The Design Of Pendulum Tuned Mass Damper Considering Its Nonlinearity

As a kind of Tuned Mass Damper(TMD),the pendulum tuned mass damper(PTMD)isalso widely used in the field of structural vibration control,which is mainly used to reduce the displacement response of tall structures under wind load.When a pendulum tuned mass damper(PTMD)is used to control the structural vibration,the angle is too large to satisfy the linear assumption.If the linear design is accepted in this case,the effect of control may be not satisfactory.For the purpose of obtaining the better control effect,it is necessary to design the PTMD nonlinear or make the PTMD be linear equation during its working.Therefore,the following three aspects are studied in this paper:First,we only analyze the motion of pendulum and the amplitudes of different pendulum angles,meanwhile compare the linear approximate pendulum period with the exact solution derived from elliptic integral.With the first two approximations of the Taylor formula,the harmonic equilibrium method is used to find the approximate solution of the period.And study its effect of the two kinds of approximations on the length of the pendulum.The same analysis as the linear approximate,the maximum difference between the exact solution and the first two approximations is obtained.It is proved that both the linear approximate and first two approximations are acceptable in terms of the period or frequency.Then,the vibration of the pendulum under sinusoidal excitation is simulated,whose approximation method is the same as the solution of period or frequency.The steady-state response amplitudes of the pendulum under different excitation frequencies and the frequency corresponding to the maximum of the amplitude-frequency curve are compared and analyzed.The results show that the nonlinearity caused by the large pendulum angle of the pendulum can be approximated by the first two approximations of the sine cosine with Taylor formula.Second,improve the pendulum tuned mass damper device to meet the requirements of linearization design.The analysis results show that the cycloidal pendulum is completely linear relation and its control effect is very well.Because the shape of the cycloidal pendulum requires high precision and the processing is invariable,an approximate linear arc baffle device is presented in this paper.The two trajectories of the ball are almost completely overlapped with arc baffle and cycloidal pendulum device,furthermore,the control effects are basically same,and the control effect is better than that of the traditional pendulum.Therefore,the pendulum TMD with the circular baffle device can be used to control the structural vibration.Three,design two kinds of devices for arc and cycloidal pendulum and traditional pendulum device,also make sure the length and ball’s weight of three cases are the same.By means of the frequency sweep and free vibration attenuation curve obtained by hammering,we can identify three parameters of the structure’s mass,stiffness and damping.And the shaking experiment is carried out.So,the relationship between the steady-state response and the excitation frequency of the three kinds of device was obtained.The control effect of the arc baffle is analyzed and verified within the range of error allowable with respect to experiment.