Unstable Branch Research Articles

Influence of Fiber Angle on the Steady State Periodic Response of Annular Sectorial Plates

Structural elements in the form of annular sectorial plates are widely used in aeronautical, biomedical, and marine engineering. When these components are exposed to dynamic load, large-amplitude vibrations occur. The vibration response analysis based on the linear strain-displacement relation typically yields a conservative estimate and can be used as a first approximation to the actual solution for thin structural elements. As a result, geometric nonlinearity must be incorporated for the efficient and fail-proof design of such elements. This paper shows non-linear and linear steady-state forced vibration responses of the annular sectorial plates. The governing equations of motion have been solved in the time domain by using a modified shooting method and an arc-length/pseudo-arc length continuation technique at the bifurcation point to obtain the complete response curve comprised of stable and unstable branches. This work investigates the effect of fibre angle on the non-linear steady-state forced vibration response of annular sectorial plates. The strain/stress fluctuation throughout the thickness of the laminated annular sectorial plate is determined to explain why hardening nonlinearity has increased. The cyclic fluctuation of the non-linear steady-state normal stress during a time period at the centre of the top and bottom surface is also provided in relation to the forcing frequency ratio of peak amplitude in the non-linear response. Due to the change in restoring forces, the frequency spectra reveal much increased harmonic involvement along with the fundamental harmonic for all fibre angles.

Shear banding predictions for wormlike micellar systems under a contraction–expansion complex flow

This study focuses on computational modeling of shear-banded wormlike micellar solutions (WLM) in a complex planar Couette flow, driven by a moving top plate over a rounded-corner 4:1:4 obstruction. The BMP+_τp model is used, which is constructed within an Oldroyd-B-like form, coupled with a thixotropic fluidity-based structure equation. Solute energy dissipation drives fluid–structure adjustment in a construction–destruction dynamics affected by viscoelasticity. This model reproduces conventional WLM features, such as shear thinning, extensional hardening/softening, viscoelasticity, apparent yield stress, and shear banding, with a bounded extensional viscosity and an N1Shear upturn at high deformation rates. The BMP+_τp characterization for shear banding is based on extremely low solvent fractions and appropriate shear-banding intensity parameters. Flow structure is analyzed through velocity, stress, and fluidity, whereupon banded and non-banded response is contrasted at appropriately selected flow rates. Solutions are obtained with our hybrid fe-fv algorithm, capturing essential shear-banded flow features reported experimentally. For a fluid exhibiting banding, banded solutions are generated at a flow rate within the flow curve unstable branch. In the fully developed simple shear flow regions, a split velocity profile is observed, with different viscosity bands at equal stress levels, enhanced with a shock-capture procedure. Non-banded solutions are derived for the lowest and highest flow rates sampled, located in the stable branches. Within the constriction zone, banded profiles are lost due to the mixed non-homogeneous deformation. Shear-banding fluids display less intense viscosity/stress features, correlated with their relatively stronger shear thinning response. The constriction resistance provokes a pressure-level adjustment, leading to fully developed Couette-like constant values upstream–downstream.

Nonlinear analysis of the semi-active particle damping vibration isolation system based on fractional-order theory

PurposeThe purpose of this study is to provide some references about applying the semi-active particle damper to enhance the stability of the pipe structure.Design/methodology/approachThis paper establishes the dynamical models of semi-active particle damper based on traditional dynamical theory and fractional-order theory, respectively. The semi-active particle damping vibration isolation system applied in a pipe structure is proposed, and its analytical solution compared with G-L numerical solution is solved by the averaging method. The quantitative relationships of fractional-order parameters (a and kp) are confirmed and their influences on the amplitude-frequency response of the vibration isolation system are analyzed. A fixed point can be obtained from the amplitude-frequency response curve, and the optimal parameter used for improving the vibration reduction effect of semi-active particle damper can be calculated based on this point. The nonlinear phenomenon caused by nonlinear oscillators is also investigated.FindingsThe results show that the nonlinear stiffness parameter p will cause the jump phenomenon while p is close to 87; with the variation of nonlinear damping parameter μ, the pitchfork bifurcation phenomenon will occur with an unstable branch after the transient response; with the change of fractional-order coefficient kp, a segmented bifurcation phenomenon will happen, where an interval that kp between 18.5 and 21.5 has no bifurcation phenomenon.Originality/valueThis study establishes a mathematical model of the typical semi-active particle damping vibration isolation system according to fractional-order theory and researches its nonlinear characteristics.

