Yujin Hu

Computation of Eigensolution Derivatives for Nonviscously Damped Systems Using the Algebraic Method

T HE computation of the eigensolution derivatives plays a significant role in dynamic model updating, structural design optimization, structural dynamic modification, damage detection andmany other applications. Themethods to calculate eigensolution derivatives are well established for undamped and viscous damped systems. These common methods can be divided into the modal method, Nelson’s method, and the algebraic method. Fox and Kapoor [1] first proposed the modal method for symmetric undamped systems by approximating the derivative of each eigenvector as a linear combination of all undamped eigenvectors. Later, Adhikari and Friswell [2] and Adhikari [3] extended the modal method to the more general asymmetric systems with viscous and nonviscous damping, respectively. To simplify the computation of eigensolution derivatives, Nelson [4] proposed a method, which requires only the eigenvector of interest by expressing the derivative of each eigenvector as a particular solution and a homogeneous solution for symmetric undamped systems. Later, Friswell and Adhikari [5] extended Nelson’s method to symmetric and asymmetric systemswith viscous damping. Recently, Adhikari and Friswell [6] extended Nelson’s method to symmetric and asymmetric nonviscously damped systems. However, Nelson’s method is lengthy and clumsy for programming. Lee et al. [7] derived an efficient algebraic method, which has a compact form to compute the eigensolution derivatives by solving a nonsingular linear system of algebraic equations for symmetric systems with viscous damping. Later, Guedria et al. [8] extended the algebraic method to general asymmetric systems with viscous damping. Recently, Chouchane et al. [9] wrote an excellent review of the algebraic method for symmetric and asymmetric systems with viscous damping and extended their method to the second-order and high-order derivatives of eigensolutions. In this note, the algebraic method will be extended to symmetric and asymmetric systems with nonviscous damping. The equations of motion describing free vibration of anN-degreeof-freedom (DOF) linear system with nonviscous (viscoelastic) damping can be expressed by [3,6]:

Eigensensitivity Analysis for Asymmetric Nonviscous Systems

T HE eigensensitivities of mechanical systems with respect to structural design parameters have become an integral part of many engineering design methodologies including optimization, structural health monitoring, structural reliability, model updating, dynamic modification, reanalysis techniques, and many other applications. Fox and Kapoor [1] computed the derivative of each eigenvector as a linear combination of all of the undamped eigenvectors. Later, Adhikari and Friswell [2] and Adhikari [3] extended the modal method to the more general asymmetric systems with viscous and nonviscous damping, respectively. Nelson [4] presented a method, which requires only the eigenvector of interest by expressing the derivative of each undamped eigenvector as a particular solution and a homogeneous solution. Later, Friswell and Adhikari [5] extended Nelson’s method to symmetric and asymmetric systems with viscous damping. Recently, Adhikari and Friswell [6] extendedNelson’s method to symmetric and asymmetric nonviscously damped systems. Fox and Kapoor [1] also suggested a direct algebraic method to calculate the eigensensitivity for symmetric undamped systems by solving a nonsingular linear system of algebraic equations. Lee et al. [7] derived an efficient algebraic method, which has a compact linear system with a symmetric coefficient matrix for symmetric systems with viscous damping. Later, Guedria et al. [8] extended the algebraic method to general asymmetric viscous damped systems. Chouchane et al. [9] reviewed the algebraic method and extended their method to the second-order and high-order derivatives of eigensolutions. Li et al. [10] extended the algebraic method to symmetric and asymmetric nonviscously damped systems. Xu andWu [11] proposed a new normalization and presented a method for the computation of eigensolution derivatives of asymmetric systemswith viscously damping. Recently,Mirzaeifar et al. [12] proposed a new method based on a combination of algebraic and modal methods for generally asymmetric viscously damped systems. More recently, Li et al. [13] proposed a method of design sensitivity analysis of asymmetric viscously damped systems with distinct and repeated eigenvalues, which can compute the left and right eigenvector derivatives separately and independently. All of the methods mentioned previously compute the eigensensitivities of asymmetric damped systems by using the left eigenvector. However, these methods have disadvantages in computational cost and storage capacity for the left eigenvector should be calculated. To avoid using the left eigenvector, an algebraic method is presented [14], which does not require the left eigenvector for asymmetric damped systems, but this method is restricted to the case of viscous damping. It should be noted that the coefficientmatrices of the algebraicmethodmay be ill conditioned due to the components of the additional constraints, and system matrices in the coefficient matrices are not all of the same order of magnitude. In addition [15], the normalization adapted in [14] and [12] will fail in some cases because it can equal zero or a very small number. This Note will present a method, which is well conditioned and can calculate the eigensensitivity of asymmetric nonviscous damped systems without using the left eigenvector. Considering an N-degree-of-freedom linear system with nonviscous (viscoelastic) damping [3,6,10]

