Zheng Dong Ma

Topological design for vibrating structures

The topological optimization technique using micro-scale voids with the homogenization method (for stress analysis of perforated structures) has been applied to solve stiffness maximization problem with success. Here, the homogenization design technique is extended to design problems concerning vibrating structures. An extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibration of a structure.

Structural topology and shape optimization for a frequency response problem

A topology and shape optimization technique using the homogenization method was developed for stiffness of a linearly elastic structure by Bendsøe and Kikuchi (1988), Suzuki and Kikuchi (1990, 1991), and others. This method has also been extended to deal with an optimal reinforcement problem for a free vibration structure by Diaz and Kikuchi (1992). In this paper, we consider a frequency response optimization problem for both the optimal layout and the reinforcement of an elastic structure. First, the structural optimization problem is transformed to an Optimal Material Distribution problem (OMD) introducing microscale voids, and then the homogenization method is employed to determine and equivalent “averaged” structural analysis model. A new optimization algorithm, which is derived from a Sequential Approximate Optimization approach (SAO) with the dual method, is presented to solve the present optimization problem. This optimization algorithm is different from the CONLIN (Fleury 1986) and MMA (Svanderg 1987), and it is based on a simpler idea that employs a shifted Lagrangian function to make a convex approximation. The new algorithm is called “Modified Optimality Criteria method (MOC)” because it can be reduced to the traditional OC method by using a zero value for the shift parameter. Two sensitivity analysis methods, the Direct Frequency Response method (DFR) and the Modal Frequency Response method (MFR), are employed to calculate the sensitivities of the object functions. Finally, three examples are given to show the feasibility of the present approach.

Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control

The inverse dynamics of robot manipulators based on flexible arm models are considered. Actuator torques required for a flexible arm to track a given trajectory are formulated and computed by using special moving coordinate systems, called virtual rigid link coordinates. Dynamic deformations of the flexible arm can be represented in a simple and compact form with use of the virtual coordinate systems

Topological optimization technique for free vibration problems

A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.

Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method

Abstract A topology and shape optimization method is presented for structural eigenfrequency optimization problems using the concept of Optimal Material Distribution (OMD). First, a mean-eigenvalue corresponding to the multiple eigenfrequencies of a structure is defined. Three optimization problems are then considered for obtaining the desired eigenfrequencies using this mean-eigenvalue: maximization of the specified structural eigenfrequencies, maximization of the distances of the specified structural eigenfrequencies from a given frequency or frequencies, and optimization of the structure for obtaining prescribed eigenfrequencies. Several examples are presented to demonstrate the capability of this new technique which can be used to deal with a wide range of practical design problems for improving the dynamic nature of a structure.

Improved mode-superposition technique for modal frequency response analysis of coupled acoustic-structural systems

A new formulation is derived by using an orthogonality condition of a coupled system. An improved compensation technique is then proposed for compensating for the effect of truncated modes, which are the lower and/or higher modes beyond the frequency domain of an MFR analysis

A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors

Abstract Existing load-dependent Ritz vector (LDRV) methods employ static recurrence procedures to generate the Ritz vectors. As such, these vector methods are best suited for low-frequency problems. For higher-frequency problems, the existing methods may engender large sets of Ritz vectors, which significantly reduces the methods’ efficiency. A new algorithm is presented for LDRV generation using a quasi-static recurrence procedure, denoted as the quasi-static Ritz vector (QSRV) method. A tuning parameter, designated as the centering frequency, controls the behavior of the QSRV approach, enabling the new method to improve upon existing LDRV methods for particular frequency ranges of interest. Compared with existing LDRV methods, the QSRV method is more efficient (in terms of the number of Ritz vectors), more accurate (in terms of response errors), and more stable (in terms of orthogonality). Numerical examples are provided to illustrate the accuracy, efficiency and generality of the proposed method.

Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems Part II: Direct Frequency Response and Its Sensitivities

An iteration method is proposed here that does not employ an inverse matrix (or triangular resolution) of the impedance matrix of coupled system. An algorithm is then derived for calculating the corresponding freqnency response sensitivity

A new component mode synthesis method: quasi-static mode compensation

A new component mode synthesis method is presented in this paper that combines the computational efficiency of the well-known constraint mode approach with the dynamic compensation accuracy obtained by higher-order expansion methods. Instead of employing static constraint modes, quasi-static modes are used to capture inertial effects of the truncated modes. The method is ideally suited for mid-band frequency analysis in which both high-frequency and low-frequency modes may be omitted. A tuning parameter, designated as the centering frequency, controls the dynamic range of the quasi-static modes. Numerical examples are provided which demonstrate the improved accuracy of the proposed method.

An efficient multibody dynamics model for internal combustion engine systems

The equations of motion for the major components in an internalcombustion engine are developed herein using a recursive formulation.These components include the (rigid) engine block, pistons, connectingrods, (flexible) crankshaft, balance shafts, main bearings, and enginemounts. Relative coordinates are employed that automatically satisfy allconstraints and therefore lead to the minimum set of ordinarydifferential equations of motion. The derivation of the equations ofmotion is automated through the use of computer algebra as the precursorto automatically generating the computational (C or Fortran) subroutinesfor numerical integration. The entire automated procedure forms thebasis for an engine modeling template that may be used to supportthe up-front design of engines for noise and vibration targets.This procedure is demonstrated on an example engine under free(idealized) and firing conditions and the predicted engine responses arecompared with results from an ADAMS model. Results obtained by usingdifferent bearing models, including linear, nonlinear, and hydrodynamicbearing models, are discussed in detail.