Calculated and Measured Free-Free Modes for a Flexible Rotor

1998 ◽  
Author(s):  
José A. Vázquez ◽  
Lloyd E. Barrett
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Modal Testing ◽  
Analytical Models ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Response Functions ◽  
Flexible Rotor ◽  
Reduced Order ◽  
Response Characteristics

Many industrial machines nowadays are sold based on analysis performed on mathematical models of the rotors, bearings, substructures, and other components. The validity of the analysts therefore depends on the accuracy of the models themselves. When the rotor is available, modal testing may be used to validate the model of the rotor by comparing the calculated and measured free-free natural frequencies and mode shapes. This work presents additional tools for the verification of analytical models against experimental data. These tools use models of the rotor constructed from the measured data and the analytical model. A comparison of the first six calculated and measured free-free natural frequencies and mode shapes for a multi-mass flexible rotor is presented. The natural frequencies compare within 1.8%. The calculated and measured mode shapes were used to construct independent reduced order models of the rotor. These models were used to perform forced response and stability analyses. Forced response functions are presented comparing the forced response characteristics obtained from the two models. This provides a comparison between the measured and calculated forced response functions for the same number of modes. For the stability analysis, identical bearing models were added to both reduced order models. The eigenvalues were calculated using both models for a range of bearing stiffness and damping coefficients and were plotted for comparison.

A Performance Study of Controlled Impact Timing on Harmonics Reduction in Operational Modal Testing

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Hong Cheet Lim ◽  
Zhi Chao Ong ◽  
Zubaidah Ismail ◽  
Shin Yee Khoo
Keyword(s):  
Modal Analysis ◽  
Modal Testing ◽  
Mode Shapes ◽  
Performance Study ◽  
Modal Assurance Criterion ◽  
Structural Dynamic ◽  
Impact Device ◽  
Load Component ◽  
Phase Angles ◽  
The Impact

As an alternative to operational modal analysis and classical experimental modal analysis (EMA), a novel method was introduced previously, namely impact-synchronous modal analysis (ISMA). The effectiveness ISMA on rotor and structural dynamic systems has been proven in previous literature. More recently, an automated impact device (AID) was introduced which utilized tachometer pulse as initiation signal and its effectiveness on ISMA was proven. An attempt to further enhance this device in term of equipment and cost is then proposed by replacing the tachometer with the in-use tri-axial accelerometer through utilizing the filtered response of cyclic load component as an initiation signal to control the impact device, which is also the primary aim for this study. Prior to modal testing, accuracy of this device is illustrated at desired phase angles of 0 deg, 90 deg, 180 deg, and 270 deg. Subsequently, frequency response function (FRF) estimations obtained for ISMA using enhanced AID has demonstrated the suppression capabilities of this device on disturbances, i.e., reduction of 93.58% at 30 Hz and 57.78% at 60 Hz, resulting in a high correlation for signature assurance criterion (SAC) and cross signature assurance criterion (CSAC). Modal parameters extracted from the EMA and ISMA using impact device are presented and compared, for the first three natural modes of the test rig. It is found that natural frequencies are deviating by less than 6%, whereas modal assurance criterion (MAC) values between the mode shapes of the two tests are found to be above 0.9.

Investigating the vibrational behaviour of a rotating two-blade propeller by using a self-tracking method

2018 ◽  
Vol 233 (3) ◽  
pp. 835-847 ◽  
Author(s):  
Mohammad-Reza Ashory ◽  
Farhad Talebi ◽  
Heydar R Ghadikolaei ◽  
Morad Karimpour
Keyword(s):  
Natural Frequency ◽  
Measurement Errors ◽  
Mode Shapes ◽  
Model Parameters ◽  
Test Results ◽  
Modal Assurance Criterion ◽  
Tracking Method ◽  
Strong Resemblance ◽  
Test Scenarios ◽  
Good Agreement

This study investigated the vibrational behaviour of a rotating two-blade propeller at different rotational speeds by using self-tracking laser Doppler vibrometry. Given that a self-tracking method necessitates the accurate adjustment of test setups to reduce measurement errors, a test table with sufficient rigidity was designed and built to enable the adjustment and repair of test components. The results of the self-tracking test on the rotating propeller indicated an increase in natural frequency and a decrease in the amplitude of normalized mode shapes as rotational speed increases. To assess the test results, a numerical model created in ABAQUS was used. The model parameters were tuned in such a way that the natural frequency and associated mode shapes were in good agreement with those derived using a hammer test on a stationary propeller. The mode shapes obtained from the hammer test and the numerical (ABAQUS) modelling were compared using the modal assurance criterion. The examination indicated a strong resemblance between the hammer test results and the numerical findings. Hence, the model can be employed to determine the other mechanical properties of two-blade propellers in test scenarios.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

