Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories

Ng, TP; Lam, K.Y.

doi:10.1007/bf01312653

Cited by 21 publications

(8 citation statements)

References 18 publications

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“…To find the dynamic instability boundaries, it is necessary to solve the eigenvalue problems (17)- (19) and (20)- (22). To this end, we use the method of successive approximations with inverse iteration.…”

Section: Problem-solving Methodmentioning

confidence: 99%

“…In the case of layered shells made of viscoelastic composites, the first-order Timoshenko-Reissner shear model [16,21,22] was sometimes used.…”

mentioning

confidence: 99%

“…Very few papers such as [2, 3] mention the possibility of examining compound shell systems with variable parameters, assuming the initial state momentless and homogeneous. The range of studies on such shells was extended because of the following complicating factors: layered structure [10,22,25], orthotropy and viscosity of elastic materials [10,[16][17][18]21], various boundary conditions and types of periodic loads [5,8,23], complex configuration of plates [19], etc. The longitudinally inhomogeneous mechanical characteristics of shells of revolution were taken into account in [2,3].…”

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confidence: 99%

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Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

Bespalova

Urusova

2011

Int Appl Mech

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The paper outlines an approach to identifying the principal dynamic-instability domain for systems composed of shells of revolution with different shapes under axisymmetric periodic loading. The original problem is reduced to one-dimensional eigenvalue problems with respect to the meridional coordinate. Results of calculations for a specific shell system are presented Keywords: shell system, periodic load, dynamic instability domain Introduction. When in service, various shell systems or their components may be subjected to periodic loads that somehow change some characteristics of the system. These are, for example, aircrafts with pulsating thrust, underwater pipelines subjected to external pressure and conveying pulsating flows of oil and gas, mine hoists that periodically interact with the pit-shaft, etc. Problems of the stability of such systems under various loads are of interest for reasons of accident prevention. The theoretical treatment of these problems in the general case involves solution of nonlinear nonstationary dynamic problems for elastic systems and analysis of varying vibration modes and scenarios for the occurrence of irregular modes. The practically important dynamic problem of identifying the instability boundaries may be solved in the linear case. The results of previous relevant studies are covered in [12,13,20].The dynamic stability of plates and cylindrical shells was adequately studied in [5, 10, 16-19, 21, 22, 24, 25]. A considerably fewer publications are concerned with conical and spherical shells [7-9, 23]. Very few papers such as [2, 3] mention the possibility of examining compound shell systems with variable parameters, assuming the initial state momentless and homogeneous. The range of studies on such shells was extended because of the following complicating factors: layered structure [10,22,25], orthotropy and viscosity of elastic materials [10,[16][17][18]21], various boundary conditions and types of periodic loads [5,8,23], complex configuration of plates [19], etc. The longitudinally inhomogeneous mechanical characteristics of shells of revolution were taken into account in [2,3].Parametric vibrations were in most cases studied using the classical Kirchhoff-Love model of thin shells or simplified Donnell's model [2,3,8,9,23]. In the case of layered shells made of viscoelastic composites, the first-order Timoshenko-Reissner shear model [16,21,22] was sometimes used.Nonstationary nonlinear problems are traditionally reduced, by the Bubnov-Galerkin method, to solution of Cauchy problems for dynamic systems with several degrees of freedom and analysis of their solutions for stability. To this end, the finite-difference and finite-element methods may be used as well.Linear problems of identifying the dynamic-instability domains are reduced to a system of Mathieu-Hill equations whose properties are well known [11]. Another approach to identifying the dynamic-instability domains of shells of revolution with longitudinally (meridionally) variable parameters was proposed in [2,3], whe...

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Section: Problem-solving Methodmentioning

confidence: 99%

“…In the case of layered shells made of viscoelastic composites, the first-order Timoshenko-Reissner shear model [16,21,22] was sometimes used.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

Bespalova

Urusova

2011

Int Appl Mech

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“…Applying the Ritz-type mixed variational method [22] to equation (17), i.e. multiplying it by ö9( ô ) and integrating it with respect to ô , form 0 to ô and from 0 to 1, in that order, the following characteristic equation is obtained for finding the critical load:…”

Section: The Solution Of the Differential Equationsmentioning

confidence: 99%

The dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities subject to a time-dependent external pressure

Aksoğan

Sofiyev

2002

The Journal of Strain Analysis for Engineering Design

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This study considers the dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities in the thickness direction, subject to a uniform external pressure, which is a power function of time. Initially, the dynamic stability and compatibility equations of a laminated elastic truncated conical shell with variable elasticity moduli and densities, subject to an external pressure, have been obtained. Then, employing Galerkin's method, those equations have been reduced to a system of timedependent differential equations with variable coefficients. Finally, applying a mixed variational method of Ritz type, the critical dynamic and static loads, the corresponding wave numbers and the dynamic factor have been found analytically. Using those results, the effects of the variations in elasticity moduli and densities, the number and ordering of the layers, the semivertex angle and the power of time in the external pressure expression are studied via pertinent computations. It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading.

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“…Nowadays in many practical engineering problems, the dynamic load acting on a structure is always involved . Once the dynamic load is obtained correctly, it is convenient to use a series of advanced methods to ensure the stability and safety of engineering structures and to satisfy the requirement of modern industry. However, for most practical engineering problems, such as the wind load applied to ocean platforms and the interaction between road and tires, it is relatively hard to measure the dynamic load due to the lack of technology or cost restrictions.…”

Section: Introductionmentioning

confidence: 99%

Time‐domain Galerkin method for dynamic load identification

Liu

Meng

Jiang

et al. 2015

Numerical Meth Engineering

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Summary This paper proposes a new method called time‐domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems. Firstly, the shape functions are adopted to approximate three parameters, such as the dynamic load, kernel function response, and measured structural response Secondly, defining a residual function could be expressed as the difference of the measured response and the computational response. Thirdly, select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero. Finally, when the shape functions are chosen as the weighting function, it establishes the forward model called TDGM. Furthermore, the regularization method could have effectiveness in solving the ill‐posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load. Compared with the traditional Green kernel function method (GKFM), TDGM can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification. Three numerical examples are provided to demonstrate the correctness and advantages of TDGM. Copyright © 2015 John Wiley & Sons, Ltd.

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Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories

Cited by 21 publications

References 18 publications

Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

The dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities subject to a time-dependent external pressure

Time‐domain Galerkin method for dynamic load identification

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