Steady-State Responses in Systems of Nearly-Identical Torsional Vibration Absorbers

2003 ◽  
Vol 125 (1) ◽  
pp. 80-87 ◽  
Author(s):  
A. S. Alsuwaiyan ◽  
Steven W. Shaw
Keyword(s):  
Steady State ◽  
Torsional Vibration ◽  
Equations Of Motion ◽  
Vibration Absorbers ◽  
Fully Nonlinear Equations ◽  
State Response ◽  
Steady State Responses ◽  
Nonlinear Equations Of Motion ◽  
The Mathematical Model ◽  
State Responses

In this paper we consider the steady-state response of a rotor fitted with a system of nearly identical torsional vibration absorbers. The absorbers are of the centrifugal pendulum type, which provide an effective mean of attenuating torsional vibrations of the rotor at a given order. The model considered employs absorbers that are tuned close to the order of the excitation, with an intentional mistuning that is selected by design, and imperfections among the absorbers which arise from manufacturing, wear, and other effects. It is shown that these systems can experience localized responses in which the response amplitude of one or more absorbers can become relatively large as compared to the response of the corresponding system with identical absorbers. The results are based on an exact steady-state analysis of the mathematical model, and they show that the strength of the localization depends on the average level of absorber mistuning (a design parameter), the magnitude of the relative imperfections among the absorbers, and the absorber damping. It is found that the most desirable situation is one in which the relative imperfections are kept as small as possible, and that this becomes more crucial when the levels of mistuning and damping are very small. The results of the analysis are confirmed by simulations of the fully nonlinear equations of motion of the rotor/absorber system. It is concluded that the presence of localization should be accounted for in absorber designs, since its presence makes the absorbers less effective in terms of vibration reduction and, perhaps more significantly, it can drastically reduce their operating range, since such absorbers typically have limited rattle space.

Trigonometric Collocation for Computation of Steady State Responses of Cracked Structures

2012 ◽  
Author(s):  
Bakeer Bakeer ◽  
Oleg Shiryayev ◽  
Ammaar Tahir
Keyword(s):  
Steady State ◽  
Fatigue Cracks ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Vibration Period ◽  
State Response ◽  
Trigonometric Collocation ◽  
Steady State Responses ◽  
Cracked Structures ◽  
State Responses

Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkage

1994 ◽  
Vol 116 (1) ◽  
pp. 264-269 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield the linear and angular positions, velocities, and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transverse, and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

scholarly journals Limitations of Bifurcation Diagrams in Boost Converter Steady-State Response Identification

2017 ◽  
Vol 8 (2) ◽  
pp. 59-65
Author(s):  
Željko Stojanović ◽  
Denis Pelin
Keyword(s):  
Steady State ◽  
Initial Period ◽  
Boost Converter ◽  
Steady State Response ◽  
Bifurcation Diagrams ◽  
State Response ◽  
Mode Of Operation ◽  
Steady State Responses ◽  
State Responses ◽  
Conduction Mode

Steady-state responses of the boost converter operating in discontinuous conduction mode of operation are identified by using bifurcation diagrams as a typical simulation tool for identification of steady-state responses. The structure of simulated bifurcation diagrams is dependent on the initial period of sampling and the initial instant of sampling. The influence of these parameters on calculation of bifurcation diagrams was studied. Some possible issues, pitfalls and misinterpretations are commented as well as some recommendations about steady-state response identification are given

scholarly journals Effects of Stator Stiffness, Gap Size, Unbalance, and Shaft’s Asymmetry on the Steady-State Response and Stability Range of an Asymmetric Rotor with Rub-Impact

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang ◽  
Xiaolong Ye
Keyword(s):  
Steady State ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Impact Behavior ◽  
Gap Size ◽  
Steady State Response ◽  
Arc Length ◽  
State Response ◽  
Asymmetric Rotor ◽  
Nonlinear Equations Of Motion

The asymmetric rotor and the rub-impact behavior are important sources of instability and may cause severe vibrations. However, the dynamics of the rotor-bearing system simultaneously considering the two factors has not gained sufficient attention in available investigations. In this paper, the steady-state response and stability of an asymmetric rotor with rub-impact were evaluated. The asymmetric rotor was modeled by beam elements with asymmetric cross section, and the nonlinear equations of motion were established in the rotating frame. The multiharmonic balance (MHB) method was employed to obtain the linearized form of the nonlinear equations of motion. Either the asymmetry of rotor or rub-impact can result in instability and make the problem difficult to solve. Thus, the arc-length method was utilized to trace the branch of the solutions. In order to improve the calculation speed and accurately predict the solution, the alternating frequency/time domain (AFT) was adopted to calculate the iteration of the arc-length method. Based on the proposed method, the effects of stator stiffness, gap size, unbalance, and asymmetric in shaft on the steady-state response and stability were obtained.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkages

1992 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

Abstract This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield linear and angular positions, velocities and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transversal and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

scholarly journals Localization in Multiple Nearly-Identical Tuned Vibration Absorbers

