Bifurcations and Uncertainty Quantifications in Nonlinear Acousto-Elastic Systems

2016 ◽  
Author(s):  
W. Dheelibun Remigius ◽  
Sunetra Sarkar
Keyword(s):  
Elastic System ◽  
Coupled System ◽  
Spectral Projection ◽  
Acoustic Oscillations ◽  
Field Equations ◽  
Acoustic Damping ◽  
Expansion Technique ◽  
Elastic Systems ◽  
Coupled Field Equations ◽  
Surrounding Fluid

The study of nonlinear aeroelastic instability mechanism of nonconservative acousto-elastic system is the focus here. The acousto-elastic system consists of a spinning disc in a compressible fluid filled enclosure. The nonlinear rotating plate is coupled with the linear acoustic oscillations of the surrounding fluid. Based on the acousto-elastic theory, the coupled field equations are discretized and solved for various rotation speeds in order to obtain the coupled system dynamics. The study shows that the coupled system undergoes a flutter instability at a particular rotation speed and the instability takes the form of supercritical Hopf bifurcation. Subsequently, the effect of randomness associated with the structural and the acoustic damping parameters are quantified on the nonlinear instability behaviour by means of a spectral projection based polynomial chaos expansion technique.

Stochastic Bifurcations of a Nonlinear Acousto-Elastic System

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
W. Dheelibun Remigius ◽  
Sunetra Sarkar
Keyword(s):  
Hopf Bifurcation ◽  
Stochastic System ◽  
Elastic System ◽  
Spectral Projection ◽  
Stochastic Bifurcation ◽  
Deterministic System ◽  
Acoustic Oscillations ◽  
Field Equations ◽  
Coupled Mode ◽  
Coupled Field Equations

The nonlinear stochastic behavior of a nonconservative acousto-elastic system is in focus in the present work. The deterministic acousto-elastic system consists of a spinning disk in a compressible fluid filled enclosure. The nonlinear rotating plate dynamics is coupled with the linear acoustic oscillations of the surrounding fluid, and the coupled field equations are discretized and solved at various rotation speeds. The deterministic system reveals the presence of a supercritical Hopf bifurcation when a specific coupled mode undergoes a flutter instability at a particular rotation speed. The effect of randomness associated with the damping parameters are investigated and quantified on the coupled dynamics and the stochastic bifurcation behavior is studied. The quantification of the parametric randomness has been undertaken by means of a spectral projection based polynomial chaos expansion (PCE) technique. From the marginal probability density functions (PDFs), it is observed that the stochastic system exhibits stochastic phenomenological bifurcations (P-bifurcation). The study provides insights into the behavior of the stochastic system during its P-bifurcation with reference to the deterministic Hopf bifurcation.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

scholarly journals A Coupled Thermodynamic Model for Transport Properties of Thin Films during Physical Aging

Polymers ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 387 ◽  
Author(s):  
Hongjiu Hu ◽  
Xiaoming Fan ◽  
Yaolong He
Keyword(s):  
Thin Films ◽  
Transport Properties ◽  
Free Volume ◽  
Physical Aging ◽  
Field Equations ◽  
Lattice Contraction ◽  
Strongly Coupled ◽  
Coupled Diffusion ◽  
Coupled Field Equations ◽  
Short Time

A coupled diffusion model based on continuum thermodynamics is developed to quantitatively describe the transport properties of glassy thin films during physical aging. The coupled field equations are then embodied and applied to simulate the transport behaviors of O2 and CO2 within aging polymeric membranes to validate the model and demonstrate the coupling phenomenon, respectively. It is found that due to the introduction of the concentration gradient, the proposed direct calculating method on permeability can produce relatively better consistency with the experimental results for various film thicknesses. In addition, by assuming that the free volume induced by lattice contraction is renewed upon CO2 exposure, the experimental permeability of O2 within Matrimid® thin film after short-time exposure to CO2 is well reproduced in this work. Remarkably, with the help of the validated straightforward permeability calculation method and free volume recovery mechanism, the permeability behavior of CO2 is also well elucidated, with the results implying that the transport process of CO2 and the variation of free volume are strongly coupled.

Exact soliton solutions for a class of coupled field equations

1993 ◽  
Vol 173 (1) ◽  
pp. 30-32 ◽  
Author(s):  
Xin-Yi Wang ◽  
Bing-Chang Xu ◽  
Philip L. Taylor
Keyword(s):  
Soliton Solutions ◽  
Field Equations ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
Exact Soliton Solutions

A Variational Approach to the Dynamics of Structures Having Mixed or Discontinuous Boundary Conditions

1984 ◽  
Vol 51 (4) ◽  
pp. 831-836 ◽  
Author(s):  
P. J. Torvik
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Natural Frequencies ◽  
Elastic Solid ◽  
Approximate Solutions ◽  
Forced Response ◽  
Field Equations ◽  
Elastic Circular Plate ◽  
Discontinuous Boundary ◽  
Elastic Systems

A procedure is developed whereby the steady-state forced response and the modes of free vibration for elastic systems having mixed or discontinuous boundary conditions can be determined. Approximate solutions are obtained as a superposition of a set of functions, each of which satisfies the field equations but not the boundary conditions. The coefficients of this expansion are obtained through applying a variational principle developed from Hamilton’s principle which for simple harmonic motion, is equivalent to Reissner’s principle. The reduction from the general elastic solid to the elastic plate is given, as are some results obtained for the first several natural frequencies of an elastic circular plate, free on a portion of the boundary and clamped on the remainder.

