MODIFICATION OF THE MODE SHAPE EXPRESSIONS FOR EULER-BERNOULLI BEAMS

In most vibration text books, the expressions for mode shape functions of Euler-Bernoulli beams in numerical evaluation can only be accurate up to the first 12 modes except for simply-supported boundary condition. The main reason is that these expressions involve the hyperbolic sine and cosine functions, which increase exponentialy as mode index increases. The mode shapes in numerical calculation will distort due to the round-off errors. In this paper, these functions are modified in a different form. With proposed modified expressions, the modes for a vibrating beam can be calculated accurately up to at least the 200th mode.