Strong Vibration Suppression Of Smart Magneto-rheological Elastomer Based Sandwich Beam

There are many kinds of vibration phenomena in the field of civil and mechanical engineering. The micro-vibration will affect the accuracy of the tiny instrument and strong vibration may cause accidents and unrecoverable damage. The research of suppression to vibration of engineering structural is very necessary. Magneto-rheological elastomer (MRE) is a smart material developed in recent years and its dynamics properties, such as stiffness and damping, can be controlled by an external magnetic field. MRF is an ideal material in active structure control for its special characters, such as fast response and stable property, no precipitate.In this paper, the suppression to the strong earthquake excitation of smart magneto-rheological elastomer sandwich beam is studied. The engineering structure is simplified to a typical horizontal and vertical sandwich beam. The micro-vibration of magneto-rheological elastomer sandwich beam with mass supporting and magneto-rheological elastomer vertical sandwich beam system has been studied by other researchers, while there is still no research on strong vibration. This paper studied the random vibration response of the horizontal and vertical sandwich beam systems. With theoretical analysis and numerical calculation, the suppression to strong vibration of MRE sandwich beam is studied.Firstly, the preparation of MRE and the static and dynamic properties of magneto-rheological elastomer material, the effects to the sandwich beam’s mechanical properties of the applied magnetic field are introduced. The time domain mathematical model of the dynamics of magneto-rheological elastomer is given in this paper. The equivalent stiffness and loss factor can be used in the frequency domain and described by the function of frequency and strength of the magnetic field. The frequency domain dynamics stiffness and loss factor is used to describe the property of MRE.Secondly, the strong vibration response of MRE sandwich beam which supports mass concentrated equipment under stochastic strong earthquake excitation is investigated to evaluate the vibration suppression capability. Partial differential equations of motion of the sandwich beam systems are obtained. Galerkin method is applied to expand the differential equations into ordinary differential equations of time to describe the multi-freedom vibration system. Then according to the frequency domain analysis method of stochastic vibration, the frequency response function and the power spectral density function of the system is obtained. Also the power spectral density function and mean square response of the sandwich beam can be obtained. Simply supported boundary and the Kanai-Tajimi earthquake excitation spectrum is studied in this paper. Finally, Matlab software is used in programming and calculation. Numerical result shows the suppression effects of the MRE sandwich beam with mass under random strong vibration. The influence of main parameters of the MRE sandwich beam to the suppression capability is also studied in this paper.Thirdly, the suppression capability of the vertical MRE sandwich beam supporting mass system under random strong earthquake excitation is studied. Partial differential equations of motion of the vertical sandwich beam system are obtained. Galerkin method is used to obtain a set of ordinary differential equations of the multi-freedom vibration system. According to random vibration theory, the frequency response function and power spectral density function of the system are obtained. Then, the power spectral density function and mean square response of the vertical sandwich beam is obtained. Although the analysis method is similar to the previous, the dynamics model is different and the corresponding mathematical description equation and its solution are also completely different. The boundary is fixed and external incentive spectrum is Kanai-Tajimi spectrum in this part. Finally, with the programming and calculations, numerical result is obtained to study the suppression capability of MRE sandwich beam under random strong vibration.The last chapter summarizes all studies in this paper and notes the issue which can be studied further. The results obtained in this paper can provide theoretical foundation for the controlling of strong vibration in engineering project.