Similitudes for vibration characteristic of composite laminated plates

2021 ◽  
pp. 107754632110377
Author(s):  
Fengxia He ◽  
Zhong Luo ◽  
Lei Li ◽  
Xiaoxia Zhang
Keyword(s):  
Natural Frequency ◽  
Prediction Accuracy ◽  
Laminated Plates ◽  
Frequency Mode ◽  
Mode Shapes ◽  
Vibration Characteristic ◽  
Modal Assurance Criterion ◽  
Full Size ◽  
Composite Laminated Plates ◽  
Scaled Models

Similitude laws can be used to extrapolate the vibration characteristic of a small, inexpensive, and easily tested model into structural behavior for the full-size prototype. In this article, a systematic similitude approach is proposed to predict the natural frequency, mode shape, and vibration response of composite laminated plates. The emphasis of this article is to predict the vibration characteristic of composite laminated plates in an effective and convenient way. Sensitivity analysis (SA) is introduced to improve the prediction accuracy of natural frequency. For distortion similarity, the prediction accuracy is improved close to 5%. Modal assurance criterion (MAC) measures the consistency of mode shapes of the full-size prototype and scaled models. The influence of stacking sequence on mode consistency is investigated. Similitude based on virtual mode and statistical energy (SVMSE) is proposed to extrapolate the transient response of the prototype to simulate the shock environment, such as satellite–rocket separation, etc. In conclusion, the prediction accuracy of natural frequency, mode consistency, and response coincidence are considered comprehensively to extrapolate the vibration characteristic of the full-size laminated plates.

Experimental Study of Blade Vibration in Centrifugal Compressors

2011 ◽  
Author(s):  
Andrew H. Lerche ◽  
J. Jeffrey Moore ◽  
Timothy C. Allison
Keyword(s):  
High Cycle Fatigue ◽  
Axial Flow ◽  
Modal Testing ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Centrifugal Compressors ◽  
Compressor Blades ◽  
Blade Vibration ◽  
Phase Cancellation ◽  
Blade Failure

Blade vibration in turbomachinery is a common problem that can lead to blade failure by high cycle fatigue. Although much research has been performed on axial flow turbomachinery, little has been published for radial flow machines such as centrifugal compressors and radial inflow turbines. This work develops a test rig that measures the resonant vibration of centrifugal compressor blades. The blade vibrations are caused by the wakes coming from the inlet guide vanes. These vibrations are measured using blade mounted strain gauges during a rotating test. The total damping of the blade response from the rotating test is compared to the damping from the modal testing performed on the impeller. The mode shapes of the response and possible effects of mistuning are also discussed. The results show that mistuning can affect the phase cancellation which one would expect to see on a system with perfect cyclic symmetry.

scholarly journals A Multiobjective Perspective to Optimal Sensor Placement by Using a Decomposition-Based Evolutionary Algorithm in Structural Health Monitoring

2020 ◽  
Vol 10 (21) ◽  
pp. 7710
Author(s):  
Tsung-Yueh Lin ◽  
Jin Tao ◽  
Hsin-Haou Huang
Keyword(s):  
Structural Health Monitoring ◽  
Evolutionary Algorithm ◽  
Health Monitoring ◽  
Sensor Placement ◽  
Frame Structure ◽  
Mode Shapes ◽  
Beam Model ◽  
Optimal Sensor Placement ◽  
Modal Assurance Criterion ◽  
Structural Health

The objective of optimal sensor placement in a dynamic system is to obtain a sensor layout that provides as much information as possible for structural health monitoring (SHM). Whereas most studies use only one modal assurance criterion for SHM, this work considers two additional metrics, signal redundancy and noise ratio, combining into three optimization objectives: Linear independence of mode shapes, dynamic information redundancy, and vibration response signal strength. A modified multiobjective evolutionary algorithm was combined with particle swarm optimization to explore the optimal solution sets. In the final determination, a multiobjective decision-making (MODM) strategy based on distance measurement was used to optimize the aforementioned objectives. We applied it to a reduced finite-element beam model of a reference building and compared it with other selection methods. The results indicated that MODM suitably balanced the objective functions and outperformed the compared methods. We further constructed a three-story frame structure for experimentally validating the effectiveness of the proposed algorithm. The results indicated that complete structural modal information can be effectively obtained by applying the MODM approach to identify sensor locations.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

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