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Natural Frequency Methods Page

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 METHODS FOR DERIVING EQUATIONS OF MOTION AND DETERMINING NATURAL FREQUENCY
Energy Method: energy.pdf
Lagrange's Equation: Lagrange.pdf
RAYLEIGH METHOD
Rayleigh's Method: Rayleigh.pdf

Bending Frequency of a Fixed-Fixed Beam via the Rayleigh Method: fixed_fixed_beam.pdf
The Fundamental Frequency of an Isolated Circular Plate: circular_elastic.pdf
The Fundamental Frequency of an Isolated Annular Plate: annular_elastic.pdf
The Natural Frequency of a Rectangular Plate Point-Supported at Each Corner: plate_point_corner.pdf
RAYLEIGH-RITZ METHOD
Rayleigh-Ritz Method for Beams and Rods: Ritz.pdf
MORE EXAMPLES
Spring-Cylinder System excited by a moving floor: cylinder_moving_floor.pdf
Semi-definite System Examples: semidefinite.pdf

See also Structural Dynamic Classical Methods Page

 Software

 Executable

 Source
This program calculates the fundamental frequency of a cantilever tapered beam with a circular cross-section.
 tapered_beam_rayleigh.exe
 tapered_beam_rayleigh.cpp

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