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 Parametric Instability of Square Laminated Plates in Hygrothermal Environment

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Manoj Kumar Rath ◽  
Shishir Kumar Sahu
Keyword(s):  
Elevated Temperatures ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Composite Plates ◽  
Laminated Plates ◽  
Load Factor ◽  
Dynamic Loadings ◽  
Instability Regions ◽  
Hygrothermal Environment ◽  
Dynamic Load Factor

The present paper investigates the parametric instability of square laminated plates subjected to periodic dynamic loadings in hygrothermal environment. The effects of various parameters like the increase in static load factor and the degree of orthotropy of simply supported composite plates at elevated temperatures and moisture concentrations on the principal instability regions are investigated using finite element method. The effects of transverse shear deformation and rotary inertia are used to study the antisymmetric angle-ply square plates. A simple laminated plate model is developed for the parametric instability of square laminated plates subjected to hygrothermal loading. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. The results show that instability of square laminated plates occurs for different parameters with an increase in temperature and moisture environment. The onset of instability occurs earlier, and the width of dynamic instability regions increases with a rise in temperature and moisture for different parameters. The effect of damping shows that there is a finite critical value of dynamic load factor for each instability region below which the square laminated plates cannot become unstable.

Vibration Analysis of Woven Fiber Metal Laminated Plates — Experimental and Numerical Studies

2018 ◽  
Vol 18 (11) ◽  
pp. 1850144 ◽  
Author(s):  
E. V. Prasad ◽  
S. K. Sahu
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Degrees Of Freedom ◽  
Laminated Plates ◽  
Thickness Ratio ◽  
Experimental Investigations ◽  
Numerical Studies ◽  
Fiber Metal ◽  
Ply Orientation

The present study deals with numerical and experimental investigations on the vibration behavior of fiber-metal-laminated (FML) plates, a new aircraft material. A finite element (FE)-based formulation is established for the plate using the first-order Reissner–Mindlin theory, including both fibers and metals of different material properties in alternate layers. A four-node isoparametric quadratic element with five degrees of freedom per node is adopted in the analysis. Convergence studies and comparison with previous studies are made to validate the present FE formulation. A set of experiments was conducted to get natural frequencies of vibration for glass FML (GFML) plates using Bruel and Kjaer (B&K) Fast Fourier Transform (FFT) analyzer with PULSE platform. The effects of different parameters such as aspect ratio, side-to-thickness ratio, ply orientation, and boundary conditions on the dynamic behavior of the FMLs are studied. Good agreement is achieved between the numerical and experimental results. Both results indicate that increasing the aspect ratio can increase the natural frequency of the FML plate, while the increase in the side-to-thickness ratio decreases the natural frequency of vibration. The boundary conditions can significantly affect the natural frequency of the FML plates due to the restraint effect at the edges.

Dynamic Stability of Woven Fiber Laminated Composite Shallow Shells in Hygrothermal Environment

2017 ◽  
Vol 17 (08) ◽  
pp. 1750084 ◽  
Author(s):  
M. Biswal ◽  
S. K. Sahu ◽  
A. V. Asha
Keyword(s):  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Shear Deformation Theory ◽  
Shell Element ◽  
Load Factor ◽  
Element Formulation ◽  
Shallow Shells ◽  
Instability Regions ◽  
Hygrothermal Environment

The dynamic stability of bidirectional woven fiber laminated glass/epoxy composite shallow shells subjected to harmonic in-plane loading in hygrothermal environment is considered. An eight-noded isoparametric shell element with five degrees of freedom is used in the analysis. In the present finite element formulation, a composite doubly curved shell model based on first-order shear deformation theory (FSDT) is used for the dynamic stability analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for the parametric study on the dynamic stability of shell panels under the hygrothermal field. The effects of various parameters like static load factor, curvature, shallowness, temperature, moisture, stacking sequence and boundary conditions on the dynamic instability regions of woven fiber glass/epoxy shell panels are investigated. The location of dynamic instability regions is shown to affect significantly due to presence of the hygrothermal field.

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.

scholarly journals Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

2020 ◽  
Vol 8 (7) ◽  
pp. 504 ◽  
Author(s):  
Giuseppe Giorgi ◽  
Josh Davidson ◽  
Giuseppe Habib ◽  
Giovanni Bracco ◽  
Giuliana Mattiazzo ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Parametric Resonance ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Kinematic Model ◽  
Numerical Instability ◽  
Floating Structure ◽  
Operational Conditions ◽  
Power Extraction

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

scholarly journals The Effect of Mooring Line Parameters in Inducing Parametric Resonance on the Spar-Buoy Oscillating Water Column Wave Energy Converter

2020 ◽  
Vol 8 (1) ◽  
pp. 29 ◽  
Author(s):  
Giuseppe Giorgi ◽  
Rui P. F. Gomes ◽  
Giovanni Bracco ◽  
Giuliana Mattiazzo
Keyword(s):  
Water Column ◽  
Parametric Resonance ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Production Efficiency ◽  
Parametric Instability ◽  
Mooring Line ◽  
Nonlinear Phenomenon ◽  
Oscillating Water Column ◽  
Highly Nonlinear

