Nonlinear Modal Interactions of a Parametrically Excited Composite Column

2017 ◽  
Author(s):  
Jerzy Warminski ◽  
Andrzej Teter
Keyword(s):  
Parametric Resonance ◽  
Dynamic Properties ◽  
Parametric Instability ◽  
Local Mode ◽  
Modal Interactions ◽  
Periodic Force ◽  
Composite Column ◽  
General Arrangement ◽  
Composite Configuration ◽  
Modes Coupling

Nonlinear dynamics of a composite column loaded by axial periodic force is presented in the paper. The simply supported channel column is made of several layers of a laminate with an general arrangement, leading to mechanical deformation couplings. A reduced model of the column is represented by a set of nonlinear equations which includes geometric nonlinear terms and parametric excitation. For the selected configuration of the composite structure parametric instability zones and vibration modes coupling occur. In contrast to isotropic materials, a modification of the reinforcing fibres layout results in a change of structure dynamic properties and a location of parametric resonance zones. Furthermore, buckling phenomenon may occur through various scenarios, by the global or local mode activation. The effect of the composite configuration on the principal parametric resonance zones is presented.

Parametric Resonance of Stiffened Rectangular Plates

1972 ◽  
Vol 39 (1) ◽  
pp. 217-226 ◽  
Author(s):  
R. C. Duffield ◽  
N. Willems
Keyword(s):  
Parametric Resonance ◽  
Parametric Instability ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Discrete Elements ◽  
Periodic Force ◽  
Simply Supported ◽  
Dynamic Forces ◽  
Instability Regions

This investigation is concerned with the onset of parametric instability of a simply supported stiffened rectangular plate subjected to in-plane sinusoidal dynamic forces. An analytical analysis is developed for the stiffened plate with the stiffeners treated as discrete elements. The results show that the location and size of the stiffeners have a significant effect on the location and contour of the boundaries of the parametric instability regions when compared with those of a flat unstiffened plate. Experimental verification is obtained for stiffened plates with a single centrally located stiffener transverse to an in-plane periodic force acting on two opposite edges.

scholarly journals Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Internal Resonance ◽  
Microscopic Theory ◽  
Fold Increase ◽  
Nonlinear Damping ◽  
Supporting Evidence ◽  
Nonlinear Dissipation ◽  
Modal Interactions ◽  
Solid State Physics ◽  
Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Parametric Resonance Characteristics of Woven Fiber Metal Laminated Plates

2019 ◽  
Vol 11 (04) ◽  
pp. 1950034 ◽  
Author(s):  
Elluri Venkata Prasad ◽  
Shishir Kumar Sahu
Keyword(s):  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Laminated Plates ◽  
Load Factor ◽  
Harmonic Loading ◽  
Resonance Behavior ◽  
Fiber Metal ◽  
Ply Orientation

The present investigation deals with the assessment of parametric resonance behavior of new aircraft material, i.e., woven fiber metal laminated (FML) plates subjected to in-plane static and harmonic loading using finite element (FE) technique and Bolotin’s method. In this analysis, a four-node isoparametric element with five degrees of freedom per node is adopted. Based on the first-order Reissner–Mindlin theory, the parametric instability of FML plate subjected to in-plane harmonic loading is examined. A MATLAB code is developed for the parametric study on the dynamic stability of FML plates. The reliability of present formulation is checked by comparing numerical results obtained from present FE analysis with the published researches in the field. The influences of several factors, viz. static load factor, aspect ratio, length-to-thickness ratio, number of layers, ply orientation and boundary conditions on the dynamic instability regions are discussed. Significant variations of these factors on dynamic instability zones of FML plates are observed. The instability zones can be used as guidelines for the prediction of the dynamic behavior of FML plates.

scholarly journals Finite Element Simulation of Dynamic Stability of Plane Free-Surface of a Liquid under Vertical Excitation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Siva Srinivas Kolukula ◽  
P. Chellapandi
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Parametric Resonance ◽  
Linear Equations ◽  
Parametric Instability ◽  
Initial Perturbation ◽  
Mathieu Equation ◽  
External Excitation ◽  
Nonlinear Potential Theory ◽  
Vertical Excitation