2013 ◽  
Vol 2 (3) ◽  
pp. 157 ◽  
Author(s):  
Abdullah Saleh Alsuwaiyan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Torsional Vibration ◽  
Forced Vibration ◽  
Absolute Magnitude ◽  
Vibration Absorbers ◽  
Steady State Analysis ◽  
Tuned Vibration Absorbers ◽  
Translational Vibration ◽  
The Mathematical Model

The forced vibration of multiple nearly identical translational vibration absorbers is considered. Localization, where the amplitudes of vibration of a group of the absorbers can become relatively large as compared to those of the corresponding perfectly tuned system is investigated. In this work, imperfections amoung the absorbers are allowed and brought into the analysis through the stiffnesses of the absorbers' springs. Steady-state analysis of the mathematical model is used to obtain the results. Results, which focus on translational absorber systems, are found to be consistent with previous results obtained for torsional vibration absorbers. It is found that strengths of the localized responses depend on the levels of imperfections, the relative imperfections among absorbers, and the absorbers' damping. Localization is shown to exist in the undamped multiple nearly-identical vibration absorbers system, or more generally, in the system where the ratio of the level of absorbers' damping to the level of imperfections in the absorbers is small. It is also shown that localized responses can be effectively avoided by introducing some intentional mistuning in the absorbers' stiffnesses. This mistuning should be small in absolute magnitude in order not to reduce the absorbers' performance and should be large when compared to the absorbers' imperfections.

scholarly journals Σύγκριση των click Auditory Brainstem Responses (ABR) και των chirp Auditory Steady-State Responses (ASSR), ηλεκτροφυσιολογικών (αντικειμενικών) μεθόδων που χρησιμοποιούνται για τον έλεγχο και τη διάγνωση της παιδικής βαρηκοΐας

2021 ◽  
Author(s):  
Κωνσταντίνος Μουρτζούχος
Keyword(s):  
Steady State ◽  
Tone Burst ◽  
Auditory Brainstem ◽  
Auditory Brainstem Responses ◽  
State Response ◽  
Auditory Steady State Response ◽  
Brainstem Response ◽  
Steady State Responses ◽  
Auditory Steady State Responses ◽  
State Responses

Τα προκλητά δυναμικά κατέχουν σημαντική θέση στον προσδιορισμό των ουδών της ακοής σε παιδιά πολύ μικρά για να εξεταστούν με τις συμβατικές συμπεριφορικές μεθόδους και σε άλλους πληθυσμούς που παρουσιάζουν δυσκολίες κατά την εξέταση. Το ABR (Auditory Brainstem Response), μέθοδος που χρησιμοποιείται κατά τα τελευταία 50 χρόνια, έχει σήμερα ευρέως αναγνωριστεί ως η πιο αποτελεσματική τεχνική προκλητών δυναμικών και χρησιμοποιείται καθημερινά, με click και tone burst ως ερεθίσματα, για την εκτίμηση της ακουστικής ικανότητας σε βρέφη και παιδιά πολύ μικρά για άλλες εξεταστικές μεθόδους. Η καταγραφή του ABR, ωστόσο, υπόκειται σε περιορισμούς ως προς το ανώτερο επίπεδο έντασης χορήγησης του ερεθίσματος, όπως επίσης και εξαιτίας της υποκειμενικής μεθόδου ελέγχου για τον προσδιορισμό του ουδού, ενώ οι καταγραφές με tone burst ερεθίσματα είναι συχνά πιο απαιτητικές ως προς την ερμηνεία τους, λόγω του ότι οι κυματομορφές μπορεί να είναι λιγότερο χαρακτηριστικές. Το ASSR (Auditory Steady-State Response) αποτελεί μια πιο πρόσφατη εναλλακτική πρόταση έναντι των καθιερωμένων ABR τεχνικών καταγραφής. Σε αντίθεση με το παροδικού τύπου ερέθισμα click που χρησιμοποιείται στις ABR καταγραφές, το διαμορφωμένο συνεχούς τύπου ερέθισμα του ASSR εκλύει μια περιοδική ή “steady-state” κυματομορφή, της οποίας τα φασματικά χαρακτηριστικά (εύρος και φάση) αναλύονται στο frequency ή και στο time domain για τον προσδιορισμό της παρουσίας ή της απουσίας απάντησης. Το αυτόματο σύστημα ανίχνευσης της απάντησης που χρησιμοποιείται στην καταγραφή του ASSR εξαλείφει την ανάγκη για υποκειμενικό τρόπο ελέγχου των απαντήσεων. Ο τύπος του ASSR ερεθίσματος που χρησιμοποιήθηκε σε αυτήν την μελέτη ήταν το narrowband CE-chirp, ένα είδος chirp που εισήλθε σχετικά πολύ πρόσφατα στις συσκευές που διατίθενται στο εμπόριο. Σκοπός αυτής της μελέτης ήταν να συγκρίνει αυτές τις δύο ηλεκτροφυσιολογικές μεθόδους και τον βαθμό στον οποίο συσχετίζονται, σε ένα μεγάλο πληθυσμό παιδιών με διάφορου βαθμού νευροαισθητήρια βαρηκοΐα, που εξετάστηκαν με φαρμακευτικό ύπνο στο Ακοολογικό Κέντρο της Κλινικής μας κατά το διάστημα 2010-14. Εξετάστηκαν συνολικά 130 παιδιά, 90 άρρενα και 40 θήλεα (n = 260 αυτιά), ηλικίας 5 έως 79 μηνών (μέση ηλικία: 32.7 ± 14.0 μήνες), με μια ποικιλία προβλημάτων και διαταραχών. Η τελική στατιστική ανάλυση για σύγκριση των δύο μεθόδων περιέλαβε αφ’ ενός τις τιμές ουδών που αποκτήθηκαν από το click ABR και αφ’ ετέρου τους μέσους όρους των ουδών που αποκτήθηκαν από το chirp ASSR στις συχνότητες 1, 2 και 4 kHz και 2 και 4 kHz. Τα αποτελέσματα αυτής της μελέτης ανέδειξαν ισχυρές συσχετίσεις μεταξύ των click ABR ουδών και των μέσων όρων των chirp ASSR ουδών στα 1000, 2000 και 4000 Hz (rs = .826, p < .001) και στα 2000 και 4000 Hz (rs = .824, p < .001) και συμφωνούν γενικά με τα αποτελέσματα παρόμοιων μελετών της διεθνούς βιβλιογραφίας. Συμπερασματικά φαίνεται ότι το ASSR είναι αναγκαίο για την ακριβή ποσοτικοποίηση της υπολειπόμενης ακοής στην ζώνη της μεγάλου προς πολύ μεγάλου βαθμού βαρηκοΐας, σε περιοχές εντάσεων άνω των ορίων των περισσοτέρων ABR συσκευών. Η «ακοολογική πληροφορία» που αποκτάται με το ASSR τεστ, ειδικά στην ανωτέρω περιοχή, είναι πολύτιμη στην λήψη αποφάσεων για περαιτέρω παρέμβαση σε παιδιά με νευροαισθητήρια βαρηκοΐα (ενίσχυση, κοχλιακή εμφύτευση), ιδίως για τα παιδιά εκείνα που δεν μπορούν να μετρηθούν με συμπεριφορικές μεθόδους. Τα αποτελέσματα αυτά ενισχύουν την χρήση του ASSR ως εναλλακτικού τεστ σε σχέση με το ABR στην εκτίμηση και αντιμετώπιση της παιδικής βαρηκοΐας.

