On determination of mode shapes of linear continuous systems

Determination of mode shapes of a vibrating system is an important step in vibration analysis. A procedure to determine the mode shapes of linear continuous systems, based on the concept of normal equation, is presented. This procedure is very eective, especially when implemented by computers. This method can be applied easily to multistep structures, such as stepped beams and bars. To demonstrate the application of the proposed method, some examples are solved.