Nonlinear optimal perturbations and formation mechanism of localized wave packet in channel flow

The subcritical transition in a two-dimensional channel flow is characterized by the emergence of localized wave packet (LWP). In this paper, the nonlinear nonmodal optimization method is used, and when the target time is long enough the minimal seed, the minimal-energy perturbation triggering the transition is found to be the localized wave packet tilted upstream with energy scaling as Re−3.8 for Re>2500. The formation of LWP from a minimal seed includes three stages. First, the disturbance kinetic energy of the minimal seed increases to a local maximum through a transient growth governed by the Orr mechanism, and second, large scale vortex structures are generated due to the nonlinear forcing mainly contributed by the wave components and causes a streamwise symmetry breaking, i.e., a long but weak upstream tail and a strong downstream front are formed. As a result, the perturbation structure approaches the unstable lower branch solution and is attracted and captured at the last stage by the stable upper branch solution of LWP in the phase space.

Subharmonic locking and frequency combs in frequency-swept semiconductor lasers.

We analyze a delay differential equationmodel for a swept semiconductor laser and demonstrate existence of various periodic solutions that are subharmonically locked to the sweep rate. These solutions provide optical frequency combs in spectral domain. We investigate the problem numerically and show that, due to the translational symmetry of the model, there exists a hysteresis loop formed by branches of steady states solutions, bridges of periodic solutions connecting stable and unstable steady state branches, and isolated branches of limit cycles. We discuss the role of bifurcation points and limit cycles embedded into the loop in the formation of the subharmonic dynamics.

Topological natures of the Gauss-Bonnet black hole in AdS space

In the recent proposal [S. W. Wei et al., Black Hole Solutions as Topological Thermodynamic Defects, Phys. Rev. Lett. 129, 191101 (2022).], the black holes were viewed as topological thermodynamic defects by using the generalized off shell free energy. In this paper, we follow such proposal to study the local and global topological natures of the Gauss-Bonnet black holes in anti--de Sitter (AdS) space. The local topological natures are reflected by the winding numbers, where the positive and negative winding numbers correspond to the stable and unstable black hole branches. The global topological natures are reflected by the topological numbers, which are defined as the sum of the winding numbers for all black hole branches and can be used to classify the black holes into different classes. When the charge is present, we find that the topological number is independent on the values of the parameters, and the charged Gauss-Bonnet AdS black holes can be divided into the same class of the Reissner-Nordstr\"om anti-de Sitter black hole black holes with the same topological number 1. However, when the charge is absent, we find that the topological number has certain dimensional dependence. This is different from the previous studies, where the topological number is found to be a universal number independent of the black hole parameters. Furthermore, the asymptotic behaviors of curve $\ensuremath{\tau}({r}_{h})$ in small and large radii limit can be a simple criterion to distinguish the different topological number. We find a new asymptotic behavior as $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}0)=0$ and $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}\ensuremath{\infty})=0$ in the black hole system, which shows topological equivalency with the asymptotic behaviors $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}0)=\ensuremath{\infty}$ and $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}\ensuremath{\infty})=\ensuremath{\infty}$. We also give an intuitional proof of why there are only three topological classes in the black hole system under the condition $({\ensuremath{\partial}}_{{r}_{h}}S{)}_{P}>0$.

Model updating of dynamic structures with strong nonlinearities using fixed frequency continuation tests

Model updating using multivalued responses is an important approach to construct strongly nonlinear models. During updating, swept frequency tests are usually used to measure the multivalued responses, but the measured responses only contain the stable branches. Accordingly, updating mainly uses these stable responses for the nonlinear model construction. Unstable responses are rarely tested or participate in the updating process, which may lead to errors in the constructed model with strong nonlinearities. Recently, fixed frequency tests using a continuation scheme have been used to measure fully multivalued responses, including both the stable and unstable branches, for structures with the strong nonlinearity. However, the measured responses were then transformed to equivalent swept frequency tests for the existing updating schemes, where this transformation may induce errors in the updating process. In this paper, a novel method for strong nonlinear model updating using the results of the fixed frequency test is proposed. Such updating is based on the directly measured data of the fixed frequency tests and can handle both the stable and unstable responses. Fixed frequency continuation using the Multi-Harmonic Balance Method (MHBM) is developed to predict the multivalued responses and their sensitivities. The multivalued responses of the prediction and measurement are directly matched in sensitivity-based updating. The proposed method is numerically verified on a 2 DOF nonlinear model. Using the proposed method, the nonlinear model is updated from linear to strongly nonlinear and the updated parameters all converge to the simulated values after 7 iterations. The proposed method is then experimentally validated on a 3 DOF nonlinear system with a non-smooth nonlinearity. A nonlinear model with a 7th order polynomial stiffness represents the equivalent system and is directly updated based on the fixed frequency test results. The updated responses are generally a good fit to the tested responses. Compared with updating using only the stable responses, the proposed updating method achieves higher precision and its updated responses are closer to the tested responses. These results show the validity and superiority of the proposed method.

