CAJ | 학술논문

由于变形体力学的广义变分原理在有限元素法和其他近似计算方法的应用方面取得重大成功,各国学者努力将广义变分原理的研究推广到分析力学中去.经过长期研究,明确了分析力学初值问题的控制方程,按照广义力和广义位移之间的对应关系,将各控制方程卷乘上相应的虚量并代数相加,考虑到系统的非保守特性,进而建立了非保守分析力学初值问题的拟变分原理和广义拟变分原理,并推导了相应的拟驻值条件.应用卷积型拟势能变分原理研究了有粘性阻尼的单自由度受迫振动系统,得到系统的振动方程及随阻尼衰减解和稳态解.
유우변형체역학적엄의변분원리재유한원소법화기타근사계산방법적응용방면취득중대성공,각국학자노력장엄의변분원리적연구추엄도분석역학중거.경과장기연구,명학료분석역학초치문제적공제방정,안조엄의력화엄의위이지간적대응관계,장각공제방정권승상상응적허량병대수상가,고필도계통적비보수특성,진이건립료비보수분석역학초치문제적의변분원리화엄의의변분원리,병추도료상응적의주치조건.응용권적형의세능변분원리연구료유점성조니적단자유도수박진동계통,득도계통적진동방정급수조니쇠감해화은태해.
The generalized variational principles in the mechanics of deformable bodies were a great success in the finite element method and other approximate calculation methods. Following this, international scholars made efforts to popularize the generalized variational principles in analytical mechanics. The governing equations of initial value problems in analytical mechanics were settled through extensive research. According to the corresponding relations between generalized forces and generalized displacements, the governing equations were convol-multiplied by corresponding virtual quantities, and then added algebraically. After considering the non-conservative characteristics of the system, the quasi-variational principles and the generalized quasi-variational principles of initial value problems in non-conservative analytical mechanics were established and the corresponding quasi-stationary condition was deduced. Based on convolution type quasi-potential variational principles, the single degree of freedom of a forced vibration system with viscous damping was studied. The system's vibration equations were obtained, as well as a decay solution with damping and a stationary solution.