Assessment of lateral dynamic instability of columns under an arbitrary periodic axial load owing to parametric resonance

2017 ◽  
Vol 395 ◽  
pp. 272-293 ◽  
Author(s):  
Youqin Huang ◽  
Airong Liu ◽  
Yonglin Pi ◽  
Hanwen Lu ◽  
Wei Gao
Keyword(s):  
Parametric Resonance ◽  
Axial Load ◽  
Dynamic 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.

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.

Dynamic Stability of Simply Supported Beams With Multi-Harmonic Parametric Excitation

2020 ◽  
pp. 2150027
Author(s):  
Chao Xu ◽  
Zhengzhong Wang ◽  
Baohui Li
Keyword(s):  
Parametric Resonance ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Elastic Structures ◽  
Simply Supported ◽  
Response Characteristics ◽  
Positive Effects ◽  
Excited Vibration ◽  
Mdof Systems ◽  
Instability Regions

Determination of the regions of dynamic instability has been an important issue for elastic structures. Under the extreme climate, the external load acting on structures is becoming more and more complicated, which can induce dynamic instability of elastic structures. In this study, we explore the dynamic instability and response characteristics of simply supported beams under multi-harmonic parametric excitation. A numerical approach for determining the instability regions under multi-harmonic parametric excitation is developed here by examining the eigenvalues of characteristic exponents of the monodromy matrix based on the Floquet theorem, and the fourth-order Runge–Kutta method is used to calculate the dynamic responses. The accuracy of the method is verified by the comparison with classical approximate boundary formulas of dynamic instability regions. The numerical results reveal that Bolotin’s approximate formulas are only applicable to the low-order instability regions with a small value of the excitation parameter of simple parametric resonance. Multi-harmonic parametric excitation can significantly change the dynamic instability regions, it may cause parametric resonance on beams for longitudinal complex periodic loads. The influence of frequency and number of multiply harmonics on the parametrically excited vibration of the beam is explored. High-order harmonics with low-frequency have positive effects on the stable response characteristics for multi-harmonic parametric excitation. This paper provides a new perspective for the vibration suppression of parametric excitation. The developed procedure can be used for multi-degree-of-freedom (MDOF) systems under complex excitation (e.g. tsunami waves and strong winds).

Transverse Vibration of a Viscoelastic Column With Initial Curvature Under Periodic Axial Load

1969 ◽  
Vol 36 (4) ◽  
pp. 814-818 ◽  
Author(s):  
K. K. Stevens
Keyword(s):  
Polymethyl Methacrylate ◽  
Transverse Vibration ◽  
Axial Load ◽  
Dynamic Instability ◽  
Complex Modulus ◽  
Lateral Vibrations ◽  
Lateral Response ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
Frequency Curves

The lateral response of a slightly curved viscoelastic column subjected to a periodic axial load P0 + P1 cos ωt is investigated. The analysis makes use of the complex modulus representation for linear viscoelastic materials. It is shown that the lateral vibrations stemming from imperfections can be of significant amplitude. Experimentally determined amplitude-frequency curves for a polymethyl methacrylate (Plexiglas) column are presented, and are found to be in excellent agreement with the theory. It is shown that there is an analogy between the dynamic instability and the static buckling of imperfect columns.

Analytical and experimental studies on out-of-plane dynamic instability of shallow circular arch based on parametric resonance

2016 ◽  
Vol 87 (1) ◽  
pp. 677-694 ◽  
Author(s):  
Airong Liu ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi ◽  
Youqin Huang ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Experimental Studies ◽  
Circular Arch ◽  
Out Of Plane

Prediction of axial hysteresis in locked coil ropes

1996 ◽  
Vol 31 (5) ◽  
pp. 341-351 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Theoretical Model ◽  
Cross Section ◽  
Axial Load ◽  
Dynamic Instability ◽  
Contact Forces ◽  
Damping Capacity ◽  
Outermost Layer ◽  
Parametric Studies ◽  
Load Perturbations ◽  
Practical Implications

In published literature, the strand constructions dealt with have almost invariably involved only wires which are circular in cross-section. There are, however, instances when shaped wires are used in, for example, half-lock and full-lock coil constructions. The paper reports details of a theoretical model which enables an insight to be gained into various characteristics of axially loaded lock coil ropes. The model is based on an extension of a previously reported orthotropic sheet concept and provides a fairly simple means of estimating wire kinematics, interwire/interlayer contact forces, effective axial stiffnesses and axial hysteresis in axially preloaded locked coil ropes experiencing uniform cyclic axial load perturbations. The theory takes interwire contact deformations and friction into account. Final numerical results based on theoretical parametric studies on some substantial cables highlight the substantial role that the outermost layer(s) with shaped wires play as regards the overall axial damping capacity of fully bedded-in (old) locked coil ropes, and it is found that (for the same lay angles and outer diameters) axial hysteresis in locked coil ropes is generally higher than spiral strands which are composed of only round wires. This finding may have significant practical implications in terms of the design against dynamic instability of structures supported by such cables.

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.

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