Multiple solutions for non-linear radiative mixed convective hybrid nanofluid flow over an exponentially shrinking surface

Hybrid nanofluids have gained too much attention due to their enhanced thermophysical properties and practical applications. In comparison to conventional nanofluids, their capacity to enhance heat transport is impressive. The simultaneous numerical calculations of hybrid and mono nanofluids across an exponentially shrinking surface in a porous medium are taken into consideration here. The analysis of the thermal energy distribution is carried out by using the convective boundary conditions. Shrinking, permeability, and magnetohydrodynamic controlled the motion of the flow. The objective of this research is to conduct stability analysis and identify the existence of dual solutions in the presence of heat source/sink and nonlinear Roseland thermal radiation. The technique, bvp4c, a collocation method is used to achieve numerical results. It is noted that the energy transport is enhanced immensely due to the presence of a mixture of nanoparticles (hybrid) in comparison to mono nanofluids. The stability analysis shows that the solutions for the upper branch were stable, while the solutions for the lower branch were unstable. Moreover, shrinking parameter contributes significantly to exhibit the dual nature of the solutions. Due to the increment in the heat generation/absorption and temperature ratio, the kinetic energy is inclined, which causes the temperature distribution to rise for both branches. For stable branches, an increase in wall stress values is evident as a result of permeability and stretching of sheet, whereas unstable branches show the opposite trend.

Dynamical evolution of U(1) gauged Q -balls in axisymmetry

We study the dynamics of $U(1)$ gauged Q-balls using fully non-linear numerical evolutions in axisymmetry. Focusing on two models with logarithmic and polynomial scalar field potentials, we numerically evolve perturbed gauged Q-ball configurations in order to assess their stability and determine the fate of unstable configurations. Our simulations suggest that there exist both stable and unstable branches of solutions with respect to axisymmetric perturbations. For solutions belonging to the stable branch, the gauged Q-balls respond to the perturbations by oscillating continuously or weakly radiating before returning to the initial configuration. For the unstable branch, the solutions are eventually destroyed and can evolve in several ways, such as dispersal of the fields to infinity or fragmentation into smaller gauged Q-balls. In some cases, we observe the formation of ring-like structures which we call "gauged Q-rings". We also investigate the stability of gauged Q-balls when the gauge coupling is small, finding that the behaviour of these configurations closely resembles that of ordinary (non-gauged) Q-balls.

Structural and dynamical phase transitions of NaNbO3 from first-principles calculations

The crystal structures and phase transitions of ${\mathrm{NaNbO}}_{3}$ are analyzed with density fonctional theory through generalized gradient approximation-PBEsol (GGA-PBEsol) and local density approximations (LDA). The phonon dispersion curves from the high-symmetry cubic perovskite phase are reported to have many unstable branches, predisposing to several combinations of phase transitions to various distorted structures. The coupling between the modes and the strain relaxation play a key role in the condensation of the ground state of sodium niobate. The instabilities at $R$ and $M$ points of the first Brillouin zone and along the line $T$ (connecting the $M$ and $R$ points) are very important for stabilizing the low-energy phases. Within the GGA-PBEsol approximation, the ground state is rhombohedral ferroelectric/antiferrodistortive (FE/AFD) $R3c$, while in LDA it is rather the orthorhombic FE/AFD $Pmc{2}_{1}$ structure that stabilizes the lowest energy in this compound. In both calculations, there is only a small energy difference between the three lowest-energy phases $Pmc{2}_{1}$ (FE/AFD[110]), $\mathit{Pbcm}$ (antiferroelectric/AFD), and $R3c$ (FE/AFD[111]), which is a key characteristic of antiferroelectricity. The GGA-PBEsol approach provides more sensible results than the LDA approximation.

