Modified Hermitian cubic spline wavelet on interval finite element for wave propagation and load identification

• We present modified Hermitian cubic spline wavelets on interval (HCSWI).
• Positive question-wave propagation and inverse question-load identification is verified.
• The results have higher precision and cost less time on mechanical structure.
• HCSWI has prominent advantages of improving the precision.

Accuracy and efficiency are significant factors in wave propagation and load identification of mechanical structure. By introducing modified Hermitian cubic spline wavelets on interval (HCSWI), a multi-scale wavelet-based numerical method is proposed. The present method can avoid the boundary problem of the original Hermitian interpolation wavelet. A modified Hermitian interpolation wavelet base can get transformation matrix, so the modified Hermitian wavelet finite element is proposed in this paper. Positive question-wave propagation and inverse question-load identification is verified by this means. The modified Hermitian wavelet finite element involves wave propagation and load identification in rod and Timoshenko beam which are obtained and then compared with results calculated by traditional finite element method (TFEM) and B-spline wavelet on interval (BSWI) finite element. The results indicate that the present method for wave propagation and load identification has higher precision and costs less time on mechanical structure.