A New Kind of Energy Transfer From the High-Frequency to Low-Frequency Mode in a Composite Laminated Plate

2010 ◽  
Author(s):  
Wei Zhang ◽  
Xiang-Ying Guo ◽  
Qian Wang ◽  
Cui-Cui Liu ◽  
Yun-cheng He
Keyword(s):  
Numerical Simulation ◽  
Natural Frequency ◽  
Thin Plate ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Mode ◽  
Rectangular Thin Plate ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Low Frequency Mode

This paper focuses on the analysis on a new kind of nonlinear resonant motion with the low-frequency large-amplitude, which can be induced by the high-frequency small-amplitude mode through the mechanism of modulation of amplitude and phase. The system investigated is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations. Experimental research has been carried out for the first time. The test plate was excited near the first natural frequency with parametric forces and the above mentioned high-to-low frequency mode has been observed, whose frequency is extremely lower than the first natural frequency. Theoretical job goes to analysis the above phenomenon accordingly. Based on the Reddy’s third-order shear deformation plate theory and the von Karman type equation, the nonlinear governing equations of the simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations are formulated. The Galerkin method is utilized to discretize the governing partial differential equations into a two-degree-of-freedom nonlinear system. Numerical simulation is conducted to investigate this non-autonomous system subsequently. The results of numerical simulation demonstrate that there is a qualitative agreement between the experimental observation and the theoretical result. Besides, the multi-pulse chaotic motions are also reported in numerical simulations.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

Multi-Pulse Chaotic Motion for a Non-Autonomous Buckled Plate by Using the Extended Melnikov Method

2007 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Two Degree Of Freedom

The multi-pulse Shilnikov orbits and chaotic dynamics for a parametrically excited, simply supported rectangular buckled thin plate are studied by using the extended Melnikov method. Based on von Karman type equation and the Galerkin’s approach, two-degree-of-freedom nonlinear system is obtained for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of the thin plate. The results obtained here show that the multipulse chaotic motions can occur in the thin plate.

scholarly journals Investigation of Flow Around a Slender Body at High Angles of Attack

2019 ◽  
Vol 30 (1) ◽  
pp. 51-61
Author(s):  
Ibraheem AlQadi Ibraheem AlQadi
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
The Body ◽  
Slender Body ◽  
Frequency Mode ◽  
Dynamic Mode ◽  
High Frequency Mode ◽  
Wide Range ◽  
Low Frequency Mode ◽  
High Angles Of Attack

A numerical investigation of flow around a slender body at high angles of attack is presented. Large eddy simulation of the flow around an ogive-cylinder body at high angles of attack is carried out. Asymmetric vortex flow was observed at angles of attack of α = 55◦ and 65◦ . The results showed that the phenomenon is present in the absence of artificial geometrical or flow perturbation. Contrary to the accepted notion that flow asymmetry is due to a convective instability, the development of vortex asymmetry in the absence of perturbations indicates the existence of absolute instability. An investigation of the unsteady flow field was carried out using dynamic mode decomposition. The analysis identified two distinct unsteady modes; high-frequency mode and low-frequency mode. At angle of attack 45◦ the high-frequency mode is dominant in the frontal part of the body and the low-frequency mode is dominant at the rear part. At α = 55◦ , the highfrequency mode is dominant downstream of vortex breakdown. At α = 65◦ , the spectrum shows a wide range of modes. Reconstruction of the dynamical modes shows that the low-frequency mode is associated with the unsteady wake and the high-frequency mode is associated with unsteady shear layer.

NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION

1993 ◽  
Vol 03 (02) ◽  
pp. 417-427 ◽  
Author(s):  
S.A. NAYFEH ◽  
A.H. NAYFEH
Keyword(s):  
Natural Frequency ◽  
High Frequency ◽  
Analytical Study ◽  
Experimental Studies ◽  
Low Frequency ◽  
Harmonic Excitation ◽  
Frequency Mode ◽  
Large Contribution ◽  
High Frequency Mode ◽  
Two Degree Of Freedom

Recent experimental studies indicate that energy can be transferred from high- to low-frequency modes in structures with weak nonlinearity. In each of these experiments, a high-frequency mode was driven near its natural frequency but the response included a large contribution due to the first mode of the structure. In this paper, an analytical study of the response of a two-degree-of-freedom nonlinear system with widely spaced modes to a simple-harmonic excitation near the natural frequency of its high-frequency mode is presented. This system serves as a paradigm for the interaction of high- and low-frequency modes.

scholarly journals Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control

2015 ◽  
Vol 775 ◽  
pp. 201-222 ◽  
Author(s):  
Ubaid Ali Qadri ◽  
Gary J. Chandler ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
High Frequency ◽  
Passive Control ◽  
Diffusion Flames ◽  
Low Frequency ◽  
Frequency Mode ◽  
High Frequency Mode ◽  
Jet Diffusion Flames ◽  
Local Stability Analysis ◽  
Low Frequency Mode

We use direct numerical simulation (DNS) of the Navier–Stokes equations in the low-Mach-number limit to investigate the hydrodynamic instability of a lifted jet diffusion flame. We obtain steady solutions for flames using a finite rate reaction chemistry, and perform a linear global stability analysis around these steady flames. We calculate the direct and adjoint global modes and use these to identify the regions of the flow that are responsible for causing oscillations in lifted jet diffusion flames, and to identify how passive control strategies might be used to control these oscillations. We also apply a local stability analysis to identify the instability mechanisms that are active. We find that two axisymmetric modes are responsible for the oscillations. The first is a high-frequency mode with wavemaker in the jet shear layer in the premixing zone. The second is a low-frequency mode with wavemaker in the outer part of the shear layer in the flame. We find that both of these modes are most sensitive to feedback involving perturbations to the density and axial momentum. Using the local stability analysis, we find that the high-frequency mode is caused by a resonant mode in the premixing region, and that the low-frequency mode is caused by a region of local absolute instability in the flame, not by the interaction between resonant modes, as proposed in Nichols et al. (Phys. Fluids, vol. 21, 2009, article 015110). Our linear analysis shows that passive control of the low-frequency mode may be feasible because regions up to three diameters away from the fuel jet are moderately sensitive to steady control forces.