AN ANALYTICAL MODEL OF OBLIQUE CUTTING WITH APPLICATION TO END MILLING

A new analytical cutting force model is presented for oblique cutting. Orthogonal cutting theory based on unequal division shear zone is extended to oblique cutting using equivalent plane approach. The equivalent plane angle is defined to determine the orientation of the equivalent plane. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of shear strain rate. The flow stress is calculated from Johnson-cook material constitutive equation. The predictions were compared with test data from the available literature and showed good correlation. The proposed model of oblique cutting was applied to predict the cutting forces in end milling. The helical flutes are decomposed into a set of differential oblique cutting edges. To every engaged tooth element, the differential cutting forces are obtained from oblique cutting process. Experiments on machining AISI 1045 steel under different cutting conditions were conducted to validate the proposed model. It shows that the predicted cutting forces agree with the measurements both in trends and values.

A TCPN based approach to model the coordination in virtual manufacturing organizations

The recent developments of communication technologies and network computing have enabled the occurrence of the advanced manufacturing strategy--agile manufacturing. The essence of the agile manufacturing strategy is to form a virtual manufacturing organization (VMO), which integrates the core competencies of member enterprises in order to respond to the global market and increasing customer requirements rapidly. In a VMO, the manufacturing processes are distributed. So modeling and coordination of these processes are very complex. In this paper, we present a Petri Net based approach to model these distributed manufacturing processes and interaction relations among them. A workflow based manufacturing process execution environment is also established to support the implementation of the distributed manufacturing processes.

Automatic sequence of 3D point data for surface fitting using neural networks

In this paper, a neural network-based algorithm is proposed to explore the sequence of the measured point data for surface fitting. In CAD/CAM, the ordered data serves as the input to fit smooth surfaces so that a reverse engineering system can be established for 3D sculptured surface design. The geometry feature recognition capability of back-propagation neural networks is also explored. Scan number and 3D coordinates are used as the inputs of the proposed neural networks to determine the curve which a data point belongs to and the sequence number of the data point on the curve. In the segmentation process, the neural network output is segment number; while the segment number and sequence number on the same curve are the outputs when sequencing those points on the same curve. After evaluating a large number of trials, an optimal model is selected from various neural network architectures for segmentation and sequence. The neural network is successfully trained by the known data and validated the unexposed. The proposed model can easily adapt for new data measured from the same part for a more precise fitting surface. In comparison to Lin et al.s [Lin, A. C., Lin, S.-Y., & Fang, T.-H. (1998). Automated sequence arrangement of 3D point data for surface fitting in reverse engineering. Computer in Industry, 35, 149-173] method, the presented algorithm neither needs to calculate the angle formed by each point and its two previous points nor causes any chaotic phenomenon of point order.