NONLINEAR VIBRATION OF A CANTILEVER WITH A DERJAGUIN–MÜLLER–TOPOROV CONTACT END

2008 ◽  
Vol 08 (01) ◽  
pp. 25-40 ◽  
Author(s):  
Q.-Q. HU ◽  
C. W. LIM ◽  
L.-Q. CHEN
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Excitation Amplitude ◽  
Response Curves ◽  
State Response ◽  
Linearized Stability ◽  
Steady State Responses ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
State Responses

In this paper, the principal resonance is investigated for a cantilever with a contact end. The cantilever is modeled as an Euler–Bernoulli beam, and the contact is modeled by the Derjaguin–Müller–Toporov theory. The problem is formulated as a linear nonautonomous partial-differential equation with a nonlinear autonomous boundary condition. The method of multiple scales is applied to determine the steady-state response. The equation of response curves is derived from the solvability condition of eliminating secular terms. The stability of steady-state responses is analyzed by using the Lyapunov-linearized stability theory. Numerical examples are presented to highlight the effects of the excitation amplitude, the damping coefficient, and the coefficients related to the contact.

Steady-State Non-Synchronous and Localized Responses of Tuned Pendulum Vibration Absorbers

1999 ◽  
Author(s):  
Abdallah S. Al-suwaiyan ◽  
Steven W. Shaw
Keyword(s):  
Steady State ◽  
Vibration Absorber ◽  
Circular Path ◽  
Vibration Absorbers ◽  
Centrifugal Pendulum Vibration Absorber ◽  
Existence And Stability ◽  
Steady State Responses ◽  
State Responses ◽  
Small Torque ◽  
Good Agreement

Abstract Previous analytical studies of Centrifugal Pendulum Vibration Absorber (CPVA) systems have focused on the dynamics of either a single absorber mass or multiple absorber masses moving along very special paths. In this paper, an approach is taken that allows one to investigate the dynamics of multi-absorber systems that have quite general paths for the absorber masses, including those used in practice. Of particular interest here are the existence and stability of certain classes of non-unison responses, including those in which the amplitude of a sub-group of absorbers is larger than the expected unison response. It is shown via the method of averaging that these steady state responses may exist and be stable for certain types of paths, including the commonly-used mistuned circular path. Furthermore, it is shown that these responses can co-exist with a stable unison response, even for very small torque levels. The analytical results are compared with numerical simulations and good agreement is found.

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