Numerical Simulation Of Dynamic Damping Properties Of Vibration-reduction Damping Rubber Materials

The control of noise and vibration is very important for aerospace and engineering fields to protect devices.Rubber materials have been widely used in kinds of damping devices due to their compact structures,extraordinary damping performances and rational processabilities.It is noted that,the dynamic damping properties of rubber materials,determining the performance of the damping devices,strongly depend on the environmental temperature,loading frequency and displacement amplitude.Therefore,it is of great engineering significance to study the non-linear dynamic damping properties(dynamic modulus and damping)of rubber damping materials under different temperatures,frequencies and amplitudes.In this paper,the nonlinear dynamic damping characteristics of rubber materials under different temperatures,frequencies and amplitudes are analyzed through mathematic constitutive model.Based on the stress-superposition model,the stress in rubber materials can be divided into elastic,viscoelastic and elastoplastic component stresses.Here,we construct a viscoelastic-elastoplastic model to represent the frequency/amplitude-dependent dynamic properties of rubber materials,the temperature effect is included through the time-temperature superposition principle,and then the model parameters are determined by numerically fitting the experimental data,leading to an explicit expression of damping and dynamic modulus of rubber materials.When constructing mathematic constitutive model,the integrate and fractional generalized Maxwell modes are considered for frequency-dependent feature,ideal and stress-hardening elastoplastic models are involved for amplitude-dependent property.Finally,the fractional generalized Maxwell viscoelastic model and stress-hardening elastoplastic model are adopted to predict the dynamic damping properties.The corresponding error is 8.67%,which agreeably predict the dynamic properties of rubber materials under different temperature,amplitude and frequency.In this paper,a neural network model are adopted to predict the dynamic properties of vibration-reduction damping rubber materials.The neural network model from the viewpoint of mathematic counting,without specified physical meanings,is adopted to analyze the nonlinear relation between dynamic properties and temperature,amplitude and frequency.The back-propagation neural network is constructed with temperature,frequency and amplitude as the characteristic input and dynamic modulus and damping as the label output data.In the neural network,three hidden layers introduce the ReLu activation function to enhance the nonlinear expression ability of the neural network and to avoid the gradient disappearance of tanh function,and gradient descent optimization algorithm are used to train the neural network based on the experimental data.The complex nonlinear mapping relationship between the three factors(temperature,frequency and amplitude)and the dynamic damping properties of rubber material is given.For a trained neural network,the damping and dynamic modulus of rubber materials under different temperatures,amplitudes and frequency can be predicted accurately and rapidly.Compared with the experimental results,the overall error of neural network is 9.18%.In this paper,the prediction ability of dynamic damping properties of rubber material by mathematical constitutive model and neural network model is studied.Due to the limited experimental cost,the experimental data obtained in the current work is limited,which leads to the inaccurate prediction of the parameter inversion of mathematical constitutive model and neural network training.Based on the experimental verification data,this paper compares the dynamic damping properties of rubber materials under different working conditions and finds that the constitutive model is superior to neural network in describing the nonlinear dynamic damping properties of rubber,which is mainly because the current limited experimental data can not meet the requirements of neural network training.In order to further train the neural network,this paper extracts the sufficient data based on the constitutive model with strong description ability,greatly enriches the sample data of neural network,and obtains the trained neural network.Based on the experimental verification data,it can be found that the prediction error of neural network based on the finite experimental data and constitutive model data is 5.97%.In the paper,the numerical simulation of the dynamic damping properties of rubber materials is carried out based on the mathematical constitutive model and neural network model.The mathematical constitutive model can explain the mechanical mechanism between the dynamic damping properties and three factors(temperature,frequency and amplitude).And the neural network model can quickly predict the nonlinear dynamic damping properties which is strongly dependent on temperature,frequency and amplitude.The current work can quickly predict the nonlinear dynamic damping performance under different working conditions,which is conducive to the rapid conceptual design of rubber damping materials.