Harmonic Response of Cylindrical Shells

1974 ◽  
Vol 96 (3) ◽  
pp. 994-999 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Shell Theory ◽  
Excitation Frequency ◽  
Radial Component ◽  
Resonant Response ◽  
Thin Cylindrical Shell ◽  
Harmonic Force ◽  
State Response ◽  
Hysteretic Damping ◽  
Mode Method ◽  
Thin Shell Theory

The normal mode method is used to determine the steady state response of a simply supported, uniform thin cylindrical shell to a radical harmonic force with hysteretic damping included in the analysis. Numerical results are given for the variation with excitation frequency of the radial component of amplitude at different points along the shell for three levels of damping. The response at the resonances, corresponding to the first few modes of each shell, and their convergence, as the number of modes included in the solution is increased, are considered in detail. Novozhilov’s thin shell theory is used in the analysis, but the effects upon resonant response of using other shell theories are discussed.

Reduction of Harmonic Response of Cylindrical Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1371-1377 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cantilever Beams ◽  
Steady State Response ◽  
Optimum Conditions ◽  
Harmonic Force ◽  
Shell Surface ◽  
Single Degree Of Freedom ◽  
Harmonic Response ◽  
State Response ◽  
Single Degree ◽  
Mode Method

The normal mode method is used to investigate the reduction in the steady-state response of a simply supported cylindrical shell when conventional absorbers are attached to the shell. Two types of excitation are considered: (a) a single radial harmonic force, and (b) a harmonic pressure distributed over the shell surface. The effect upon response of varying the absorber parameters is studied. Optimum conditions for specific cases are obtained and compared with those required to minimize response when absorbers are added to cantilever beams and to the classical single degree of freedom system.

scholarly journals Calculation method of locking torque based on elastic thin shell theory for hydraulic locking sleeve

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769269
Author(s):  
Ming Yan ◽  
Hai-Chao Liu
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Calculation Model ◽  
Thin Cylindrical Shell ◽  
Deformation Equation ◽  
Test Platform ◽  
Large Elastic Deformation ◽  
Five Axis ◽  
Thin Shell Theory ◽  
Rotational Freedom

The hydraulic locking sleeve is a key component of precision instruments such as five-axis machine tools, giant astronomical telescope, and satellite antenna. This is subjected to the action of pressure load causing large elastic deformation and locking the rotational freedom of feed shaft at any angle. The maximum locking torque is an important parameter for designing the hydraulic locking sleeve. First, the hydraulic locking sleeve is simplified as elastic thin cylindrical shell structure. Neglecting the bending and twisting effects, the calculation equations describing the deformation and stress state between the hydraulic locking sleeve and rotary shaft are derived by applying the theory of elastic thin shell. Then, taking into account that one end of the hydraulic lock sleeve is fixed to the shaft sleeve seat by the end face flange; the calculating formula of the maximum locking torque of the hydraulic locking sleeve is obtained by modifying the deformation equation based on moment model. Finally, a test platform of hydraulic locking sleeve is designed, which can measure the maximum locking torque of the hydraulic locking sleeve. The error between the calculation result of locking torque theoretical calculation model and the experimental measured value is <15%. As a result, the causes of the error are analyzed, and the effects of the shaft sleeve length, wall thickness, and radius on the maximum locking torque are calculated.

Non-Axisymmetric Dynamic Response of Imperfectly Bonded Buried Orthotropic Thin Empty Cylindrical Shell Due to Incident Shear Wave (SH Wave)

2011 ◽  
Vol 2 (2) ◽  
pp. 40-56
Author(s):  
Rakesh Singh Rajput ◽  
Sunil Kumar ◽  
Alok Chaubey ◽  
J. P. Dwivedi
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Shear Wave ◽  
Shell Theory ◽  
Surrounding Medium ◽  
Sh Wave ◽  
Thin Cylindrical Shell ◽  
Sh Waves ◽  
Stiffness And Damping ◽  
Thin Shell Theory

Non-axisymmetric dynamic response of imperfectly bonded buried orthotropic thin empty pipelines subjected to incident shear wave (SH-wave) is presented here. In the thin shell theory the effect of shear deformation and rotary inertia is not considered. The pipeline has been modeled as an infinite thin cylindrical shell imperfectly bonded to surrounding. A thin layer is assumed between the shell and the surrounding medium (soil) such that this layer possesses the properties of stiffness and damping both. The degree of imperfection of the bond is varied by changing the stiffness and the damping parameters of this layer. Although a general formulation including P-, SV-, and SH-wave excitations are presented, numerical results are given for the case of incident SH-waves only. Comparison of axisymmetric and non-axisymmetric responses are also furnished.

Analysis of Spectral Characteristics of Sound Waves Scattered from a Cracked Cylindrical Elastic Shell Filled with a Viscous Fluid

2013 ◽  
Vol 38 (3) ◽  
pp. 335-350 ◽  
Author(s):  
Olexa Piddubniak ◽  
Nadia Piddubniak
Keyword(s):  
Viscous Fluid ◽  
Shell Theory ◽  
Elastic Shell ◽  
Spectral Characteristics ◽  
Steel Shell ◽  
Sound Waves ◽  
Thin Cylindrical Shell ◽  
Shell Surface ◽  
Theory Approximation ◽  
Directivity Patterns

Abstract The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weak- ened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff-Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical analysis is carried out for a steel shell filled with oil and immersed in seawater. The modules and phases of the scattering amplitudes versus the dimensionless wavenumber of the incident sound wave as well as directivity patterns of the scattered field are investigated taking into consideration the orientation of the slit on the elastic shell surface. The plots obtained show a considerable influence of the slit and viscous fluid filler on the diffraction process.

