Dynamic Actuation and Quadratic Magnetoelastic Coupling of Thin Magnetostrictive Shells

2005 ◽  
Vol 128 (3) ◽  
pp. 385-391 ◽  
Author(s):  
H. S. Tzou ◽  
W. K. Chai ◽  
M. Hanson
Keyword(s):  
Mathematical Model ◽  
Thin Shell ◽  
Shell Theory ◽  
Thin Shells ◽  
Free Energy Function ◽  
Dynamic Coupling ◽  
Double Curvature ◽  
System Equations ◽  
Gibb’S Free Energy ◽  
Thin Shell Theory

Smart adaptive structures and structronic systems have been increasingly investigated and developed in the last two decades. Although smart structures made of piezoelectrics, shape-memory materials, electrostrictive materials, and electro-/magnetorheological fluids have been evaluated extensively, studies of magnetostrictive continua, especially generic mathematical model(s), are still relatively scarce. This study is to develop a generic mathematical model for adaptive and controllable magnetostrictive thin shells. Starting with fundamental constitutive magnetostrictive relations, both elastic and magnetostrictive stresses, forces, and moments of a generic double-curvature magnetostrictive shell continuum subject to small and moderate magnetic fields are defined. Dynamic magnetomechanical system equations and permissible boundary conditions are defined using Hamilton's principle, elasticity theory, Kirchhoff-Love thin shell theory and the Gibb's free energy function. Magnetomechanical behavior and dynamic characteristics of magnetostrictive shells are evaluated. Simplifications of magnetostrictive shell theory to other common geometries are demonstrated and magnetostrictive/dynamic coupling and actuation characteristics are discussed.

Constitutive Modeling of Controllable Electrostrictive Structronic Thin Shells

2002 ◽  
Author(s):  
H. S. Tzou ◽  
W. K. Chai
Keyword(s):  
Smart Materials ◽  
Thin Shell ◽  
Shell Theory ◽  
Piezoelectric Materials ◽  
Thin Shells ◽  
Free Energy Function ◽  
Double Curvature ◽  
Coupling Equations ◽  
System Equations ◽  
Thin Shell Theory

Electrostrictive material is one of the key smart materials, with tremendous potentials in many engineering applications, e.g., sonar, actuators, artificial muscles, etc. The (direct) electrostrictive effect of electrostrictive materials is a quadratic dependence of stress or strain on applied electric field and this nonlinear electromechanical effect contributes significant actuation performance as compared with that of conventional piezoelectric materials. A generic electrostrictive thin shell theory and its dynamic electro-mechanical system equations are derived based on a generic double-curvature thin shell defined in the paraelectric phase. Generic mathematical models and permissible boundary conditions of electrostrictive thin shells are defined based on Hamilton’s principle, elasticity theory, Kirchhoff-Love thin shell theory and Gibbs elastic free energy function. Electro-mechanical behaviors and dynamic characteristics of electrostrictive shells are evaluated. Simplifications of the generic electrostrictive shell theory to other common geometries are demonstrated, electrostrictive/dynamic coupling equations derived, and their electromechanical characteristics discussed.

Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies

2019 ◽  
Vol 24 (3) ◽  
pp. 451-457
Author(s):  
Yeong-Bin Yang ◽  
Jae-Hoon Kang
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Thin Shells ◽  
Thick Shell ◽  
Cylindrical Coordinates ◽  
Thin Shell Theory

Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary conditions. The sinusoidal-shaped shells are very similar to paraboloidal shells in shape. The frequencies of the sinusoidal-shaped shells from the present 3-D method are compared with those from 2-D thin shell theories for paraboloidal shells. The present 3-D method is applicable to very thick as well as thin shells.

Vibration of thick curved shells, with particular reference to turbine blades

1970 ◽  
Vol 5 (3) ◽  
pp. 200-206 ◽  
Author(s):  
S Ahmad ◽  
R G Anderson ◽  
O C Zienkiewicz
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Turbine Blades ◽  
Shell Element ◽  
Thin Shells ◽  
Thick Shell ◽  
Shear Deformations ◽  
Vibration Problems ◽  
Thin Shell Theory

The application of a new thick shell element is described with reference to vibration problems. The element is derived from the general isoparametric solid and therefore allows shear deformations to be included. It can take up highly distorted shapes and is useful in such studies as vibration of turbine blades for which it is superior to elements based on thin-shell theory. This element can also be used for thin shells with caution, excessive length/thickness ratios being avoided.

