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

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.

A Study of the Hydroelastic Instabilities of Supercavitating Hydrofoils

1960 ◽  
Vol 4 (04) ◽  
pp. 28-38
Author(s):  
Paul Kaplan ◽  
C. J. Henry
Keyword(s):  
Dynamic Instability ◽  
Experimental Studies ◽  
Surface Flow ◽  
Small Range ◽  
Equal Importance ◽  
Static Instability ◽  
Elastically Restrained ◽  
Density Ratios ◽  
Oscillating Foil ◽  
Stream Direction

Presented herein are the results of a theoretical study of the static and dynamic hydroelastic instabilities of rigid supercavitating hydrofoils on elastic supports. A two-dimensional theory is used to define the unsteady hydrodynamic force and moment acting on the oscillating foil, which is assumed to be elastically restrained in translation normal to the free-stream direction and in rotation about a prescribed axis which is normal to the plane of flow. All other motions are neglected. The effects of variation in the elastic and inertial properties, as well as the effect of varying the position of the upper surface flow-separation point on the possibility of either form of instability, are determined. Also, the effect of cavitation number over a small range near zero is hypothesized. The theory predicts that dynamic instability (bending-torsion flutter) is possible at the density ratios typical of supercavitating operation. This is in contrast to the results for fully-wetted flow, where the occurrence of flutter is unlikely at the structural-to-fluid density ratios typical of hydrodynamic operation. The flutter possible in supercavitated operation is also more severe than that indicated for fully-wetted flow. Furthermore, it is shown that for the supercavitating hydrofoil, static instability (torsional divergence) and dynamic instability are of equal importance which again differs from the results in fully-wetted flow where static instability was shown to be the more important practical problem. Recommendations are made for experimental studies to verify these theoretical 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.

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).

Effect of fixation stitches on out-of-plane response of textile non-crimp fabric composites

2018 ◽  
Vol 48 (7) ◽  
pp. 1151-1166 ◽  
Author(s):  
Somen K Bhudolia ◽  
Kenneth KC Kam ◽  
Pavel Perrotey ◽  
Sunil C Joshi
Keyword(s):  
Fracture Toughness ◽  
Composite Laminates ◽  
Peak Load ◽  
Experimental Studies ◽  
Critical Energy ◽  
Critical Energy Release Rate ◽  
Mode I Fracture Toughness ◽  
Out Of Plane ◽  
Static Indentation ◽  
Sem Investigation

Non-crimp fabrics are fabric tapes stitched to an adjacent orthogonal fabric with no associated crimp. In the current research, the effect of fixation polyester stitches in improving through-the-thickness properties of non-crimp fabric composite laminates is investigated. Detailed experimental studies on interlaminar fracture toughness and static indentation properties of stitched and unstitched thin ply carbon fibre epoxy composites have been conducted. About 23% higher peak load and 37% higher energy absorption were noticed during static indentation tests for the stitched ply composites. A detailed SEM investigation has shown that the stitch-stitch interaction ‘within a bi-angle ply’ and ‘between the bi-angle ply’ plays a significant role in reducing the delamination extent. The critical energy release rate during Mode I fracture toughness of stitched composites was found to be 26.5% higher and SEM investigation depicted that the stitches promote the intra-laminar delamination and enhance the toughness of the composite.

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

Parametric Resonance Based Piezoelectric Micro-Scale Resonators: Modeling and Theoretical Analysis

2011 ◽  
Author(s):  
Pooya Ghaderi ◽  
Andrew J. Dick
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Single Mode ◽  
Electric Signal ◽  
Dynamic Force ◽  
Mode Behavior ◽  
Out Of Plane ◽  
Three Degree Of Freedom ◽  
Plane Oscillations ◽  
Beam Component

In this study, a two-component auto-parametric resonator utilizing piezoelectric actuation is proposed. The resonator consists of a plate component which serves as the exciter and a beam component which serves as the oscillator. When an electric signal is applied, the plate component experiences in-plane oscillations which serve to provide axial excitation to the beam component. The system is designed to operate in auto-parametric resonance with a plate to beam principal frequency ratio of 1:2. Due to the oscillations of the beam component, a dynamic force and a moment are applied to the plate and can cause out-of-plane oscillations of the plate component. Internal-resonance can also exist between the beam oscillations and the out-of-plane vibrations of the plate component. A model is derived in order to describe these three motions and the coupling between them. By assuming single mode behavior for each motion, the model is discretized and represented with a three degree-of-freedom model. The model is solved analytically by using the method of multiple scales. Results of the perturbation method agree well with the numerical simulation. The results for the system with strong and weak coupling between the resonator components are presented and compared.

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