On the exact soliton solutions for a class of coupled field equations

1993 ◽  
Vol 182 (2-3) ◽  
pp. 300-301 ◽  
Author(s):  
Xiaowu Huang ◽  
Jiahua Han ◽  
Kaiyi Qian ◽  
Wei Qian
Keyword(s):  
Soliton Solutions ◽  
Field Equations ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
Exact Soliton Solutions

scholarly journals Vibration analysis of nonlinear and linear elastic systems

2021 ◽  
Vol 47 (4) ◽  
pp. 141-150
Author(s):  
A. S. Lichkovakha ◽  
B. A. Shemshura ◽  
S. A. Kuznetsov
Keyword(s):  
Elastic System ◽  
Elastic Characteristic ◽  
Progressive Change ◽  
Vehicle Suspensions ◽  
Linear Elastic ◽  
Eccentric Compression ◽  
Elastic Systems ◽  
Elastic Mechanism ◽  
High Flexibility ◽  
Elastic Elements

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

MEMS Integrated Electro-Fluid-Elastic Modeling for Aerospace Applications

2006 ◽  
Author(s):  
Alessandro Fumagalli ◽  
Giuseppe Quaranta ◽  
Paolo Mantegazza
Keyword(s):  
Jacobian Matrix ◽  
Dynamical Analysis ◽  
Published Data ◽  
Field Equations ◽  
Fully Integrated ◽  
Aerospace Applications ◽  
Integrated Methodology ◽  
Proposed Model ◽  
Elastic Systems ◽  
Good Agreement

MEMS physics is characterized by multi-fields interactions. In this paper, a fully integrated methodology is proposed for dynamical analysis of electro-fluid-elastic systems, typical of MEMS-based microresonators and microswitches. Finite Elements/Volumes Method is used to solve field equations. These are coupled by an opportune procedure of interface between domains, resulting in a nonlinear algebraic differential system of equations describing the system. This is directly integrated in time, becoming fully algebraic, and solved by a Newton technique. Full Jacobian matrix computation results in a very hard task. Analytical block approximation for Jacobian matrix is proposed. Model is validated comparing results with commercial codes and with published data, showing good agreement, high convergence properties and reduced computational efforts.

scholarly journals Rastall gravity extension of the standard $$\Lambda $$CDM model: theoretical features and observational constraints

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Özgür Akarsu ◽  
Nihan Katırcı ◽  
Suresh Kumar ◽  
Rafael C. Nunes ◽  
Burcu Öztürk ◽  
...  
Keyword(s):  
General Relativity ◽  
Cold Dark Matter ◽  
Friedmann Equation ◽  
Momentum Conservation ◽  
Density Parameter ◽  
Acoustic Oscillations ◽  
Field Equations ◽  
Accurate Analysis ◽  
Material Sources ◽  
Effective Source

AbstractWe present a detailed investigation of the Rastall gravity extension of the standard $$\Lambda $$ Λ CDM model. We review the model for two simultaneous modifications of different nature in the Friedmann equation due to the Rastall gravity: the new contributions of the material (actual) sources (considered as effective source) and the altered evolution of the material sources. We discuss the role/behavior of these modifications with regard to some low redshift tensions, including the so-called $$H_0$$ H 0 tension, prevailing within the standard $$\Lambda $$ Λ CDM. We constrain the model at the level of linear perturbations, and obtain the first constraints through a robust and accurate analysis using the latest full Planck cosmic microwave background (CMB) data, with and without including baryon acoustic oscillations (BAO) data. We find that the Rastall parameter $$\epsilon $$ ϵ (null for general relativity) is consistent with zero at 68% CL (with a tendency towards positive values, $$-0.0001< \epsilon < 0.0007$$ - 0.0001 < ϵ < 0.0007 (CMB+BAO) at 68% CL), which in turn implies no significant statistical evidence for deviation from general relativity, and also a precision of $$\mathcal {O}(10^{-4})$$ O ( 10 - 4 ) for the coefficient $$-1/2$$ - 1 / 2 of the term $$g_{\mu \nu }R$$ g μ ν R in the Einstein field equations of general relativity (guaranteeing the local energy-momentum conservation). We explore the consequences led by the Rastall gravity on the cosmological parameters in the light of the observational analyses. It turns out that the effective source, with a present-day density parameter $$\Omega _\mathrm{X0}=-0.0010\pm 0.0013$$ Ω X 0 = - 0.0010 ± 0.0013 (CMB+BAO, 68% CL), dynamically screens the usual vacuum energy at high redshifts, but this mechanism barely works due to the opposition by the altered evolution of cold dark matter. Consequently, two simultaneous modifications of different nature in the Friedmann equation by the Rastall gravity act against each other, and do not help to considerably relax the low redshift tensions, including the so-called $$H_0$$ H 0 tension. Our results may offer a guide for the research community that studies the Rastall gravity in various aspects of gravitation and cosmology.

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