An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.

Exact Solutions of Moderately Thick Laminated Shells

Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells

A generalized Duhamel-Neumann form of Hooke's law is used to develop laminated plate equations which include the effect of expansional strains. Such strains are induced in composite materials by temperature, absorption by a polymeric matrix material of a swelling agent such as water vapor, and by sudden expansion of absorbed gases in the matrix. Solutions to specific boundary value problems are presented for both symmetric and nonsymmetric laminates. Numerical results indicate that in addition to inducing residual stresses, expansional strains can substantially affect the gross response characteristics of a composite material.

Effect of Environment on the Elastic Response of Layered Composite Plates

This paper is concerned with free vibration characteristics of the functionally graded graphene reinforced porous nanocomposite cylindrical shell with spinning motion. It is assumed that the graphene platelet (GPL) nanofillers and internal pores are randomly oriented and uniformly dispersed in each concentric cylindrical shell, and both the GPL weight fraction and the porosity coefficient vary continuously along the thickness direction. Effective material properties of the nanocomposite which are position-dependent are derived employing the modified Halpin-Tsai model and the rule of mixture. Three types of the GPL patterns and four types of the porosity distributions are considered. Frequencies of forward and backward travelling waves and critical spinning speeds are derived from the equations of motion which are established based on the first order shear deformation theory and the Hamilton's principle. Detailed parametric studies on dimensionless natural frequencies and critical spinning speeds of the GPL reinforced porous nanocomposite cylindrical shell are carried out, especially, effect of initial hoop tension on vibration characteristics of the spinning cylindrical shell is numerically discussed.

Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion

Many electroactive functional materials have been used in small- and microscale transducers and precision mechatronic control systems for years. It was not until the mid-1980s that scientists started integrating electroactive materials with large-scale structures as in situ sensors and/or actuators, thus introducing the concept of smart materials, smart structures, and structronic systems. This paper provides an overview of present smart materials and their sensor/actuator/structure applications. Fundamental multifield optomagnetopiezoelectric-thermoelastic behaviors and novel transducer technologies applied to complex multifield problems involving elastic, electric, temperature, magnetic, light, and other interactions are emphasized. Material histories, characteristics, material varieties, limitations, sensor/actuator/structure applications, and so forth of piezoelectrics, shape-memory materials, electro- and magnetostrictive materials, electro- and magnetorheological fluids, polyelectrolyte gel...

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Smart Materials, Precision Sensors/Actuators, Smart Structures, and Structronic Systems

Axisymmetric vibrations of radially polarized piezoelectric ceramic cylinders

A general thermoelastic theory for thin aeolotropic plates that are heterogeneous in the thickness direction may be formulated in terms of two simultaneous equations for the transverse deflection, w, and the Airy stress function, F. From these equations, thermal coupling terms appear, in addition to the interaction of stretching and bending. Applying the theory to the case of uniform heating of long rectangular heterogeneous plates yields explicit equations for the transverse deflection, the in-plane forces, and couples that arise in a uniformly heated plate. A cross-thermoelastic phenomenon is exemplified in the stress-resultants and couples relations. The linear theory may be extended to include finite deflections. The pre-thermal and post-thermal buckling states, in a heterogeneous plate, require the simultaneous determination of w and F.

Thermoelasticity of Heterogeneous Aeolotropic Plates

On vibrations of heterogeneous orthotropic cylindrical shells.

This paper is concerned with the steady−state radial−shear vibrations of an axially polarized piezoelectric ceramic tube of infinite length, whose cylindrical surfaces are either traction−free or subjected to a relative displacement. Open− and short−circuit resonant frequency equations are formulated and the deviation between frequency pairs examined numerically. Fundamental resonant frequency curves are given for traction−free PZT−4 cylinders having arbitrary geometry, which approach the infinite plate solutions for large radius/thickness ratios. The theory is applied to the vibrations of annular accelerometers operating in the radial−shear mode.Subject Classification: 40.26.

Yehuda Stavsky

Papers

Axisymmetric vibrations of radially polarized piezoelectric ceramic cylinders

Thermoelasticity of Heterogeneous Aeolotropic Plates

On vibrations of heterogeneous orthotropic cylindrical shells.

Radial vibrations of axially polarized piezoelectric ceramic cylinders

Vibrations of radially polarized composite piezoceramic cylinders and disks