This paper presents a method for solving the dynamic response problems of a driven valve system and the stress problem of valve springs for internal combustion engines. In this system there is hysteresis behavior in the spring constants during the rotation of the cam shaft. To treat this nonlinearity, the rigidity of each section is assumed to be one of a partly linear spring. For the valve trains, the cam profile is complex in general. To treat a general cam profile, this paper applies a combination method of the Fourier expansion, the Laplace transform and the analytical connection methods, and gives a response of valve trains. This paper also presents a theoretical result for the stresses in the valve spring due to the motion of the valve train based on the three dimensional curved beam theory.

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