Free vibration of thick isotropic and orthotropic cylindrical shells
The vibration of free, thick cylindrical shells that are composed of either isotropic materials or orthotropic materials like modern composite laminates are studied. The formulation starts with an approximate five-term displacement field that has been used previously. The subsequent approximate strains, stresses, and force and moment resultants are successively substituted into a variational form of Hamilton's principle to yield the governing vibration equations and boundary condition equations. The two sets of equations are solved simultaneously to obtain dimensionless frequencies. The constitutive law for the material is assumed to be orthogonal with respect to the mid-surface coordinate system. Explicit shear coefficients are assumed for all resultants that have a shear stress in their definition. The computer algorithm that solves the equations is explained along with the exception testing for any found frequency. Results mainly consist of contour plots of the first fundamental frequency for a particular circumferential wave number, n, and symmetric or antisymmetric form. Differences with an accurate series solution for the isotropic case are given. Through-thickness shear coefficients are found that would make this formulation agree with the isotropic series solution. A study of higher frequencies is presented and favorably compared to the series solution. Two typical sets of results are presented for orthotropic materials representative of composite laminates that are stiff in the longitudinal and tangential directions. A concluding summary and areas of future work are discussed. 29 refs.
- Research Organization:
- Lawrence Livermore National Lab., CA (United States)
- Sponsoring Organization:
- DOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5523256
- Report Number(s):
- UCRL-LR-109428; ON: DE92011653
- Country of Publication:
- United States
- Language:
- English
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ANALYTICAL SOLUTION
CIVIL ENGINEERING
COMPUTER CODES
COMPUTER PROGRAM DOCUMENTATION
CYLINDERS
DIFFERENTIAL EQUATIONS
DIMENSIONS
ENGINEERING
EQUATIONS
EQUATIONS OF MOTION
FREQUENCY ANALYSIS
FUNCTIONS
HAMILTONIAN FUNCTION
ISOTROPY
MATHEMATICS
MECHANICAL VIBRATIONS
O CODES
PARTIAL DIFFERENTIAL EQUATIONS
STRAINS
STRESS ANALYSIS
STRESSES
WAVE FUNCTIONS