结构动力学习题集.pdfVIP

课程名称：结构动力学 所属院校：北京交通大学 课程级别：硕士研究生 习题集 1.12 重物w 悬挂在简支梁跨中的一个弹簧上（图P1.12 ），梁长为L ，弯曲刚度为EI ，弹簧 刚度为k ，假定梁无质量，试求其固有频率。 1.19 将汽车粗略地理想化为一个集中质量支撑在一个弹簧－阻尼器系统上，如图 P1.19 所 示。汽车以恒定不变的速度v 通过路面，路面的平整度为路面位置的一个已知函数。试推导 运动方程。 (从自重下的平衡位置处起算) 带*号的题需用计算机编程求解 1/13 课程名称：结构动力学 所属院校：北京交通大学 任课教师：刘 林 课程级别：硕士研究生 Problem Plus1 for Ch1 (please do it in English) Derive the equations of motion for the following pendulum system. The rod length is L , and its mass density is uniform across its surface area. Assume b L (so make small angle approximations). Mass density is ρ but total mass of rod is m. Note: the term “rod” does not imply a simple rod. a. Derive the equation of motion of the system. b. Simplify the equation of motion assuming the displacement angle, θ, is small c. Determine the natural frequency of the rod system based on the simplified equation of motion in part (b). d. The same rod is taken and now rotated about a new pivot point (as shown below). Find the natural frequency of the new rod system configuration. Again, make small angle approximations to find the rod’s equation of motion. e. Compare the natural frequency from part (c) and (d). The new pivot point is termed the CENTER of PERCUSSION 带*号的题需用计算机编程求解 2/13 课程名称：结构动力学 所属院校：北京交通大学 任课教师：刘 林 课程级别：硕士研究生 Problem Plus2 for Ch1 (please do it in English) Determine the equation of motion of the following system using the Principle of Virtual Work.