对矩形截面非圆柱(锥形、桶形、双曲形)螺旋弹簧的自由振动问题进行了研究.在弹簧的运动微分方程中,首次考虑了簧丝截面的翘曲变形对固有频率的影响.采用改进的Riccati传递矩阵法对包括14个自由度的一阶变系数常微分方程组进行了求解.为了证明理论的有效性,对两端固支矩形截面非圆柱螺旋弹簧的固有频率进行了求解,同时给出了各种参数变化对两端固支矩形截面锥形弹簧固有频率的影响.计算表明,翘曲变形对矩形截面非圆柱螺旋弹簧的固有频率有着重大的影响,在自由振动分析中必须加以考虑.%Free vibration analysis of non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with rectangular cross-section is performed. The effects of the warping deformation of wire cross-section on the natural frequencies are first studied in the differential equations of motion for the springs. Improved Riccati transfer matrix method is introduced to solve the first order ordinary differential equations with variable coefficients, which consist of 14 degrees of freedom. The natural frequencies of non-cylindrical helical springs with rectangular cross-section and clatnped-clamped boundary condition are calculated to validate the proposed method, and the effects of various parameters on the natural frequencies of the clamped-clamped conical springs with rectangular cross-section are also investigated. Calculations show that the warping effect upon the natural frequencies is prominent, which should be considered in the free vibration analysis of the springs.
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