On the Derivation of Parametric Terms in the Equations of Elastic Stability of Thin Shells

1985 ◽  
Vol 9 (3) ◽  
pp. 121-124
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Elastic Stability ◽  
Energy Functional ◽  
Thin Shells ◽  
Thin Shell Theory

In this paper, the parametric terms in the equations of elastic stability of thin shells will be derived in a way that appears to be simpler than those found in the literature. The result matches the solution given by Bolotin in 1967 but has been obtained by avoiding the energy functional of thin shell theory. The parametric terms account for the influence of prebuckling loads, membrane forces and their derivatives and are therefore of some significance in formulating the comprehensive stability equations for a variety of shell geometries.

Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies

2019 ◽  
Vol 24 (2) ◽  
pp. 451-457
Author(s):  
Yeong-Bin Yang ◽  
Jae-Hoon Kang
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Thin Shells ◽  
Thick Shell ◽  
Cylindrical Coordinates ◽  
Thin Shell Theory

Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary conditions. The sinusoidal-shaped shells are very similar to paraboloidal shells in shape. The frequencies of the sinusoidal-shaped shells from the present 3-D method are compared with those from 2-D thin shell theories for paraboloidal shells. The present 3-D method is applicable to very thick as well as thin shells.

Kinetic Analysis of a Cylindrical Shell Partially Treated with Constrained Layer Damping

2010 ◽  
Vol 34-35 ◽  
pp. 1299-1304 ◽  
Author(s):  
Xiang Zhang ◽  
Jing Jun Lou ◽  
Shao Chun Ding
Keyword(s):  
Mathematical Model ◽  
Cylindrical Shell ◽  
Thin Shell ◽  
Function Method ◽  
Shell Theory ◽  
Equation Of Motion ◽  
Constrained Layer Damping ◽  
Transfer Function Method ◽  
Passive Constrained Layer Damping ◽  
Thin Shell Theory

This paper presents a transfer function method for a cylindrical shell with a partially passive constrained layer damping (PCLD) treatment. A thin shell theory based on Donnell-Mushtari-Vlasov assumption is employed to yield a mathematical model. The equation of motion and boundary conditions of a cylindrical shell with partially PCLD are derived. The paper provides theory supports for PCLD structure’s engineering applications in submarine weapon field.

scholarly journals Numerical Analysis of Cylindrical Shell under Axial Impact

2021 ◽  
Vol 236 ◽  
pp. 05040
Author(s):  
WX Zhang
Keyword(s):  
Cylindrical Shell ◽  
Thin Shell ◽  
Shell Theory ◽  
Arch Dam ◽  
Material Strength ◽  
Bending Stress ◽  
Double Curvature ◽  
Flat Shell ◽  
Water Conservancy ◽  
Thin Shell Theory

The shell mainly resists the external load by the mid plane stress distributed uniformly along the thickness, rather than the bending stress varying along the thickness. Compared with the traditional flat plate, the shell can make full use of the material strength, so it has greater bearing capacity. In water conservancy projects, shells are widely used, such as double curvature flat shell gate, arch dam and so on. Thin shell theory is a classical theory in shell.

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.

A NEW KIND OF SINGULAR STIFF PROBLEMS AND APPLICATION TO THIN ELASTIC SHELLS

1995 ◽  
Vol 05 (01) ◽  
pp. 47-66 ◽  
Author(s):  
D. CAILLERIE ◽  
E. SANCHEZ-PALENCIA
Keyword(s):  
Asymptotic Behavior ◽  
Local Structure ◽  
Thin Shell ◽  
Spectral Properties ◽  
Shell Theory ◽  
Stiff Problems ◽  
Medium Frequency ◽  
Limit Solution ◽  
General Configuration ◽  
Thin Shell Theory

We consider the asymptotic behavior of the solution of a class of problems involving a small parameter ε and ε2. This generalizes the “singular stiff” problems arising in classical thin shell theory. The new problems appear in theory of composite shells, when the local structure implies coupling between membrane stresses and flexions. According to specific hypotheses, this kind of problems contains singular perturbations and penalty problems where the limit solution belongs to a subspace G1 of the general configuration space V. In addition to the coercive problem, spectral properties are considered in the small and medium frequency ranges, including spectral families in the case without compactness.

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