Topology Optimization Of Constrained Damped Laminates Based On Energy Flow Analysis

Constrained layer damping treatment is a common method in engineering,because it has good effect on reducing vibration and noise especially for plate and shell parts.Constrained layer damping structure is sandwich structure in which the interlayer employs viscoelastic material and the base and constrained layer employ elastic material.Constrained layer damping structure transforms the vibration of structure into mechanical energy by shear deformation of viscoelastic material.With the change of temperature and frequency,the parameters of viscoelastic materials also change.It is verified that constrained layer damping structures have good restraint effect on high frequency vibration.However,due to the shortcomings of traditional finite element method,such as low accuracy and high computational cost,the research on constrained layer damping plate is more focused on low frequency.As an important method of structural optimization,topology optimization has the advantages of wide application range and high computational efficiency.It is obvious that combining topology optimization to energy finite element method is an effective way to study the vibration of constrained layer damping plate.Firstly,this paper study the topology optimization of constrained layer damping plate based on power flow analysis.By combining the topology optimization method and power flow analysis theory,an optimization method for constrained damping laminates is proposed.Power flow analysis takes into account the relationship between the magnitude and phase of force and velocity response,which can better reflect the actual working state than using displacement or velocity response alone.Complex stiffness method is employed to model constrained layer damping unit.Sensitivity of topology optimization for minimizing power flow is calculated and topology optimization program is executed.The numerical examples illustrate that the power flow response of the whole structure can be reduced if the constrained layer damping structure is imposed on the position of large power flow.Secondly,the optimization of CLD plate is processed for acoustic radiation.Acoustic pressure and power response of constrained damper plate are calculated with the complex stiffness model from the previous chapter.The sensitivities aiming at minimizing acoustic pressure and power is deduced and the best topology configuration of constrained layer damping plate is obtained.Thirdly,the energy finite element method is introduced to research the optimal structure of constrained layer damping plate at the case of high frequency excitation.Unit matrix of energy finite element method is calculated and energy transfer coefficient and reflection coefficient of flexural wave are obtained.Couple matrix is constructed by the energy transfer coefficient and reflection coefficient.Finally,the unit matrix and couple matrix are assembled into global matrix and the energy density response of constrained layer damping plate is solved.Finally,the constrained damping element is equivalent to a homogeneous element with equal thickness in order to optimize the constrained damping plate.The optimization model is reduced to bi-material topology optimization.The sensitivity of energy finite element method is derived and SIMP method is used to optimize the constrained layer damping plate.Several constrained layer damping plate under different boundary condition is optimized and optimal configurations are obtained.