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On the Nonlinear Vibrations of Free-Free Beams
Journal of Applied Mechanics, 1971A nonlinear partial differential equation which describes the natural free-free vibrations of beamlike structures is derived, and then solved approximately by reduction to a nonlinear ordinary differential equation through the use of the Duffing and Ritz-Kantorovich methods.
Hu, K.-K., Kirmser, P. G.
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Partitioning of the Vibrational Free Energy
The Journal of Physical Chemistry Letters, 2021Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels.
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Vibration of a Free Rectangular Parallelepiped
Journal of Applied Mechanics, 1983A series solution of the general equations of linear elasticity is used to determine accurate natural frequencies for the vibrations of a rectangular parallelepiped with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Resulting frequences are tabulated for comparison with previous
Hutchinson, J. R., Zillmer, S. D.
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Free Vibration of the Rectangular Parallelepiped
The Journal of the Acoustical Society of America, 1970The “associated-periodicity” extension of Fourier analysis is used to obtain an exact solution of the classical, three-dimensional elasticity problem of free vibration of the rectangular parallelepiped. This problem has been completely stated for more than a century and has been solved for only a very few special cases.
Fromme, J. A., Leissa, A. W.
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On the free vibration of shallow shells
Journal of Sound and Vibration, 1995Summary: A finite element method for free vibration analysis of generalized shallow shells is described. Results for natural frequencies of corner-supported hyperbolic paraboloidal, cylindrical and spherical shells are presented and compared with those of other investigators to establish the correctness of the method.
Chakravorty, D., Bandyopadhyay, J. N.
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FREE VIBRATIONS OF ROCKET NOZZLES
Symposium on Structural Dynamics and Aeroelasticity, 1965Fig. 4 Flowfield of a parallel flow nozzle exhausting normal to a concave surface in a vacuum (h/re = 10, RJh = 1.1, R = 60 ft/°R, Me = 4.0, 6e = 0°, 7 = 1.2, Bs = 1.0). 2 Roberts, L., "The action of a hypersonic jet on a dust layer/' IAS Paper 63-50 (1963). 3 Van Dyke, M. and Gordon, H. D., "Supersonic flow past a family of blunt axisymmetric bodies,"
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Free Vibration of Flexible Cables
Volume 8: 27th Conference on Mechanical Vibration and Noise, 2015The free undamped vibrations of cables undergoing stretching, bending and twisting are investigated. To this end, a geometrically exact model of elastic cables accounting for bending and torsional stiffness is employed. The cable kinematics retain the full geometric nonlinearities.
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Free Vibration of Skewed Bridges
Journal of Vibration and Control, 2001Determination of period of vibration is an essential step in understanding the seismic behavior of bridges. In this paper, an analytical solution for the free vibration problem of slab-beam, single-span skewed bridges is derived. It is assumed that the deck acts as a rigid diaphragm, but the effects of cross-frame and elastomeric bearing stiffnesses at
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Free-Free Vibration Extraction From Available Vibration Data
Recent Advances in Solids and Structures, 2000Abstract This paper presents a procedure for identifying the free-free vibration data of a structure from the available vibration data of the same structure with boundary conditions. For a structure in a mechanical system, depending upon the dynamic formulation used, we may need a set of free-free modal data or a set of constrained modal
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