Modelling and analysis of an air-over-hydraulic brake system

Abstract This study presents the development and validation of an analytical dynamic model of an air-over-hydraulic (AOH) brake system for a commercial vehicle (CV). The brake system model includes the controller, intensifier, brake lines, wheel cylinder, and foundational drum brake, which are presented for the interaction with the application system. A generalized AOH brake system, based on systems analysis level for the components, is formulated in detail. The pipeline hysteresis and fluid fluctuation of the brake system have been investigated in detail. Many experiments were performed on a bench setup of the AOH brake system and real vehicles. The experimental data is compared with the model simulation results. Preliminary results show that the simulation matches the experimental data closely. The models, which are developed from physical laws, are intended for use in the design and analysis of vehicle control systems for CVs.

Finite element modelling of human auditory periphery including a feed-forward amplification of the cochlea

A three-dimensional finite element model is developed for the simulation of the sound transmission through the human auditory periphery consisting of the external ear canal, middle ear and cochlea. The cochlea is modelled as a straight duct divided into two fluid-filled scalae by the basilar membrane (BM) having an orthotropic material property with dimensional variation along its length. In particular, an active feed-forward mechanism is added into the passive cochlear model to represent the activity of the outer hair cells (OHCs). An iterative procedure is proposed for calculating the nonlinear response resulting from the active cochlea in the frequency domain. Results on the middle-ear transfer function, BM steady-state frequency response and intracochlear pressure are derived. A good match of the model predictions with experimental data from the literatures demonstrates the validity of the ear model for simulating sound pressure gain of middle ear, frequency to place map, cochlear sensitivity and compressive output for large intensity input. The current model featuring an active cochlea is able to correlate directly the sound stimulus in the ear canal with the vibration of BM and provides a tool to explore the mechanisms by which sound pressure in the ear canal is converted to a stimulus for the OHCs.

Inclusion of Higher Modes in the Eigensensitivity of Nonviscously Damped Systems

C = viscous damping matrix ck = coefficients for mode basis vectors D s = dynamic stiffness matrix EH = modal-truncated error due to higher modes G s = Laplace transform of g t g t = matrix of kernel functions in the time domain K = stiffness matrix L = number of lower modes M = mass matrix m = order of the characteristic polynomial N = degrees of freedom of the system p = design parameter s = Laplace domain parameter t = time u s = Laplace transform of u t u t = response vector v i = ith approximate vector v i = ith exact vector δ t = Dirac delta function θi = normalization constant for ith mode λi = ith eigenvalue φi = ith eigenvector

Pillared graphene as an ultra-high sensitivity mass sensor

Hybrid structure of graphene sheets supported by carbon nanotubes (CNTs) sustains unique properties of both graphene and CNTs, which enables the utilization of advantages of the two novel materials. In this work, the capability of three-dimensional pillared graphene structure used as nanomechanical sensors is investigated by performing molecular dynamics simulations. The obtained results demonstrate that: (a) the mass sensitivity of the pillared graphene structure is ultrahigh and can reach at least 1 yg (10−24 g) with a mass responsivity 0.34 GHz · yg−1; (b) the sizes of pillared graphene structure, particularly the distance between carbon nanotube pillars, have a significant effect on the sensing performance; (c) an analytical expression can be derived to detect the deposited mass from the resonant frequency of the pillared graphene structure. The performed analyses might be significant to future design and application of pillared graphene based sensors with high sensitivity and large detecting area.

Accurate method for harmonic responses of non-classically damped systems in the middle frequency range

This paper is aimed at eliminating the influence of the problem of the harmonic response analysis of non-classically damped systems with lower-higher-modal truncation. Based on the Neumann expansion theorem and the frequency shifting technique, the relationships satisfied by eigensolutions and system matrices are established and an explicit expression on the lower-higher-modal truncation error of harmonic responses can be expressed as a sum of available modes and system matrices. A correction method, which only involves the available modes and system matrices, is then presented to calculate the harmonic responses. The method maintains original-space without having to involve the state-space equation of motion such that it is efficient in computational effort and storage capacity. The method is convergent if and only if all the modes whose resonant frequencies lie within the range of excitation frequencies are available. Finally, a two-stage floating raft isolation system and a sandwich plate are used to to validate the effectiveness of the presented method.