Wanyou Li

A Moving-Load Model for Disc-Brake Stability Analysis

There are many elasto-mechanical systems that involve two components in moving contact where large-amplitude vibration and noise can be excited. This paper models the vibration and dynamic instability of a car disc brake as a moving load problem in which one component (the disc) is amenable to analytical treatment while the other component (the pads, calliper and mounting) has to be dealt with by the finite element method. A method is presented for solving the dynamic instability of the car disc brake as a nonlinear eigenvalue problem. The same approach can tackle other moving load problems.

Free In-Plane Vibration Analysis of Rectangular Plates With Elastically Point-Supported Edges

In comparison with the transverse vibrations of rectangular plates, far less attention has been paid to the in-plane vibrations even though they may play an equally important role in affecting the vibrations and power flows in a built-up structure. In this paper, a generalized Fourier method is presented for the in-plane vibration analysis of rectangular plates with any number of elastic point supports along the edges. Displacement constraints or rigid point supports can be considered as the special case when the stiffnesses of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve the convergence of the Fourier series solution by eliminating all the discontinuities potentially associated with the original displacements and their partial derivatives along the edges when they are periodically extended onto the entire x-y plane as mathematically implied by the Fourier series representation. This analytical solution is exact in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. Numerical examples are given about the in-plane modes of rectangular plates with different edge supports. It appears that these modal data are presented for the first time in literature, and may be used as a benchmark to evaluate other solution methodologies. Some subtleties are discussed about corner support arrangements.

Moving Force-Induced Vibration of a Rotating Beam with Elastic Boundary Conditions

In this paper, an analytical technique, the so-called Fourier Spectral method (FSM), is extended to the vibration analysis of a rotating Rayleigh beam considering the gyroscopic effect. The model presented can have arbitrary boundary conditions specified in terms of elastic constraints in the translations and rotations or even in terms of attached lumped masses and inertias. Each displacement function is universally expressed as a linear combination of a standard Fourier cosine series and several supplementary functions introduced to ensure and accelerate the convergence of the series expansion. Lagranges equation is established for all the unknown Fourier coefficients viewed as a set of independent generalized coordinates. A numerical model is constructed for the rotating beam. First, a numerical example considering simply supported boundary conditions at both ends is calculated and the results are compared with those of a published paper to show the accuracy and convergence of the proposed model. Then, the method is applied to one real work piece structure with elastically supported boundary conditions updated from the modal experiment results including both the frequencies and mode shapes using the method of least squares. Several numerical examples of the updated model are studied to show the effects of some parameters on the dynamic characteristics of the work piece subjected to moving loads at different constant velocities.

Prediction of break-out sound from a rectangular cavity via an elastically mounted panel

The break-out sound from a cavity via an elastically mounted panel is predicted in this paper. The vibroacoustic system model is derived based on the so-called spectro-geometric method in which the solution over each sub-domain is invariably expressed as a modified Fourier series expansion. Unlike the traditional modal superposition methods, the continuity of the normal velocities is faithfully enforced on the interfaces between the flexible panel and the (interior and exterior) acoustic media. A fully coupled vibro-acoustic system is obtained by taking into account the strong coupling between the vibration of the elastic panel and the sound fields on the both sides. The typical time-consuming calculations of quadruple integrals encountered in determining the sound power radiation from a panel has been effectively avoided by reducing them, via discrete cosine transform, into a number of single integrals which are subsequently calculated analytically in a closed form. Several numerical examples are presented to validate the system model, understand the effects on the sound transmissions of panel mounting conditions, and demonstrate the dependence on the size of source room of the measured transmission loss.

Interring gas dynamic analysis of piston in a diesel engine considering the thermal effect

Understanding the interaction between ring dynamics and gas transport in ring pack systems is crucial and needs to be imperatively studied. The present work features detailed interring gas dynamics of piston ring pack behavior in internal combustion engines. The model is developed for a ring pack with four rings. The dynamics of ring pack are simulated. Due to the fact that small changes in geometry of the grooves and lands would have a significant impact on the interring gas dynamics, the thermal deformation of piston has been considered during the ring pack motion analysis in this study. In order to get the temperature distribution of piston head more quickly and accurately, an efficient method utilizing the concept of inverse heat conduction is presented. Moreover, a sensitive analysis based on the analysis of partial regression coefficients is presented to investigate the effect of groove parameters on blowby.

