Abstract: The wavelet-DQ method combines the classic differential quadrature (DQ) method, the multi-resolution analysis theory, and a constructor of scaling function-based interpolation base functions. This is a new method for solving boundary value problems of differential equations. This method is applied to analyze the longitudinal vibration of an elastic straight rod with variable cross-section, to obtain the frequency equation. With different parameters, the natural frequencies of clamped-clamped, free-free wedge-shaped straight rod and cone-shaped straight rod are obtained. Numerical results show that the method is simple and enjoys high-precision. This method can be applied to other mechanical problems in numerical analysis.

Key words: Variable cross-section straight rod, longitudinal vibration, frequency, wavelet-DQ method