Free vibration of coil springs of arbitrary shape

This paper is concerned with the method for solving the vibration problem of coil springs of arbitrary shape. In the analysis the exact field transfer matrix is derived from the solution of the fundamental equation of the three‐dimensional curved beam theory. The transfer matrix is given by combining this field transfer matrix and the point transfer matrix. The analysis derives the frequency equation which is applicable to coil springs of general shape. Numerical calculations have been carried out for hyperboloidal springs and barrel springs. Experimental tests also have been carried out to verify the present results.