Optimization Design Of Pore Structure For Sound-absorbing Porous Materials And Damping Material’s Microstructure And Layout

Noise pollution has become one of the most serious environmental issues we face all over the world. To control the noise, there exist two main effective means including sound suppression during propagating (absorption and isolation) and vibration reduction of the source. Sound-absorbing porous material has been found to be one of the most effective materials for suppressing the sound’s propagation, whose sound absorbing performance greatly depends on the geometric characteristic of the pore structure (i.e. the size and shape of the pore). Therefore, there is a need to study the design of the pore structure of sound-absorbing materials for optimal sound absorption properties. Damping layer treatment is recognized as an effective technique to reduce vibration of equipment, in which the material properties, arrangements as well as the concurrent design between them are of great importance in determining the damping performance of structure. Hence, design methods for the optimal distribution of damping materials and damping materials with prescribed physical properties (i.e. microstructure of the damping material) are necessary. Motivated by the two main above mentioned demands, based upon the idea of structure optimization, the methods for designing pore structures of porous materials with optimal sound absorption are investigated; the optimization method and the corresponding solving method for designing microstructures of viscoelastic damping materials are presented; and the optimal distribution of damping material are studied in order to reduce the vibration and suppress the noise control. The main content and results are obtained as follows:1. Optimization model and solution of multilayer porous materials with cylindrical gradient changed pores for sound absorption. A design method for determining the size of the cylindrical holes through the material thickness to enhance sound absorption performance is proposed. Analytical approaches for obtaining sound absorption coefficients of multi-layered material with two different boundary conditions are derived by using a surface impedance method and a transfer matrix method respectively. Then, a mathematical model is constructed to obtain the optimal pore structure design, by introducing the hole sizes of the multilayer porous material as the design variables and the sound absorption performance at specific frequencies as the objective. Gradient pore structures with greater sound absorption than materials with uniform radius pores are obtained by using the optimization model. The sound absorption coefficient of the optimal gradient multilayer design is increased significantly comparing to the optimum single layer design. In addition, a numerical simulation of the optimal gradient design by using COMSOL is presented to verify the method proposed. 2. Optimization design for the pore structure of periodic porous sound-absorbing materials with non-uniform cylindrical pores is also presented. Knowing that the size and distribution of the pores are decisive design factors for sound absorption materials, the acoustic model derived by Johnson. Champoux and Allard ("JCA model") is used to investigate the influences of the micro-structural configuration on sound absorption performance, and the macro-acoustic parameters used in JCA model is determined by finite element analysis of the velocity field in the microstructures. Thus, a design methodology is developed for non-uniform pore structures with optimal sound absorption performance under specific frequencies, with which some high performance pore structural configurations are obtained. Inspired by the optimal results, a numerical model of perforated closed-cell metallic foams is constructed. The numerical results show that perforation can be used for enhancing the sound absorption of closed-cell foams.3. A methodology is proposed for designing porous fibrous metal with optimal sound absorption in frequency bands. A simplified geometrical model of porous fibrous metal is developed for analyzing the sound absorption performance, and the JCA model is used to construct the relationship between the micro-structural parameters (fiber radius and gap) and macroscopic sound absorption performance. The effects of the micro-structural parameters, namely fiber radius and fiber gap, on sound absorption are analyzed, and the results show that sound absorption is substantially sensitive to fiber gap while not materially sensitive to fiber radius. Moreover, a mathematical model is then constructed to obtain the optimized microstructure design, with the fiber gap and radius as design parameters and average absorption performance of the porous fibrous metal under a set frequency band as the objective. Utilizing the constructed optimization model, three optimal micro-structures for low frequency (20<f<500Hz), medium frequency (500<f<2000Hz) and high frequency (2000<f<15000Hz) are presented, respectively. For a given thickness of porous fibrous material layer, a matching relationship between fiber radius and optimal porosity under set frequency bands is constructed. Based upon the matching relationship, a preparation process for porous fibrous metal with the optimal sound absorption under set frequency bands is proposed.4. Assigning the optimal damping performance of the structure as the objective function, the topology optimization models for designing microstructural configurations and macro layout of damping material are constructed. The main contents are described as follows.(1) The topology optimization method for designing the microstructures of cellular viscoelastic materials with a prescribed shear modulus. The effective behavior of viscoelastic materials is derived through the use of a finite element based homogenization method. Only isotropic matrix material is considered and under such an assumption it is found that the effective loss factor of the viscoelastic material is independent on the geometrical configuration of the microstructure. Based upon the idea of a Solid Isotropic Material with Penalization (SIMP) method of topology optimization, the relative material densities of the elements in the microstructure are considered as the design variables. Meanwhile, the topology optimization problem of viscoelastic cellular material with a prescribed property and with constraints on the isotropy is established. The numerical results show that the topology optimization method can formulate the design of a viscoelastic material with prescribed properties, and can determine interesting topological patterns for guiding the viscoelastic cellular material design. Furthermore, microstructure design of viscoelastic material with prescribed properties plays a crucial role in improving the damping properties of the macrostructures.(2) The optimization method for finding optimal the microstructural configurations of the viscoelastic material (i.e. the optimal effective properties of material) with the maximum modal loss factors of macrostructures. The modal loss factor of damping structure is obtained by using the modal strain energy method (MSE). With the design variables of the relative material densities of the elements in the microstructure, and the objective function of the modal loss factor of the structure, the topology optimization model for designing microstructural configurations of viscoelastic material is constructed. The sensitivities of modal loss factor with respect to design variables are derived analytically. Besides, the influences of the size of macrostructure on the optimal microstructure are discussed. The results show that for cases of macrostructure with high-frequency vibration, the optimal configuration of microstructure is solid materials; for cases of macrostructure with low-frequency vibration, the configuration of porous material can help to increase the damping effects of macrostructure.(3) Design of the damping layout in the vibrational structure by using topology optimization. With the maximizing modal loss factors of structures as the objective, an optimization model for distribution of the damping material on structure surface is proposed and a corresponding optimization scheme is developed. By minimizing vibration amplitudes at specified positions as objective function, the method of topology optimization for designing bi-material damping structure is proposed. The numerical results show that the proposed topology optimization methods can achieve optimal layout of the damping material on structure surface with a given maximum amount of damping material, and can obtain optimal configuration of bi-material damping structure.