Y. Stavsky

On vibrations of heterogeneous orthotropic cylindrical shells.

Abstract : A refined Love-type theory of motion is established for orthotropic composite cylindrical shells. An extensional-rotational dynamic coupling effect is shown to exist, expressed by R sub 1 inertia terms. An extended version of the theory is formulated to account for dynamic stability problems involving time-dependent and non-conservative forces. The frequency spectra of free natural vibrations are investigated for numerous layered shells, using Love and Donnell-type theories, including the effects of R sub 1 terms. Heterogeneity is found to considerably affect the results for the natural frequencies; for certain shells produced of a fixed amount of materials, differing only in their arrangement, a suitable composition raises the lowest frequency by a factor of 1.50. A study of the error involved in a Donnell-type theory is carried out. For length-to-radius ratios of about 5 the resulting first lowest frequency may be higher by a factor of 1.10 than the one given by the present Love-type theory. However, when higher frequencies are considered this factor may go down to 0.66. These deviations are, in several instances, associated with different predictions of the corresponding lowest characteristic mode shapes. Higher errors, strongly depending on shell heterogeneity, are noted as the length-to-radius ratios increase beyond 5.

Radial vibrations of axially polarized piezoelectric ceramic cylinders

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.

Axisymmetric Vibrations of Isotropic Composite Circular Plates

A Kirchhoff‐type theory is established for axisymmetric motions of heterogeneous isotropic circular plates. It is shown that a coupled extensional‐flexural inertia term exists, in addition to the classical extensional and rotatory inertia terms. An analogy is found between the composite plate problem and the vibrations of homogeneous shallow spherical shells. The obtained sixth‐order system of equations is solved in closed form in terms of Bessel functions, with an argument determined from a characteristic cubic equation. A transcendental frequency equation is then derived for a circular composite plate with clamped edge conditions. Numerous examples are studied, showing the significant effect of plate heterogeneity on its vibrational response. Possibility of composite systems to transcend the frequencies of the individual constituents is clearly indicated by the theoretical results and checked experimentally.

Vibrations of radially polarized composite piezoceramic cylinders and disks

Abstract Eigenfrequency equations are derived for the resonance and antiresonance of long tubes and thin disks composed of n radially polarized piezoceramic materials bonded at their cylindrical interfaces. Numerical solutions are presented for steel/PZT-4/steel transducers, along with the corresponding effective electromechanical coupling factors. The results obtained provide for an efficient design of piezoceramic bandpass filters and other composite transducer devices.

Free vibrations of spinning composite cylindrical shells

Abstract The free vibrations of rotating laminated filament-wound cylindrical shells have been investigated. The exact solution procedure was formulated for general field equations and general boundary conditions, arbitrary combinations of lamina materials and fiber orientation. A parametric investigation of the free vibrations spectra has been carried out. The main characteristics of spinning composite shells are presented and discussed as functions of the filament-winding angles, various layups and the rotational velocity.

Radial vibrations of orthotropic laminated hollow spheres

The three-dimensional elasticity problem of the radial vibrations of a composite hollow spherical shell laminated of spherically orthotropic layers is considered. After formulating the equations, the exact determinantal equation from which the frequencies of vibration can be extracted is developed. Some calculated results for combinations of isotropic and orthotropic materials indicate the sensitivity of the frequencies to the geometry and material make up of the shells.

Asymmetric Vibrations of Polar Orthotropic Laminated Annular Plates

A theory of general nonsymmetric motion of heterogeneous orthotropic annular plates in terms of radial, circumferential, and transverse displacements is formulated. The eighth-order system of equations obtained generalizes earlier results on axisymmetric vibrations of laminated plates, as well as asymmetric vibrations of symmetrically laminated plates. The eigenvalue problem is solved numerically by the Goodman-Lance method. Accuracy of solution is retained by using the Godunov-Conte criterion of orthonormaliz ing the base solutions at each point where the least angle between the relevant pair of base vectors is less than a specified tolerance. Numerous examples are presented indicating the effect of plate heterogeneity on the vibration spectrum. An interesting feature is that the density of the eigenfrequencies in laminated plates may be higher than that of the homogeneous plates.

Thermoelasticity of heterogeneous orthotropic cylindrical shells

Abstract The axisymmetric linear quasi-static thermoelastic equations for composite orthotropic cylindrical shells are solved in closed form for fixed-end boundary conditions. The case of semi-infinite shell is explicitly evaluated and various combinations of laminated shells are examined. It is shown that 1. (1) shell heterogeneity, or the layer reversal effect for two-layer shells, may significantly affect the stress field obtained and its level; 2. (2) the combined action of the composed layers transcends the sum of the individual properties and provides, in many cases, new performance unattainable by the constituents when acting as homogeneous shells; 3. (3) a cross-thermoelastic effect is exhibited by the stress distribution for the considered composite shells.

Axisymmetric vibrations of orthotropic composite circular plates

Abstract A sixth order system of equations of motion is formulated in terms of the radial and transverse displacements for axisymmetric vibrations of circular plates laminated of polar orthotropic plies. Previous results for heterogeneous isotropic circular plates are included as a special case in the present theory. It is shown that a coupling exists between extensional and flexural vibrations through the plate elastic coefficients Brr and Bθθ, and an inertia term R1. The eigenvalue problem is solved numerically, by using a finite difference method, and results are presented for various two and triple layer composites. The eigenfrequencies are found to be quite sensitive to material anisotropy and plate lay-up.

A boundary-perturbation finite element method for plane elasticity problems

Abstract A boundary perturbation (BP) technique is combined with a finite element (FE) scheme to facilitate the solution of two-dimensional boundary value problems associated with imperfect boundaries. In this method the actual imperfect boundary is first replaced by a simpler and smoother curve, referred to as the ‘ideal boundary’. This leads to the replacement of the original problems which are associated with the ideal boundary. Finally, the simplified problems are solved sequentially by using the finite element method. A general BP formulation is presented in the context of plane elasticity for an arbitrary smooth ideal boundary with an arbitrary smooth distortion, up to and including second order terms. Various computational aspects of the method are discussed. Numerical results for problems in two-dimensional elasticity are given, which demonstrate the applicability of the proposed technique.