Dual solutions of radiative Ag-MoS_2/water hybrid nanofluid flow with variable viscosity and variable thermal conductivity along an exponentially shrinking permeable Riga surface: Stability and entropy generation analysis

ABSTRACT In this analysis, the Silver-Molybdenum disulfide ()/water hybrid nanofluid flow past a permeable exponentially shrinking Riga surface with thermal radiant energy is considered. The novelty of this work is to find out the effects of variable viscosity, variable thermal conductivity with hybrid nanofluid’s slip velocity, and convective thermal boundary conditions over a shrinking Riga surface on velocity, temperature, skin-friction coefficient, Nusselt number, and entropy generation. The MATLAB programming platform with a fourth-order method to solve boundary value problem (bvp4c) was employed to get a good account of all pertinent flow parameters before solving the controlling partial differential equations numerically. Here of Silver () and of Molybdenum disulfide () nanoparticles in the hybrid model are considered in the base fluid water. The basic achievement of this analysis is to explore the Nusselt number, skin friction coefficient along with entropy formation, and Bejan number. The irreversibility factor is calculated using the thermodynamics second law. The findings also point to the presence of dual-nature solutions in the shrinking sheet region for a given value of a high mass suction parameter, with a stable upper solution branch and unstable lower solution branch. Two solutions are found for the limited range of shrinking parameter when and the solutions terminate at in the shrinking region. Additionally, the first solution generates a positive minimum eigenvalue (), whereas the second solution generates a negative eigenvalue (), indicating the solution’s stability. Nusselt number is enhanced for variable viscosity parameter but diminished by variable thermal conductivity parameter for the stable solution. The entropy generation and the Bejan number both increase significantly with the increment of the thermal radiant-energy parameter, Biot number, and Eckert number. These results are crucial in the long term because they allow us to optimize heat transmission for cooling and heating applications. Hence, this investigation is incredibly significant in the present era, particularly in the automotive industry, home industry, paper plastics, ceramics, food packaging, food colorants, cancer treatment, cosmetics, pharmaceuticals, fabrics, paints, and soaps as well.

Mott Quantum Critical Points at Finite Doping.

We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded" so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin-the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling-is much more general. A strong analogy with cuprate superconductors is traced.

Stabilizing a strongly nonlinear structure through shaker dynamics in fixed frequency voltage control tests

Bifurcations are commonly encountered during force controlled swept and stepped sine testing of nonlinear structures, which generally leads to the so-called jump-down or jump-up phenomena between stable solutions. There are various experimental closed-loop control algorithms, such as control-based continuation and phase-locked loop, to stabilize dynamical systems through these bifurcations, but they generally rely on specialized control algorithms that are not readily available with many commercial data acquisition software packages. A recent method was developed to experimentally apply sequential continuation using the shaker voltage that can be readily deployed using commercially available software. By utilizing the stabilizing effects of electrodynamic shakers and the force dropout phenomena in fixed frequency voltage control sine tests, this approach has been demonstrated to stabilize the unstable branch of a nonlinear system with three branches, allowing for three multivalued solutions to be identified within a specific frequency bandwidth near resonance. Recent testing on a strongly nonlinear system with vibro-impact nonlinearity has revealed jumping behavior when performing sequential continuation along the voltage parameter, like the jump phenomena seen during more traditional force controlled swept and stepped sine testing. This paper investigates the stabilizing effects of an electrodynamic shaker on strongly nonlinear structures in fixed frequency voltage control tests using both numerical and experimental methods. The harmonic balance method is applied to the coupled shaker-structure system with an electromechanical model to simulate the fixed voltage control tests and predict the stabilization for different parameters of the model. The simulated results are leveraged to inform the design of a set of experiments to demonstrate the stabilization characteristics on a fixture-pylon assembly with a vibro-impact nonlinearity. Through numerical simulation and experimental testing on two different strongly nonlinear systems, the various parameters that influence the stability of the coupled shaker-structure are revealed to better understand the performance of fixed frequency voltage control tests.

New detection systems for an enhanced sensitivity in key stellar (n,γ) measurements

Neutron capture cross-section measurements are fundamental in the study of astrophysical phenomena, such as the slow neutron capture (s-) process of nucleosynthesis operating in red-giant and massive stars. However, neutron capture measurements via the time-of-flight (TOF) technique on key s-process nuclei are often challenging. Difficulties arise from the limited mass (∼mg) available and the high sample-related background in the case of the unstable s-process branching points. Measurements on neutron magic nuclei, that act as s-process bottlenecks, are affected by low (n,γ) cross sections and a dominant neutron scattering background. Overcoming these experimental challenges requires the combination of facilities with high instantaneous flux, such as n_TOFEAR2, with detection systems with an enhanced detection sensitivity and high counting rate capabilities. This contribution reviews some of the latest detector developments in detection systems for (n,γ) measurements at n_TOF, such as i-TED, an innovative detection system which exploits the Compton imaging technique to reduce the dominant neutron scattering background and s-TED, a highly segmented total energy detector intended for high flux facilities. The discussion will be illustrated with results of the first measurement of key the s-process branching-point reaction 79Se(n,γ).

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.

