Vibrations of segmented shells
- 225 Downloads
An analytical and experimental investigation was performed to determine the natural frequencies and mode shapes of a cone-cylinder segmented shell. The finite-element technique was used to predict the natural frequencies and mode shapes of a clamped segmented shell. In the experimental phase of the program, the shell was excited by an electromagnet and the natural frequencies were determined with the aid of a microphone. Holographic interferometry was used to identify the mode shapes for each resonant frequency. The analytical and experimental results were in good agreement with one another.
KeywordsMechanical Engineer Fluid Dynamics Experimental Investigation Resonant Frequency Mode Shape
coefficient of thei-th term in the assumed displacement field
number of circumferential waves
number of meridional half-waves
i-th generalized coordinate
- \(\dot q_i\)
velocity ofq i
shell meridional coordinate
kinetic energy of the shell, in.-lb
meridional displacement of the shell, in.
strain energy of the shell, in.-lb
circumferential displacement of the shell, in.
normal displacement of the shell, in.
work of the conservative, external loading, in.-lb
shell circumferential coordinate
angle between axis of revolution and normal to shell, rad
natural frequency, rad/sec
rotation of the middle surface
Unable to display preview. Download preview PDF.
- 1.Weingarten, V. I. and Gelman, A. P., “Free Vibrations of Cantilevered Conical Shells,” ASCE, J. of the Eng. Mech. Div. EMG, 127–138 (Dec. 1967).Google Scholar
- 2.Margolias, D. S. and Weingarten, V. I., “Free Vibrations of Pressure Loaded Paraboloidal Shells,” to be published in AIAA J.Google Scholar
- 3.Lashkari, M., “Elastic Stability and Dynamic Analysis of Hyperboloidal Shells of Revolution,” PhD Dissertation, Univ. of Southern California (June 1971).Google Scholar
- 4.Margolias, D. S., “The Effect of External Loading on the Natural Frequencies of Paraboloidal Shells,” PhD Dissertation, Univ. of Southern California (June 1970).Google Scholar
- 5.Sanders, J. L., Jr., “Non-Linear Theories for Thin Shells,”Quarterly of App. Math.,21 (1),21–36 (1963).Google Scholar
- 6.Stroke, G. W., An Introduction to Coherent Optics and Holography, Academic Press, NY (1966).Google Scholar
- 7.DeVelis, J. B. andReynolds, G. O., Theory and Application of Holography, Addison-Wesley Publishing Co., Reading, MA (1967).Google Scholar
- 8.Smith, H. M., Principles of Holography, Wiley-Interscience, a division of John Wiley & Sons, Inc., NY (1969).Google Scholar
- 9.Gabor, D., “A New Microscopic Principle,”Nature,161,777–778 (1948).Google Scholar
- 10.Gabor, D., “Microscopy by Reconstructed Wave Fronts,”Proc. Royal Soc., Series A, London,197,457–464 (1949).Google Scholar
- 11.Leith, E. N. and Upatneiks, J., “Wavefront Reconstruction with Continuous-Tone Objects,” J. Opt. Soc. Am.,53 (1963).Google Scholar
- 12.Leith, E. N. and Upatnieks, J., “Wavefront Reconstruction with Diffused Illumination and Three Dimensional Objects,” J. Opt. Soc. Am.,54 (1964).Google Scholar
- 13.Powell, R. L. andStetson, K. A., “Interferometric Vibration Analysis by Wavefront Reconstruction,”J. Opt. Soc. Am.,55 (12),1593–1598 (Dec. 1965).Google Scholar
- 14.Haines, K. A. andHildebrand, B. P., “Surface Deformation Measurement Using the Wavefront Reconstruction Technique,”App. Op.,5 (4),595–602 (April 1966).Google Scholar
- 15.Lashkari, M., “Elastic Stability and Dynamic Analysis of Hyperboloidal Shells of Revolution,” PhD Thesis, The University of Southern California (1971).Google Scholar