Although it is widely accepted that accurate modeling of wave energy converters is essential for effective and reliable design, it is often challenging to define an accurate model which is also fast enough to investigate the design space or to perform extensive sensitivity analysis. In fact, the required accuracy is usually brought by the inclusion of nonlinearities, which are often time-consuming to compute. This paper provides a computationally efficient meshless nonlinear Froude–Krylov model, including nonlinear kinematics and an integral formulation of drag forces in six degrees of freedom, which computes almost in real-time. Moreover, a mooring system model with three lines is included, with each line comprising of an anchor, a jumper, and a clump weight. The mathematical model is used to investigate the highly-nonlinear phenomenon of parametric resonance, which has particularly detrimental effects on the energy conversion performance of the spar-buoy oscillating water column (OWC) device. Furthermore, the sensitivity on changes to jumper and clump-weight masses are discussed. It is found that mean drift and peak loads increase with decreasing line pre-tension, eventually leading to a reduction of the operational region. On the other hand, the line pre-tension does not affect power production efficiency, nor is it able to avoid or significantly limit the severity of parametric instability.

Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance

2017 ◽  
Vol 24 (19) ◽  
pp. 4419-4432 ◽  
Author(s):  
Airong Liu ◽  
Zhicheng Yang ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Damping Ratio ◽  
Analytical Investigation ◽  
Engineering Practice ◽  
Test Results ◽  
Periodic Load ◽  
Shallow Arches ◽  
Excitation Frequencies ◽  
Critical Regions

When an arch is subjected to a periodic load, it may lose in-plane stability dynamically owing to parametric resonance. Previous investigations have been concentrated on in-plane dynamic buckling of pin-ended shallow arches. However, in engineering practice, fixed arches with different rise-to-span ratios are often encountered. Little research on in-plane dynamic instability of deep fixed arches has been reported in the literature. This paper is concerned with experimental and analytical investigations for in-plane dynamic instability of fixed circular arches with rise-to-span ratios 1/8–1/2 under a central periodic load owing to parametric resonance. Experiments are carried out to determine the in-plane frequency and damping ratio of arches, to investigate critical regions of frequencies and amplitudes of the periodic load for in-plane dynamic instability of arches, and to explore effects of the rise-to-span ratio and additional weights on dynamic instability. The analytical method for determining the region of excitation frequencies and amplitudes of the periodic load causing in-plane instability of the arch is established using the Hamilton’s principle by accounting for effects of additional concentrated weights. Comparisons of analytical solutions with test results show that they agree with each other quite well. These results show that the rise-to-span ratio significantly influences the bandwidth of regions of critical excitation frequencies for in-plane dynamic instability of arches. The critical frequencies of the periodic load and their bandwidth increase with a decrease of the rise–span ratio of the arch, whereas the corresponding amplitude of the periodic load decreases at the same time. It is also found that the central concentrated weight influences in-plane dynamic instability of arches significantly. As the weight increases, the critical frequencies of excitation and their bandwidth for in-plane dynamic instability of arches decreases, whereas the corresponding amplitude of excitation increases.

Dynamic Instability in Quartering Seas—Part III: Nonlinear Effects on Periodic Motions

1997 ◽  
Vol 41 (03) ◽  
pp. 210-223 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Periodic Motion ◽  
Horizontal Plane ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Nonlinear Phenomena ◽  
Specific Sequence ◽  
The Stability ◽  
Two Stages

The loss of stability of the horizontal-plane periodic motion of a steered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go through the surf-riding stage. However, about this point the discussion was essentially conjectural. In order to provide substance we present here a theoretical approach that is organized in two stages: Initially, we demonstrate the existence of a mechanism of parametric instability of yaw on the basis of a rudimentary, single-degree model of maneuvering motion in waves. Then, with a more elaborate model, we identify the underlying nonlinear phenomena that govern the large-amplitude horizontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in the stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jump to resonance. Possible means for controlling the onset of such undesirable behavior are also investigated.

Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Jinyu Zhu ◽  
W.-C. Xie ◽  
Ronald M. C. So ◽  
X. Q. Wang
Keyword(s):  
Lyapunov Exponents ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Singular Perturbation Method ◽  
Bounded Noise ◽  
Two Degrees Of Freedom ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Combined Resonance ◽  
Moment Lyapunov Exponents

The dynamic stability of a two degrees-of-freedom system under bounded noise excitation with a narrowband characteristic is studied through the determination of moment Lyapunov exponents. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For weak noise excitations, a singular perturbation method is employed to obtain second-order expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The different cases when the system is in subharmonic resonance, combination additive resonance, and combined resonance in the absence of noise, respectively, are considered. The effects of noise and frequency detuning on the parametric resonance are investigated.

scholarly journals WAVELESS APPROXIMATION THEORIES OF GRAVITY

2008 ◽  
Vol 17 (02) ◽  
pp. 265-273 ◽  
Author(s):  
JAMES A. ISENBERG
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Elliptic Equations ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Accurate Approximation ◽  
Time Step ◽  
Einstein Theory ◽  
Physical Systems ◽  
Theories Of Gravity

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

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