When partially filled liquid containers are excited vertically, the plane free-surface of the liquid can be stable or unstable depending on the amplitude and frequency of the external excitation. For some combinations of amplitude and frequency, the free-surface undergoes unbounded motion leading to instability called parametric instability or parametric resonance, and, for few other combinations, the free-surface undergoes bounded stable motion. In parametric resonance, a small initial perturbation on the free-surface can build up unboundedly even for small external excitation, if the excitation acts on the tank for sufficiently long time. In this paper, the stability of the plane free-surface is investigated by numerical simulation. Stability chart for the governing Mathieu equation is plotted analytically using linear equations. Applying fully nonlinear finite element method based on nonlinear potential theory, the response of the plane free-surface is simulated for various cases.

scholarly journals Dynamic Instability of High-Speed Rotating Shaft with Torsional Effect

2018 ◽  
Vol 15 (4) ◽  
pp. 6034-6051
Author(s):  
A. M. A. Wahab ◽  
Z. Yusof ◽  
Z. A. Rasid ◽  
A. Abu ◽  
N. F. M. N. Rudin
Keyword(s):  
Parametric Resonance ◽  
High Speed ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Degree Of Freedom ◽  
Rotating Shaft ◽  
Torsional Deformation ◽  
High Rotational Speed ◽  
The Difference ◽  
Frequency Ratios

Today’s design of machine rotor requires the rotor to operate at a high rotational speed to improve the efficiency of the machine. However, the existence of disturbances such as periodic axial load may cause parametric resonance to the rotor system in addition to the common force resonance. Previous studies on this parametric resonance of shaft typically included the element of translational and rotary inertia, gyroscopic moments and bending and shear deformation but surprisingly neglected the effect of the axial torque. This paper investigated the parametric instability behaviour of the shaft rotating at high speed while considering the torsional effect of the shaft. Based on the finite element method, a shaft model that includes torsional deformation as one of its degree of freedom was established. The Mathieu-Hill equation was derived, and then the Bolotin’s method was used to solve the equation by establishing the parametric instability chart. Two types of the rotary system were studied: a shaft with different boundary conditions and shaft with different bearing types. The results were initially validated with past findings. Following that the results were compared to the results correspond to the Timoshenko’s beam formulation that omits the torsional degree of freedom. The effect of axial torsional deformation was found to be very significant especially at high speed. The developed model in this study shows that at the shaft speed of 40000 rpm, the effect of torsional deformation has given the difference of more than 100% in the frequency ratios correspond to the 4DOF and 5DOF models for the case of fix-free boundary condition.

Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions

1998 ◽  
Vol 120 (2) ◽  
pp. 461-467 ◽  
Author(s):  
R. Dufour ◽  
A. Berlioz
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Parametric Resonance Analysis of a Submerged Floating Pipeline Considering Uncertainties

2019 ◽  
Author(s):  
Hezhen Yang ◽  
Fei Xiao
Keyword(s):  
Parametric Resonance ◽  
Parametric Instability ◽  
Dynamic Responses ◽  
Wave Forces ◽  
Pipeline System ◽  
Hill Stability ◽  
Resonance Analysis ◽  
Stability Diagrams ◽  
Novel Concept ◽  
Pipeline Design

Abstract The submerged floating pipeline is floating at a certain ocean depth with tethers anchored to the seabed. This novel concept of pipeline can be a promising solution for challenging seabed conditions. Because the pipeline is floating at the mid-deep water and does not interact directly with the seabed, there is no need to do any seabed intervention work and wave forces on the pipeline can also be ignored. But the dynamic response of this type of pipeline under strong currents poses several challenges for design of floating pipeline. This work investigates the parametric resonance of submerged floating pipeline between two floating structures. The parametric resonance can lead to the huge motions and fatigue damage of the pipeline. Thus, it is essential to investigate the parametric resonance of the submerged floating pipeline system under combined parametric and vortex excitations considering uncertainties. Hill’s equation of dynamic responses of the pipeline are derived and hill stability diagrams are used to analyses the corresponding motion stability. The effect of the significant uncertain factors on the probability of the parametric stability is investigated using the metamodel method. According to analyses, some effective measures are given to the designers to avoid the parametric instability for the submerged floating pipeline design.

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