Dynamic response and stability analysis of brake chatter with stochastic parameter perturbation

In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker-Planck-Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ-correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.

Noise-induced bifurcations in the stochastic chemostat model with general nutrient uptake functions

The paper examines the dynamic response of a two-bogie vehicle to the symmetrical and antisymmetrical excitations, due to bounce and pitch of the axles’ planes, derived from the track vertical irregularities. Part I introduced the theoretical model and the response functions of the vehicle, as well as the theoretical elements required for the analysis of the dynamic response of the vehicle to the track stochastic irregularities. Part II comprises the results of the numerical analysis of the vehicle dynamic response in three reference points of the carbody, based on which a series of properties of the vertical vibrations behaviour of the railway vehicle is pointed out at. The excitation modes that trigger the carbody response in its reference points are identified. Hence, the influence of the geometrical filtering effect of the excitation modes upon the ride quality and ride comfort is established.

Bifurcation dynamics in a stochastic population model with Beverton–Holt growth

The generation of continuous random processes with jointly specified probability density and covariation functions is considered. The proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system, excited by white Gaussian noise and described by a system of a first-order stochastic differential equations (SDE). The authors explore how the statistical characteristics of the equation's solution depends on the form of its operator and on the intensity of the input noise. Some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non-Gaussian continuous processes are considered. The approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its Markov model as well as in simulation of continuous correlated processes with the known probability density function. >

Numerical study of turbulent wall jet over multiple-inclined flat surface

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of the stable branches approaches the unstable one once per period. We prove that there exists a critical noise intensity, depending on the forcing period and on the minimal distance between equilibrium branches, such that the probability that solutions of the SPDE make transitions between stable equilibria is exponentially small for subcritical noise intensity, while they happen with probability exponentially close to 1 for supercritical noise intensity. Concentration estimates of solutions are given in the $$H^s$$ Sobolev norm for any $$s<\frac{1}{2}$$ . The results generalise to an infinite-dimensional setting those obtained for 1-dimensional SDEs in [5].

In this paper, mean first-passage time (MFPT) and stochastic resonance (SR) are investigated in an asymmetric bistable system driven by multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and two-state theory, the expression of MFPT and the signal-to-noise ratio (SNR) are derived. The results show that the influences of the asymmetric coefficient on the MFPTs in two opposite directions are entirely different. SNR is a non-monotonic function of the additive noise intensity and asymmetric coefficient, therefore, an SR is found in this system. Whereas SNR is a monotonic function of the multiplicative noise intensity and no SR appears. This demonstrates that the effect of the multiplicative noise intensity on SNR is different from that of the additive noise intensity in the system.

Recent studies have demonstrated that both virus-to-cell infection and cell-to-cell transmission play an important role in the process of HIV infection. In this paper, stochastic perturbation is introduced into HIV model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and three distributed delays. The stochastic integro-delay differential equations is transformed into a degenerate stochastic differential equations. Through rigorous analysis of the model, we obtain the solution is unique, positive and global. By constructing appropriate Lyapunov functions, the existence of the stationary Markov process is derived when the critical condition is bigger than one. Furthermore, the extinction of the virus for sufficiently big noise intensity is established. Numerically, we investigate that the small noise intensity of fluctuations could help to sustain the number of virions and CTL immune response within a certain range, while the big noise intensity may be beneficial to the extinction of the virus. We also examine that the influence of random fluctuations on model dynamics may be more significant than that of the delay.

During cancer treatment, noise often affects signaling networks and spatiotemporal dynamics, while elevated psychological stress or anxiety in patients contributes to suboptimal treatment outcomes. In line with research findings on glioma pathogenesis, a novel hybrid multiscale agent-based model is presented, which couples stochastic differential equations, stochastic partial differential equations and a set of rules on cell phenotype switching together from micro and macro levels. The therapeutic effects of temozolomide (TMZ) alone, BKM120 alone, and the combination of TMZ with BKM120 are simulated in two dimensions. Subsequently, the impacts of different noise intensities and psychological pressure on the growth of glioma cells are separately investigated. Additionally, the impacts of different activation rates of AKT and PI3K on the size of glioma are analyzed, respectively. Ultimately, the three-dimensional (3D) tumor spheroid model is constructed to display the internal characteristics of the tumor. Results reveal that (1) the noise on the whole cuts down the growth and proliferation of glioma cells; (2) AKT, being closely related to cell cycle, greatly regulates tumor cell number; (3) the synergy of psychological intervention and drug therapy shows a significant improvement over drug therapy alone; (4) 3D simulations clearly demonstrate a treatment-proliferation game by angiogenesis. These results raise comprehension of the overall behavior of the glioma system and enable predictions of clinical treatment outcomes.

Recent literature on building energy performance simulation leans toward implementing uncertainty analysis (UA), instead of deterministic solutions, to handle ever-existing and pivotal uncertainties in building design decision-making process. Variations in weather temperature, degradation of building envelope material properties over time, and random behavior of occupants, among all, are the key sources of uncertainty in building energy consumption predictions. The UA couples to the sensitivity analysis (SA) to identify the most influential inputs on the uncertainties of the building energy consumption. This paper describes a newly-developed UA and SA predictive tool for building energy performance simulations. Energy performance simulations are based on a resistance-capacitance thermal model for the building. For a hypothetical residential building in College Station, Texas, USA, the present work describes and compares predicted probability distribution and sensitivity indexes produced by the UA-SA tool using a transient (dynamic) response analysis (TRA) and static response analysis (SRA). For brevity, the analysis considers uncertainty only for the exterior walls’ parameters including thickness, thermal conductivity, heat transfer coefficient, density, and heat capacity; i.e., a five-dimensional problem is solved. Compared to the TRA, predictions from the SRA underestimate the annual energy consumption up to 30%; however, SRA is significantly faster. Nonetheless, sensitivity indexes from the SRA and TRA closely match.

