The geometrically nonlinear impact dynamical equations of a structural system with tilted spring supports were established under the action of semi-sinusoidal impulse. To evaluate the shock characteristics of the tilted spring supports, a new concept of three-dimensional shock response spectra was proposed. The ratio of the maximum shock response acceleration of the system to the peak pulse acceleration, the angle of the tilted spring support and the dimensionless pulse duration were three basic parameters of the three-dimensional shock response spectra. The effects of the angle of tilted spring support, the dimensionless pulse duration, the dimensionless peak pulse acceleration and damping ratio on the shock response were analyzed using the fourth order Runge-Kutta method. It is shown that there is a sensitive area of the shock response to the dimensionless pulse duration, and this area can be avoided by controlling the stiffness of the tilted spring support. The effects of the angle of the tilted support of the system are noticeable. As the angle of the tilted support of the system is reduced, the sensitive area of the maximum shock response of the system will be expanded. As the peak pulse acceleration is increased, the maximum shock response of the system will fluctuate violently and the sensitive area will be expanded. Increasing the damping can obviously improve the anti-shock characteristics of the system.%以斜支承弹簧系统为研究对象,考虑半正弦波脉冲激励,建立系统几何非线性冲击动力学方程.以系统响应加速度峰值与脉冲激励幅值之比为描述系统的响应指标,系统支承角及无量纲脉冲时间为变量,构建系统三维冲击谱.利用四阶龙格-库塔数值积分讨论系统支承角、无量纲脉冲激励时间、无量纲脉冲激励幅值以及系统阻尼等对系统响应的影响.研究表明,系统响应对脉冲激励时间存在敏感区域,控制系统的刚度可避开敏感区；系统支承角对响应影响较大,随支承角的减小,系统响应峰值敏感区域变大；随脉冲激励幅值增加系统响应峰值波动加剧,且敏感区域变大；增加系统阻尼可有效地改善系统抗冲击特性.
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