Effect of Membrane Load on the Stability of an Electrostatically Actuated Initially Curved Circular Micro Plate

Abstract The effects of membrane load on the axisymmetric bistable behavior of circular curved micro plates are studied via an axisymmetric reduced order (RO) model, incorporating radial prestress. The model is based on Kirchhoff’s hypothesis and Föppl-von-Kármán’s kinematics. The model is first validated for a “mechanical” (displacement-independent) load, against an RO model with 20 degrees-of-freedom (DOF), a finite differences (FD) solution, and finally, a finite elements (FE) model, serving as the reference. All solutions implement the “Riks” continuation method to track unstable branches, which can swerve in a complex form due to the presence of higher buckling modes. A convergence study is carried out for the snap-through location and load, as well as for the critical elevation and prestress required for bistability. Based on the validated results of the mechanical analysis, the reliability of the model for predicting the effect of prestress on the plate behavior under nonlinear (displacement-dependent) electrostatic load is then investigated while using FD as the reference. The study furnishes an expended RO model for curved plates, which includes the effect of prestress. The resulting model can further be used to estimate the value of residual membrane load present in electrostatically actuated curved plates, as well as predict the threshold for bistability.

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

PurposeThis paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.Design/methodology/approachIn this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.FindingsSeveral numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.Originality/valueThe authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

Dynamics of a gas bubble in a straining flow: Deformation, oscillations, self-propulsion

The dynamics of a gas bubble suspended in an axisymmetric straining flow is examined with modern tools of global stability analysis. The complete bifurcation diagram of a bubble constrained to remain trapped at the stagnation point is determined. It is made of a stable branch, along which the bubble oscillates, and an unstable branch along which it develops non-oscillating waisted shapes prefiguring breakup. Two unstable non-oscillating modes also allow a free bubble to drift away from the stagnation point, not only along the elongation axis but also within the compressional plane thanks to a specific self-propulsion mechanism.

Structure and generation mechanism of blue whirls

Blue whirls are newly discovered blue rotating flames transitioned from fire whirls generated on liquid fuel surfaces. Compared with the traditional fire whirls, blue whirls have a distinct flame structure and are almost soot-free. Studies of the blue whirl are expected to promote the development of clean combustion theory and technology. In this paper, we numerically and theoretically investigate the lifting process of fire whirls and blue whirls, and then discuss their structure and transition mechanisms. In contrast to the explanations in the literature, it is found that blue whirls can be created without the occurrence of bubble-type vortex breakdown in the rotating flow. The blue whirl can be considered as a special form of lifted fire whirl with a considerable liftoff distance and without being blown out. According to the simulation, both blue whirls and fire whirls have the typical triple-flame structure. The unique structure of blue whirls is closely related to the thermal expansion of gas and the restriction of the radial flow by the axis. The theoretical solution of the unified lifting curve for fire whirls and blue whirls is obtained, which is qualitatively in agreement with the numerical result. There are 4 different branches in the lifting curve, two of which are stable, respectively representing fire whirls with small liftoff distances, and blue whirls with larger liftoff distances. The unstable branches between the stable branches lead to non-continuous transitions between fire whirls and blue whirls, as observed in the experiment. The current study explains the existing physical phenomenon and makes valuable predictions that may guide future experiments and simulations.

Nonlinear Dynamics of Turbine Generator Shaft Trains: Evaluation of Bifurcation Sets Applying Numerical Continuation

Abstract The nonlinear dynamics of turbine generator shaft trains for power generation are investigated in this paper. Realistic models of rotors, pedestals, and nonlinear bearings of partial arc and lemon bore configuration are implemented to compose a nonlinear set of differential equations for autonomous (balanced) and nonautonomous (unbalanced—per ISO) cases. The solution branches of the dynamic system are evaluated with the pseudo-arc length continuation programed by the authors, and the respective limit cycles are evaluated by an orthogonal collocation method and investigated on their stability properties and quality of motion for the respective key design parameters for the rotor dynamic design of such systems, namely, bearing profile and respective pad length, preload and offset, pedestal stiffness and elevation (misalignment), and rotor slenderness. Model order reduction is applied to the finite element rotor model and the reduced system is validated in terms of unbalanced response and stability characteristics. The main conclusion of the current investigation is that the system has the potential to develop instabilities at rotating speeds lower than the threshold speed of instability (evaluated by the linear approach) for specific unbalance magnitude and design properties. Unbalance response (with stable and unstable branches) is evaluated in severely reduced time compared to this applying time integration methods, enabling nonlinear rotor dynamic design of such systems as a standard procedure, and revealing the complete potential of motions (not only local).