Nonlinear Vibrations of Fractionally Damped Systems

This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing\u27s equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior

Frequency Driven Phasic Shifting and Elastic-Hysteretic Partitioning Properties of Fractional Mechanical System Representation Schemes

Based on the Louiville–Riemann fractional formulation of lumped hysteretic mechanical system simulations, asymptotic-type relationships are derived. These are employed to determine how such operators, which act as viscoelastic elements, partition system energy into conservative and nonconservative components. Special emphasis is given to: (a) determine how operator order serves to weigh such a splitting, (b) determine how partitioning affects system phasing and amplitude response, and (c) to establish how conservative and nonconservative effects modulate during a given system cycle. The generality of the undertaken approach is such that multi-element fractional Kelvin Voigt formulations subject to spectrally rich inputs can be handled, i.e., the multi-modal splitting of energies. As a result of the insights derived, improved frequency dependent simulations of system amplitude, phasing and energetics will be possible

Diophantinized Fractional Representations for Nonlinear Elastomeric Media

This paper explores the use of diophantinized fractional fits for the nonlinear constitutive representation of elastomeric media. These are caste in terms of either the principal stretches or the strain invariants. Both polynomial and rational forms are considered. To construct the requisite complete and physically admissible basis space, the diophantinized set of fractional powers is bound by the curvature properties of the experimental data set. This set is then employed in conjunction with a remezed least square scheme to obtain an optimal fit. To verify the scheme a sample application case is presented

Diophantine Type Fractional Derivative Representation of Structural Hysteresis, Part I: Formulation

Based on a diophantine representation of the operational powers, a fractional derivative modelling scheme is developed to simulate frequency dependent structural damping. The diophantine set of powers is established by employing the curvature properties of the defining empirical data set. These together with a remezed least square scheme are employed to construct a Chebyschev like optimal differintegro simulation. Based on the use of the rational form resulting from the diophantine representation, a composition rule is introduced to reduce the differintegro simulation to first order form. The associated eigenvalue/vector properties are then explored. To verify the robustness-stability accuracy of the overall modelling procedure, correlation studies are also presented. Part I of this series focuses on the diophantine representation, its use in formulating a numerically more workable first order form as well as formal representations of its transient and steady state solutions. This will include investigations of the asymptotic properties of the various formulations. Part II will introduce the model fitting scheme along with a look at eigen properties and fitting effectiveness

Diophantine Type Fractional Derivative Representation of Structural Hysteresis, Part II: Fitting, Computational Mechanics

Part I of this series introduced the diophantinized fractional model and the decompositional formulation. The various important properties of fractional continuum formulation and its decomposed version were developed. In Part II the dynamic properties of the diophantine representation are investigated. The model fitting scheme will be developed to handle an arbitrary frequency dependent structural hysteriesis. This is followed up with the results of benchmark studies which demonstrate the effectiveness of fitting

The Dynamics of Rotor with Rubbing

This paper presents the description of some phenomena associated with dynamic behavior of rotors interacting with stationary components. Numerical simulations show rotor vibration spectrum rich in subharmonic, quasi-periodic, and chaotic vibrations. The nonlinear calculation techniques are applied to demonstrate the changes of the vibration patterns for different operating conditions. Some conclusions are discussed with regard to unique characteristics of rub-induced rotor response, initial conditions, as well as appropriate ranges of system parameters. Of special interest are the changes in the apparent nonlinearity of the system dynamics as rubs are induced at different rotor speeds. In particular, starting with 2nd order sub/superharmonics, which are symptomatic of quadratic nonlinearity, progressively higher order polynomial behavior is excited, i.e., cubic, giving rise to 3rd order sub/superharmonics. As the speed is transitioned between such apparent nonlinearities, chaotic like behavior is induced because of the lack of whole or rational tone tuning between the apparent system frequency and the external source noise. The cause of such behavior will be discussed in detail along with the results of several parametric studies

The Dynamics of Rotor with Rubbing

This paper presents the description of some phenomena associated with dynamic behavior of rotors interacting with stationary components. Numerical simulations show rotor vibration spectrum rich in subharmonic, quasi-periodic, and chaotic vibrations. The nonlinear calculation techniques are applied to demonstrate the changes of the vibration patterns for different operating conditions. Some conclusions are discussed with regard to unique characteristics of rub-induced rotor response, initial conditions, as well as appropriate ranges of system parameters. Of special interest are the changes in the apparent nonlinearity of the system dynamics as rubs are induced at different rotor speeds. In particular, starting with 2nd order sub/superharmonics, which are symptomatic of quadratic nonlinearity, progressively higher order polynomial behavior is excited, i.e., cubic, giving rise to 3rd order sub/superharmonics. As the speed is transitioned between such apparent nonlinearities, chaotic like behavior is induced because of the lack of whole or rational tone tuning between the apparent system frequency and the external source noise. The cause of such behavior will be discussed in detail along with the results of several parametric studies

Panel: Looking Backwards and Forwards

Ten years ago, at 90 nanometers, EDA was challenged and deemed inadequate in dealing with increasing complexity, power consumption, and sub-wavelength lithography, thus harming the progress of mobile phones. Today, at 10 nanometers, integration capacity has increased by two orders of magnitude, power consumption has been successfully "tamed", and 193 nanometer immersion lithography is still relied upon. Also thanks to EDA, tools, methodologies, and flows that were originally devised for design enablement for the emerging technology nodes, have been successfully redeployed at the established technology nodes, where they represent a critical design differentiation factor. However, the battleground is changing again: after the billions of phones, trillions of "things" lie ahead. Moving forward, emerging and established technology nodes, digital and analog, hardware and software will be equally critical. What is EDA doing and, more important, what should EDA do - and is not doing - in order for the next decade to be as great as the past one? This panel session, moderated by EPFL Professor Giovanni De Micheli, gathers academia, semiconductor, and EDA industry to discuss the challenges and requirements of the new era

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS

Diophantine Type Fractional Derivative Representation of Structural Hysteresis, Part II: Fitting, Computational Mechanics

Part I of this series introduced the diophantinized fractional model and the decompositional formulation. The various important properties of fractional continuum formulation and its decomposed version were developed. In Part II the dynamic properties of the diophantine representation are investigated. The model fitting scheme will be developed to handle an arbitrary frequency dependent structural hysteriesis. This is followed up with the results of benchmark studies which demonstrate the effectiveness of fitting