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首页> 外文期刊>Journal of Mechanical Design >Steady-State Response of Periodically Time-Varying Linear Systems, With Application to an Elastic Mechanism
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Steady-State Response of Periodically Time-Varying Linear Systems, With Application to an Elastic Mechanism

机译：时变线性系统的稳态响应及其在弹性机构中的应用

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This paper presents the development of an efficient and direct method for evaluating the steady-state response of periodically time-varying linear systems. The method is general, and its efficacy is demonstrated in its application to a high-speed elastic mechanism. The dynamics of a mechanism comprised of elastic members may be described by a system of coupled, inhomogeneous, nonlinear, second-order partial differential equations with periodically time-varying coefficients. More often than not, these governing equations may be linearized and, facilitated by separation of time and space variables, reduced to a system of linear ordinary differential equations with variable coefficients. Closed-form, numerical expressions for response are derived by dividing the fundamental time period of solution into subintervals, and establishing an equal number of continuity constraints at the intermediate time nodes, and a single periodicity constraint at the end time nodes of the period. The symbolic solution of these constraint equations yields the closed-form numerical expression for the response. The method is exemplified by its application to problems involving a slider-crank mechanism with an elastic coupler link.
机译：本文提出了一种评估周期性时变线性系统稳态响应的高效直接方法的开发。该方法是通用的，其有效性在高速弹性机构中的应用得到了证明。由弹性构件组成的机构的动力学可以通过具有周期性时变系数的耦合，非均匀，非线性，二阶偏微分方程组的系统来描述。通常，这些控制方程可以被线性化，并且由于时间和空间变量的分离而变得容易，可以简化为具有可变系数的线性常微分方程组。通过将求解的基本时间段划分为子间隔，并在中间时间节点处建立相等数量的连续性约束，并在该周期的结束时间节点处建立单个周期性约束，可以得出用于响应的闭合形式的数值表达式。这些约束方程的符号解产生了响应的闭式数值表达式。通过将该方法应用于涉及具有弹性联接器连杆的曲柄滑块机构的问题来举例说明该方法。

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