New Insight Into Energy Harvesting via Axially-Loaded Beams

2009 ◽  
Author(s):  
Mohammed F. Daqaq
Keyword(s):  
Steady State ◽  
Energy Harvesting ◽  
Axial Load ◽  
Excitation Frequency ◽  
Axial Loading ◽  
Response Amplitude ◽  
Resistive Load ◽  
Steady State Response ◽  
State Response ◽  
Axially Loaded

Driven by the study of Leland and Wright [1], this manuscript delves into the qualitative understanding of energy harvesting using axially-loaded beams. Using a simple nonlinear electromechanical model and the method of multiple scales, we study the general nonlinear physics of energy harvesting from a piezoelectric beam subjected to static axial loading and traversal dynamic excitation. We obtain analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. We utilize these expression to study the effect of the axial loading on the overall nonlinear behavior of the harvester. It is demonstrated that, in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in i) increasing the electric damping in the system thereby enhancing the energy transfer from the beam to the electric load, ii) amplifying the effect of the external excitation on the structure, and hence, increases the steady-state response amplitude and output voltage, and iii) increasing the bandwidth of the harvester by enhancing the effective nonlinearity of the system.

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

Turbulence-Induced Vibration Analysis of an Open Curved Thin Shell

2010 ◽  
Author(s):  
Mitra Esmailzadeh ◽  
Aouni A. Lakis
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Root Mean Square ◽  
Thin Shell ◽  
Shell Theory ◽  
Pressure Field ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Cross Spectral Density ◽  
Thin Shell Theory

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of the structure in terms of the cross-spectral density of random pressure fields. The cross-spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis et al.

Study on Static Assembly Interference Pressure between a Thin-Wall Flexible Cup and a Hollow Flexible Shaft

2011 ◽  
Vol 179-180 ◽  
pp. 212-219
Author(s):  
Guo Ping Wang ◽  
Hua Ling Chen ◽  
She Miao Qi ◽  
Jiu Hui Wu ◽  
Lie Yu
Keyword(s):  
Cylindrical Shell ◽  
Pressure Distribution ◽  
Superposition Principle ◽  
Special Solution ◽  
Thin Wall ◽  
Thin Cylindrical Shell ◽  
Bending Deformation ◽  
Flexible Shaft ◽  
First Time ◽  
Thin Shell Theory

Distribution of static interference pressure between a thin-wall flexible cup and a flexible shaft fluctuates heavily along the axis of the cup and is quite different from pressure distribution of common interference styles. In this article, aiming at solving distribution of static interference pressure between a thin-wall flexible cup with much thicker bottom and a hollow flexible shaft, mechanical model and mathematical model of solving the problem were built based on classic thin shell theory. Special difference is that precise special solution of bending equation of thin cylindrical shell was used to substitute the special solution which is original from bending deformation of thin cylindrical shell in no moment status. And a brand new general solution, the relational expression between bending deformation of thin wall of the cup and distribution of the static interference pressure, was obtained. Then, a method used to solve the pressure distribution was presented by solving integral equation and applying superposition principle for the first time. Through using the method to solve an example and comparing calculated results with FEM results, it was proved that the method is correct and effective.

Collapse of Thin Orthotropic Elliptical Cylindrical Shells Under Combined Bending and Pressure Loads

1979 ◽  
Vol 46 (2) ◽  
pp. 363-371 ◽  
Author(s):  
J. Spence ◽  
S. L. Toh
Keyword(s):  
Shell Theory ◽  
Nonlinear Boundary ◽  
Cylindrical Shells ◽  
Normal Pressure ◽  
Nonlinear Ordinary Differential Equations ◽  
Pure Bending ◽  
Finite Deflection ◽  
Shooting Technique ◽  
Theoretical Predictions ◽  
Thin Shell Theory

The elastic collapse of thin orthotropic elliptical cylindrical shells subject to pure bending alone or combined bending and uniform normal pressure loads has been studied. Nonlinear finite deflection thin shell theory is employed and this reduces the problem to a set of nonlinear ordinary differential equations. The resulting two-point nonlinear boundary-value problem is then linearized, using quasi-linearization, and solved numerically by the “shooting technique.” Some experimental work has been carried out and the results are compared with the theoretical predictions.

Quantification of Arterial Stiffness Reduced Effect of Vessel Geometry

2008 ◽  
Author(s):  
Shinichiro Ota ◽  
Toshitaka Yasuda ◽  
Takashi Saito
Keyword(s):  
Mechanical Properties ◽  
Cylindrical Shell ◽  
Arterial Stiffness ◽  
Wall Thickness ◽  
Shell Theory ◽  
Dynamic Strain ◽  
Thin Cylindrical Shell ◽  
Inner Pressure ◽  
Latex Tube ◽  
Mechanical Factors

Arteriosclerosis is such as phenomena hardening of arteries, with thickening and loss of elasticity. Previous indexes include effect of geometric and mechanical factors as the radius, the wall thickness and mechanical properties of arteries. In this study, we proposed viscoelasticity indexes formulated by thin cylindrical shell theory estimated dynamic strain, and this index was independent of wall thickness and radius of arterial vessels. To confirm the validity of these indexes, we evaluated the parameters of viscoelasticity using the latex tube with different wall thickness of blood vessel model. We measured a radius of the latex tube and an inner pressure maintained by a pulsatile pump in a mock circuit filled with the water. Estimating the parameters of elasticity using these measured values, we concluded that a proposal index was independent of the wall thickness of the artery.

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