Study On Transient Vibration Response Of Micro-cantilever Beam Under Random Excitation

MEMS is a kind of miniaturized equipment,which can sense the environment,process and analyze the information.It is an independent intelligent system.Micro-cantilever is the most typical structure of MEMS devices,and its dynamic characteristics directly affect the design and performance of the system.As a micro sensor,the micro-cantilever beam has been widely used and studied in almost all fields.However,the micro-cantilever beam is prone to vibration caused by random excitation in logistics transportation and warehouse storage,so it is necessary to study the transient vibration response of the micro-cantilever beam under random excitation.Using lumped parameter modeling method,the micro-cantilever beam system is equivalent to the spring mass damping system.Then,by using the pole residue method,the closed solution of the transient mean square response of the micro-cantilever beam in MEMS under the excitation of Gaussian white noise is derived.The results show that the pole residue method is not only more efficient than the time domain method and frequency domain method,but also avoids the tedious process of calculating the integral in time domain.Finally,the effects of damping ratio and noise intensity on the transient mean square response of the micro cantilever beam system are discussed.Many degrees of freedom is studied in micro cantilever beam system transient vibration response under random excitation.First of all,from the input and the system transfer function to calculate the output of the pole and residue.Second,according to the input function and the system transfer function of the pole and residue,algebra calculation,get the response function of the pole and residue.Then,from the response of the pole and residue and the time domain solution of a given problem.Finally,a two-degree-of-freedom micro-cantilever beam is taken as an example to verify the effectiveness of the pole residue method.Because the output of the new method is a continuous function of time,the theoretical accuracy of the new method is higher than that of any time domain method.