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刚弹耦合动力学在国防和民用经济建设中有着广阔的应用前景,但目前还没有完全成熟的理论研究成果。鉴于此,针对刚弹耦合特性,建立初值问题拟变分原理;应用变分方法,推导拟变分原理的拟驻值条件,即得到刚弹耦合动力学的控制方程;给出刚弹耦合动力学初值问题拟变分原理应用的2个算例,1个是应用控制方程求得自由梁的奇数阶振型的解析解,1个是应用变分直接方法 Ritz方法求得自由梁的偶数阶振型的解析解。研究表明,刚弹耦合动力学初值问题拟变分原理为建立有限元计算模型提供了依据。
Just-bouncing coupling kinetics has broad application prospects in national defense and civil economic construction, but there is not yet a full-fledged theoretical research. In view of this, the quasi-variational principle of the initial value problem is established for the just-elastic coupling property. The quasi-stationary value condition of the quasi-variational principle is deduced by using the variational method, that is, the governing equation of the just- Two examples of quasi-variational principles for the initial value problem of dynamics are given. One is the analytic solution of the odd-order modes of a free beam obtained by using the governing equation. One is the solution of a free beam using the Ritz method of the variational direct method Analytic Solutions of Even Order Modes. The research shows that the quasi-variational principle of the initial value problem of the just-coupled dynamic coupling provides the basis for establishing the finite element model.