Multi-Pulse Orbits With a Melnikov Method and Chaotic Dynamics in Motion of Composite Laminated Rectangular Thin Plate

2008 ◽  
Author(s):  
Ming-Hui Yao ◽  
Wei Zhang ◽  
Xiang-Ying Guo ◽  
Dong-Xing Cao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the extended Melnikov method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

scholarly journals Inertial regimes in a curved electromagnetically forced flow

2017 ◽  
Vol 813 ◽  
pp. 860-881 ◽  
Author(s):  
J. Boisson ◽  
R. Monchaux ◽  
S. Aumaître
Keyword(s):  
Magnetic Field ◽  
Secondary Flow ◽  
High Frequency ◽  
Characteristic Length ◽  
Low Frequency ◽  
Frequency Mode ◽  
Square Duct ◽  
High Frequency Mode ◽  
Duct Geometry ◽  
Low Frequency Mode

We investigated experimentally the flow driven by a Lorentz force induced by an axial magnetic field $\boldsymbol{B}$ and a radial electric current $I$ applied between two fixed concentric copper cylinders. The gap geometry corresponds to a rectangular section with an aspect ratio of $\unicode[STIX]{x1D702}=4$ and we probe the azimuthal and axial velocity profiles of the flow along the vertical axis by using ultrasonic Doppler velocimetry. We have performed several runs at moderate magnetic field strengths, corresponding to moderate Hartmann numbers $M\leqslant 300$. At these forcing parameters and because of the geometry of our experimental device, we show that the inertial terms are not negligible and an azimuthal velocity that depends on both $I$ and $B$ is induced. From measurements of the vertical velocity we focus on the characteristics of the secondary flow: the time-averaged velocity profiles are compatible with a secondary flow presenting two pairs of stable vortices, as pointed out by previous numerical studies. The flow exhibited a transition between two dynamical modes, a high- and a low-frequency one. The high-frequency mode, which emerges at low magnetic field forcing, corresponds to the propagation in the radial $r$-direction of tilted vortices. This mode is consistent with our previous experiments and with the instability described in Zhao et al. (Phys. Fluids, vol. 23 (8), 2011, 084103) taking place in an elongated duct geometry. The low-frequency mode, observed for high magnetic field forcing, consists of large excursions of the vortices. The dynamics of these modes matches the first axisymmetric instability described in Zhao & Zikanov (J. Fluid Mech., vol. 692, 2012, pp. 288–316) taking place in an square duct geometry. We demonstrated that this transition is controlled by the inertial magnetic thickness $H^{\prime }$ which is the characteristic length we introduce as a balance between the advection and the Lorentz force. The key point here is that when the inertial magnetic thickness $H^{\prime }$ is comparable to one geometric characteristic length ($H/2$ in the vertical or $\unicode[STIX]{x0394}r$ in the radial direction) the corresponding mode is favoured. Therefore, when $H^{\prime }/(H/2)\approx 1$ we observe the high-frequency mode taking place in an elongated duct geometry, and when $H^{\prime }/\unicode[STIX]{x0394}r\approx 1$ we observe the low-frequency mode taking place in square duct geometry and high magnetic field.

SHILNIKOV-TYPE MULTIPULSE ORBITS AND CHAOTIC DYNAMICS OF A PARAMETRICALLY AND EXTERNALLY EXCITED RECTANGULAR THIN PLATE

2007 ◽  
Vol 17 (03) ◽  
pp. 851-875 ◽  
Author(s):  
M. H. YAO ◽  
W. ZHANG
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Thin Plate ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Dynamical Analysis ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Chaotic Motions ◽  
Parametric And External Excitations

The Shilnikov-type multipulse orbits and chaotic dynamics for a simply supported rectangular thin plate under combined parametric and external excitations are studied in this paper for the first time. The rectangular thin plate is subjected to spatially and temporally varying transversal and in-plane excitations, simultaneously. The formulas of the rectangular thin plate are derived from the von Kármán equation and Galerkin's method. The method of multiple scales is used to find the averaged equation in the case of 1:2 internal resonance. Based on the averaged equation, the theory of normal form is used to obtain the explicit expressions of normal form associated with a double zero and a pair of purely imaginary eigenvalues using the Maple program. The dissipative version of the energy-phase method is utilized to analyze the multipulse global bifurcations and chaotic dynamics of a parametrically and externally excited rectangular thin plate. The global dynamical analysis indicates that there exist the multipulse jumping orbits in the perturbed phase space of the averaged equation for a parametrically and externally excited rectangular thin plate. These results show that the chaotic motions of the multipulse Shilnikov-type can occur for a parametrically and externally excited rectangular thin plate. Numerical simulation results are presented to verify the analytical predictions. It is also found from the results of numerical simulation that the Shilnikov-type multipulse orbits exist for a parametrically and externally excited thin plate.

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