Formulas for Structural Dynamics: Tables, Graphs and Solutions
By Olga I. Lebed

Definitions

Analytical methods of structural dynamics for redundant systems

See also Force method.

See also Slope-deflection method.

Assumed functions
Linearly independent functions of the spatial coordinate, which satisfy all the boundary conditions of the problem.
Beam Model

See also Bernoulli Euler theory (Elementary beam theory).

See also Timoshenko theory.

See also Love theory.

Bernoulli Euler theory (Elementary beam theory)
The Bernoulli Euler theory takes into account the inertia forces due to the transverse translation and neglects the effect of shear deflection and rotary inertia.
Bolotin functions
Approximate dynamic reactions of beams with distributed masses.
Boundary conditions (BC)
Mathematical conditions that concern linear and angular displacements, the bending moment and shear force at the ends of the beam. Geometric BC describe the transverse and angular displacements at the ends of the beam; natural BC describe the bending moment and shear force at the ends of the beam.
Boussinesq's problems
Free vibration of infinite (and half-infinite) uniform Bernoulli Euler beams.
Castigliano's theorem
The partial derivative of the strain energy in terms of the unit action is equal to the displacement induced by the actual loading along the direction of the said unit action.
Characteristic equation

See also Frequency equation (FE) (characteristic equation).

Chladni figures
The experimental nodal lines for various modes of vibrating plates.
Clapeyron theorem
The products of external forces applied to a deformable body and the components of the displacements, in the directions of these forces at their points of application, are equal to twice the value of the corresponding strain energy of the body.
Copyright The McGraw-Hill Companies, Inc. 2001 under license agreement with Books24x7
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