Magneto-elastc Random Vibration Of Currentcarrying Micro-beams In A Magnetic Field

With the development of science and technology,the study of random vibration of infrastructure such as beams and plates has entered the micro level.In this paper,we study the random vibration problems of three-dimensional simple-supported,solid-supported and double-layer microbeams under the coupling of magnetoelectric field.The main research contents of this paper are as follows:Based on the modified theory of even stress and the theory of magnetoelasticity,the equations of motion of the download flow microbeams in the external magnetic field are established,and the equations of magnetoelastic random vibration are derived.By modal analysis,the mean and power spectral density function of the random displacement response of simply supported and solid-supported microbeams passing through stationary and non-stationary random currents under applied magnetic field are obtained respectively.A simple-supported and solid-supported microbeams with stationary random currents are analyzed by using Matlab,and a power spectral density diagram of displacement response at different random currents,magnetic field intensities and intrinsic lengths are drawn.The results show that the random vibration of microbeams can be controlled by controlling the intensity of random current and magnetic field.Using the equivalent relation between the double-layer micro-beam and the single-layer micro-beam and the theory of magnetoelasticity,the motion equation of the two-layer micro-beam is established in the case of download flow in the external magnetic field,and the random vibration equation of the two-layer micro-beam is derived.By modal analysis,Digital features of the double-layer microbeams passing through the stationary and non-stationary random currents with applied magnetic field are obtained such as the mean value of random displacement response and power spectral density function.A numerical example is analyzed by Matlab which is the double-layer microbeams with stationary random current,and then the power spectral density diagram of displacement response under different height ratio and elastic modulus ratio is drawn.Discussed the change rule of the double-layer micro-beam under the control of threedifferent system parameters to control the height ratio and elastic modulus ratio of the double-layer micro-beam.