scholarly journals Analysis and optimization of the effects of frictional and viscous dampers on dynamical systems

2019 ◽  
Vol 38 (2) ◽  
pp. 255-269
Author(s):  
Marlon Wesley Machado Cunico ◽  
Jennifer Desiree Medeiros Cavalheiro
Keyword(s):  
Frequency Domain ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Mechanical Systems ◽  
Static Friction ◽  
Coulomb Force ◽  
Dynamic Responses ◽  
Dynamical Response ◽  
Viscous Dampers ◽  
Three Degrees Of Freedom

Over the last several years, the complexity of products has been increasing in parallel to the product cost thus becoming one of main focal points for development. On the other hand, although several applications struggle to fix vibration problems, highlighting the importance of damper design, literature that compares the benefits and disadvantages between of dry-frictional, viscous, and Coulomb–viscous dampers is still rare. Owing to this, the main goal of this work is to present a study that compares the dynamical response of mechanical systems against several damper types. For this research, we analyzed the effects of three types of damper (viscous, Coulomb–viscous, and dry-frictional dampers) on two mechanical systems. The first system consists of a mass-spring-damper with one degree of freedom, while the second system is a rotational machine with three degrees of freedom. The sensibility analyses of each damper were also studied, where the viscosity, Coulomb force, static friction, and Stribeck decay were the variables. In this work, mechanical systems were studied in a forced vibration condition and analyzed in the time and frequency domain in addition to identifying the main transfer functions in the frequency domain. In this analysis, the displacement, receptance, and force reaction were considered to be the study responses. After analyzing the main effect of damper coefficients on the general dynamic responses, we performed an optimization study in order to evidence the optimal configurations of either majorly viscous or frictional damper. Lastly, we analyzed the main behavior of this optimized damper on three-degrees-of-freedom rotational dynamic system.

An Extension of Rayleigh's Principle

1994 ◽  
Vol 22 (2) ◽  
pp. 83-90
Author(s):  
Alfonso Díaz-Jiménez ◽  
Gentil A. Estévez-Bretón
Keyword(s):  
Present Article ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Natural Generalization ◽  
Vibrational Frequencies ◽  
Exact Results ◽  
Two Degrees Of Freedom ◽  
Elegant Method ◽  
Three Degrees Of Freedom

Steidel's extension of Rayleigh's method for calculating the natural vibrational frequencies of mechanical systems with two degrees of freedom provides an elegant method to obtain exact results. In the present article this approach, which perhaps has not been exploited as much as it could be, is first reviewed and then several examples of the procedure are given. An extension of the method to three degrees of freedom is presented, and a natural generalization of Rayleigh's principle is suggested.

scholarly journals A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems

2016 ◽  
Vol 63 (2) ◽  
pp. 297-314 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco I. Leine
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Harmonic Balance ◽  
Degrees Of Freedom ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Constrained Mechanical Systems ◽  
Nonlinear Force

Abstract In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

scholarly journals Active Disturbance Rejection for a Three Degrees of Freedom Gyroscope

2018 ◽  
Vol 51 (13) ◽  
pp. 372-377 ◽  
Author(s):  
Juan E. Andrade García ◽  
Alejandra Ferreira de Loza ◽  
Luis T. Aguilar ◽  
Ramón I. Verdés
Keyword(s):  
Disturbance Rejection ◽  
Degrees Of Freedom ◽  
Active Disturbance Rejection ◽  
Three Degrees Of Freedom

scholarly journals Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

2021 ◽  
pp. 014233122110313
Author(s):  
Afef Hfaiedh ◽  
Ahmed Chemori ◽  
Afef Abdelkrim
Keyword(s):  
Real Time ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Class I ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Control Scheme ◽  
And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

scholarly journals Cyclic Deformation of Microcantilevers Using In-Situ Micromanipulation

2021 ◽  
Author(s):  
A. H. S. Iyer ◽  
M. H. Colliander
Keyword(s):  
Degrees Of Freedom ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Structural Components ◽  
Cyclic Testing ◽  
Phase Boundaries ◽  
Bulk Specimen ◽  
Arbitrary Position ◽  
Three Degrees Of Freedom

Abstract Background The trend in miniaturisation of structural components and continuous development of more advanced crystal plasticity models point towards the need for understanding cyclic properties of engineering materials at the microscale. Though the technology of focused ion beam milling enables the preparation of micron-sized samples for mechanical testing using nanoindenters, much of the focus has been on monotonic testing since the limited 1D motion of nanoindenters imposes restrictions on both sample preparation and cyclic testing. Objective/Methods In this work, we present an approach for cyclic microcantilever bending using a micromanipulator setup having three degrees of freedom, thereby offering more flexibility. Results The method has been demonstrated and validated by cyclic bending of Alloy 718plus microcantilevers prepared on a bulk specimen. The experiments reveal that this method is reliable and produces results that are comparable to a nanoindenter setup. Conclusions Due to the flexibility of the method, it offers straightforward testing of cantilevers manufactured at arbitrary position on bulk samples with fully reversed plastic deformation. Specific microstructural features, e.g., selected orientations, grain boundaries, phase boundaries etc., can therefore be easily targeted.

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