MODIFICATION OF THE MODE SHAPE EXPRESSIONS FOR EULER-BERNOULL BEAMS

In most vibration text books, the expressions for mode shape functions of Euler–Bernoulli beams in numerical evaluation can only accurate up to the first 12 modes except simply-supported boundary condition. The main reason is that these expressions involve the hyperbolic sine and cosine functions, which are exponential increasing as mode index increasing. 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 vibrating beam can be calculated up to at least the 200th mode accurately.