Jianbin Du

Topological Design for Minimum Dynamic Compliance of Structures under Forced Vibration

This paper deals with topology optimization of elastic, continuum structures without damping that are subjected to time-harmonic, dynamic loading with prescribed excitation frequency and amplitude. An important objective of such a design problem is often to drive the eigenfrequencies of the structure as far away as possible from the excitation frequency in order to avoid resonance and reduce the vibration level of the structure. The total structural volume, the boundary conditions, and the material are given.

On Topological Design Optimization of Structures Against Vibration and Noise Emission

This paper presents a brief introduction to topological design optimization, and gives an overview of the application of this novel method to problems of design of linearly elastic continuum-type structures (without damping) against vibration and noise subject to given external excitation. The design objective of such problems is often to drive the structural eigenfrequencies of vibration as far away as possible from an external excitation frequency, or a band of excitation frequencies, in order to avoid resonance phenomena with high vibration and noise levels. This objective may be achieved in different ways, e.g., by (i) maximizing the fundamental or a higher order eigenfrequency of the structure, (ii) maximizing the distance (gap) between two consecutive eigenfrequencies, (iii) maximizing the dynamic stiffness of the structure subject to forced vibration, or by (iv) minimizing the sound power radiated from the structural surface into an acoustic medium. The mathematical formulations of these topology optimization problems and several illustrative numerical results are presented.

Topology Optimization of Vibrating Bi-Material Structures with Respect to Sound Radiation

This paper deals with topological design optimization of vibrating bi-material elastic structures of given volume, domain and boundary conditions, with the objective of minimizing the sound power radiated from the structural surfaces into a surrounding acoustic medium. The structural vibrations are excited by a time-harmonic mechanical loading with prescribed forcing frequency and amplitude, and structural damping is not considered. It is assumed that air is the acoustic medium and that a feedback coupling between the acoustic medium and the structure can be neglected. Certain conditions are assumed, where the sound power radiated from the structural surface can be estimated by using a simplified approach instead of solving the Helmholz integral equation. This implies that the computational cost of the structural-acoustical analysis can be considerably reduced. Numerical results are presented for plate and pipe-like structures with different sets of boundary conditions.

Introductory Notes on Topological Design Optimization of Vibrating Continuum Structures

This paper presents a brief introduction to topological design optimization, and together with five sequential papers gives an overview of the application of this rather novel method to problems of design of linearly elastic continuum-type structures against vibration and noise. The objective of such problems is often to drive the structural eigenfrequencies of vibration as far away as possible from a prescribed external excitation frequency - or band of excitation frequencies - in order to avoid resonance phenomena with high vibration and noise levels. This objective may, e.g., be achieved by (i) maximizing the fundamental eigenfrequency of the structure, (ii) maximizing the distance (gap) between two consecutive eigenfrequencies, (iii) maximizing the dynamic stiffness of the structure subject to forced vibration, or by (iv) minimizing the sound power flow radiated from the structural surface into an acoustic medium. The mathematical formulations of these optimization problems and several illustrative examples are presented in this series of papers.

Topological Design for Minimum Sound Emission from Structures under Forced Vibration

This paper is devoted to topology optimization problems formulated with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed excitation frequency, amplitude, and spatial distribution. Several numerical results are presented and discussed for bi-material plate-like structures with different sets of boundary and loading conditions.

Structural Topology Optimization with Respect to Eigenfrequencies of Vibration

A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order, subject to a given amount of structural material and prescribed boundary conditions. Mathematical formulations and methods of numerical solution of these topology optimization problems are presented for linearly elastic structures without damping in this paper, and several illustrative results are shown.

Topological Design of Vibro-Acoustic Structures Using a Generalized Incremental Frequency Method

Topology design optimization of vibro-acoustic structures are studied, where the structures are assumed to be subjected to time-harmonic mechanical loading with given amplitude and a prescribed low or high excitation frequency. One of the difficulties of such a problem is that the design often easily converges to a local optimum because the excitation frequency may be located in an interval between two less appropriate consecutive resonance frequencies. In this paper, we seek for a new design strategy of overcoming the previous methods and deal with the problem in a ‘global’ and efficient manner. An ‘incremental frequency technique’ (IF technique) is first presented to show that it is often important to consider different design paths in order to obtain a desirable solution of the vibro-acoustic topology optimization problem. Then, a ‘generalized incremental frequency method’ (GIF method) based on the IF technique is proposed for any high or low prescribed value of the external excitation frequency. The excitation frequency is defined to be ‘low’ for positive values up to and including the fundamental resonance frequency of the structure, and to be ‘high’ for values beyond that. The GIF method provides a way of searching for different local optimized solutions in a systematic manner in different disjointed resonance frequency sub-intervals, and hereby the optimum solution of the problem may be identified from among a small number of obtained candidate local optimum solutions. Numerical examples show that the optimum designs obtained in different resonance frequency intervals normally exhibit different periodicity of structural topology. Numerical tests on the design of minimization of dynamic compliance also show that the ‘best’ (i.e. global optimum) design subject to a prescribed value of the external excitation frequency may not be identified in an interval between two consecutive resonance frequencies that have the same orders as the two resonance frequencies embracing the excitation frequency of the initial design chosen for the topological optimization procedure. The method developed in this paper may be applied to general vibro-acoustic design problems (e.g. minimization of sound power/emission/pressure, minimization of dynamic compliance/global displacement amplitude, minimization of force amplitude transmitted from the vibrating structure to the foundation, etc.) with multiple disjointed design sub-spaces, and may also be extended further for optimization problems concerning multiple external excitation frequencies or excitation frequency bands.

Bi-Level Design Optimization of the Hatch Door Mechanism

Optimization model and solution method are developed in the present paper to improve the design of the hatch door mechanism of a regional airliner. The real motion trajectory of the hatch door normally has deviations from the ideal trajectory due to existence of machining errors. In order to decrease such deviations, a bi-level optimization model is developed for the design of the size tolerance limits of the key parts. The design objective is to minimize the extremum deviation of the trajectory of the objective point of the hatch door. The extremum deviation is obtained by solution of the inner-level size optimization problem for the fixed size tolerance limits. The optimization models for motion control of the hatch door mechanism are solved by the response surface method.

Microscopic Layout Design of Metamaterial

A novel design method based on layout evolution of the periodic micro unit cell of the metamaterial is presented for improvement of the mechanical behavior of the composite structure. The macro properties of the metamaterial depend strongly on its microscopic layout, and hereby may possibly be improved by microstructural design. Topology optimization model and the solution method based on inverse homogenization process are developed to find the best layout of the microstructure. The proposed method may be applied to improve the static and vibro-acoustic behavior of the structure, which is validated by several numerical examples.

Topological Design for Minimum Sound Radiation from Structures Subjected to Forced Vibration

Problems of passive topological design optimization of structures against vibration and noise have only been undertaken during the last decade, cf. [1] and papers cited therein. The problems have dealt with maximization of intrinsic properties like fundamental eigenfrequencies, higher order eigenfrequencies and eigenfrequency gaps of freely vibrating structures, and minimization of the dynamic compliance of structures subjected to forced vibration [1].