Sound Radiation from an Elastically Restrained Plate Covered by an Acoustic Decoupling Layer

The sound radiation from elastically restrained plates covered by a decoupling layer is studied using the Spectrogeometric Method (SGM), which is a meshless and parametric modeling technique. By adopting the Rayleigh-Ritz procedure and the Rayleigh integral, a vibroacoustic coupling system is established. This model studies the situation when the plate is immersed in heavy fluid, such as water, in which the strong coupling between the structure and sound field should be fully considered. The influence of the boundary conditions on the radiated sound power and sound reduction provided by the decoupling layer based on the locally reacting model is studied. The nonuniform distributed decoupling layer is also studied to analyze the sound reduction effect. The sound intensity on the outer surface of the decoupling layer is investigated and tends to be uniform along the plate scale with increasing thickness of the decoupling layer.

Reconstruction of Input Excitation Acting on Vibration Isolation System

Vibration isolation systems are widely employed in automotive, marine, aerospace, and other engineering fields. Accurate input forces are of great significance for mechanical design, vibration prediction, and structure modification and optimization. One-stage vibration isolation system including engine, vibration isolators, and flexible supporting structure is modeled theoretically in this paper. Input excitation acting on the vibration isolation system is reconstructed using dynamic responses measured on engine and supporting structure under in-suit condition. The reconstructed forces reveal that dynamic responses on rigid body are likely to provide more accurate estimation results. Moreover, in order to improve the accuracy of excitation reconstructed by dynamic responses on flexible supporting structure, auto/cross-power spectral density function is utilized to reduce measurement noise.

Structural Modifications for Torsional Vibration Control of Shafting Systems Based on Torsional Receptances

Torsional vibration of shafts is a very important problem in engineering, in particular in ship engines and aeroengines. Due to their high levels of integration and complexity, it is hard to get their accurate structural data or accurate modal data. This lack of data is unhelpful to vibration control in the form of structural modifications. Besides, many parts in shaft systems are not allowed to be modified such as rotary inertia of a pump or an engine, which is designed for achieving certain functions. This paper presents a strategy for torsional vibration control of shaft systems in the form of structural modifications based on receptances, which does not need analytical or modal models of the systems under investigation. It only needs the torsional receptances of the system, which can be obtained by testing simple auxiliary structure attached to relevant locations of the shaft system and using the finite element model (FEM) of the simple structure. An optimization problem is constructed to determine the required structural modifications, based on the actual requirements of modal frequencies and mode shapes. A numerical experiment is set up and the influence of several system parameters is analysed. Several scenarios of constraints in practice are considered. The numerical simulation results demonstrate the effectiveness of this method and its feasibility in solving torsional vibration problems in practice.

Vibration Analysis of Conical Shells by the Improved Fourier Expansion-Based Differential Quadrature Method

An improved Fourier expansion-based differential quadrature (DQ) algorithm is proposed to study the free vibration behavior of truncated conical shells with different boundary conditions. The original function is expressed as the Fourier cosine series combined with close-form auxiliary functions. Those auxiliary functions are introduced to ensure and accelerate the convergence of series expansion. The grid points are uniformly distributed along the space. The weighting coefficients in the DQ method are easily obtained by the inverse of the coefficient matrix. The derivatives in both the governing equations and the boundaries are discretized by the DQ method. Natural frequencies and modal shapes can be easily obtained by solving the numerical eigenvalue equations. The accuracy and stability of this proposed method are validated against the results in the literature and a very good agreement is observed. The centrosymmetric properties of these newly proposed weighting coefficients are also validated. Studies on the effects of semivertex angle and the ratio of length to radius are reported.

A Hybrid Finite Element-Fourier Spectral Method for Vibration Analysis of Structures with Elastic Boundary Conditions

A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM) and the applicability of the finite element method (FEM), is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.