Exercise Problems

Problem 2.5.1 Use Lagrange equation to derive the equation of motion of the following system. Here, mass is subjected to a periodic force . Also, it is connected to a nonlinear spring in the right side.

Figure 2.5.4: Multi degree of freedom system with nonlinear spring.

Hints:

Kinetic energy:

Potential energy:

Rayleigh's dissipation function can be written

Problem 2.5.2: Derive the equation of motion of the following system using Lagrange principle. Consider the spring force as and the damping force as .

Figure 2.5.5: Vibration isolator with cubic nonlinear spring and damper

(Ref: Zhenlong Xiao, Xingjian Jing, Li Cheng, The transmissibility of vibration isolators with cubic nonlinear damping under both force and base excitations, Journal of Sound and Vibration, 332(5),1335-1354, 2013. )