Site response analysis is essential in assessing the offshore pipeline integrity as well as the stability of subsea structures during an earthquake event. Depending on the functionality, the length of offshore pipeline can be tens to hundreds of kilometers running through different underlying soil conditions as well as traversing submarine slopes. Therefore, it is important to identify the effect of variable site conditions on the earthquake response to accurately predict the stability of offshore pipeline as well as subsea structures. A study was undertaken to determine the ground responses along an offshore pipeline route across escarpments and connected to subsea structures at the termination points. The pipeline route was divided into multiple segments depending on the soil variability. Due to high site seismicity, the soft soil is susceptible to high shear strain during strong earthquake shaking; thus requiring non-linear dynamic site-response analysis to accurately capture soil dynamic response. A finite element based non-linear site response analysis was selected for the entire pipeline route. The dynamic site response analyses were carried out using PLAXIS 2D and the soil behavior was modeled considering non-linear variation of stiffness and damping with shear strain. The input ground motions to the dynamic site response analysis were site specific stiff soil earthquake motions scaled to Abnormal Level Earthquake (ALE) and Extreme Level Earthquake (ELE). The segment-specific response spectra and time histories at mudline were developed as input to the seismic design of pipelines and subsea structures. Despite a stable escarpment during a seismic event, the site response analysis showed localized high deformation which can significantly affect the pipeline seismic response. Considerable variations in mudline response spectra was observed depending on strength, thickness and depth of soft soils. This paper provides an overview of dynamic site response analysis performed for an offshore site, and focuses on the effects of variable ground models, as well as escarpment on the seabed level seismic motions for subsea pipeline and structures seismic design. The importance of accounting each of these effects in the development of a robust and safe seismic design has been highlighted.

This paper presents how non-linear waves and wave loading induce non-Gaussian dynamic response of fixed offshore structures, and the effects this may have to fatigue life and extreme dynamic response of such platforms. Furthermore, the validity of different theoretical wave and wave load models is discussed. The basis for the paper is full-scale measurements of waves and dynamic response recorded on a jacket platform in the North Sea and time domain computer simulations of the response of this platform using a finite element structural model. INTRODUCTION Fixed deep water platforms will because of the large water depths and high deck masses behave highly dynamically. Such platforms must therefore be designed against irregular environmental load processes with the energy distributed over a wide frequency range. This demands the use of stochastic methods for dynamic response analysis both for prediction of fatigue life and extreme load effects. The practical procedures for such analysis which are available today are based on Gaussian environmental excitation processes, linearized load models, linear structural models, and, consequently, on Gaussian dynamic response. Full-scale measurements from existing platforms have, however, indicated that the dynamic response of fixed structures generally is non-Gaussian [1, 2, 3]. In this paper it is, based on the results of systematic analysis of full-scale measurements of waves and dynamic response, discussed which are the sources of non-Gaussian dynamic response and what are the consequences of this to fatigue life and extreme response. Furthermore, the capabilities of existing methods for non-linear dynamic response analysis is outlined through comparison of measured and simulated dynamic response. The effects of the observed type of non-linear load effects to fatigue life and extreme response of deepwater platforms are discussed in [4, 7]. FULL-SCALE MEASUREMENTS The Instrumented Platform The applied data are recorded on the Val hall quarters platform. This platform is four legged and x-braced double corner piles. The water depth is 70 m. Typical dimensions for wave loaded structural elements are 1.5 m for the legs and 0.7 m for the bracing. The platform is connected with a bridge to two neighboring platforms. The platform is instrumented for measuring of wind speed and direction, wave heights, current speed and direction, strain in one of the braces of an x-joint and platform accelerations at cellar deck and mudline levels. The platform is shown in Figure 1 together with the two connected platforms. In Figure 2 a more schematic picture of the platform is given which also indicates the location of the different sensors. The Applied Data The data involved in the study are the wave data, current data and strain data in the location indicated in Figure 3. Key parameters for the different data types are given in Table 1. The standard length of each recording period is 20 minutes. The study included 28 recording periods, all representing sea states where the mean wave direction was within the 30 degrees sector indicated in Figure 3. The distribution of the recording periods with respect to sea state severity is given in Table 2

Dielectric elastomers are widely used in many fields due to their advantages of high deformability, light weight, biological compatibility, and high efficiency. In this study, the stochastic dynamic response and bifurcation of a dielectric elastomer balloon (DEB) with viscoelasticity are investigated. Firstly, the rheological model is adopted to describe the viscoelasticity of the DEB, and the dynamic model is deduced by using the free energy method. The effect of viscoelasticity on the state of equilibrium with static pressure and voltage is analysed. Then, the stochastic differential equation about the perturbation around the state of equilibrium is derived when the DEB is under random pressure and static voltage. The steady-state probability densities of the perturbation stretch ratio are determined by the generalized cell mapping method. The effects of parameter conditions on the mean value of the perturbation stretch ratio are calculated. Finally, sinusoidal voltage and random pressure are applied to the viscoelastic DEB, and the phenomenon of P-bifurcation is observed. Our results are compared with those obtained from Monte Carlo simulation to verify their accuracy. This work provides a potential theoretical reference for the design and application of DEs.

On the verification of superposition method of kinematic interaction and inertial interaction in dynamic response analysis of soil-pile-structure systems