Tiejun Yang

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

Dynamic Analysis of Circular Cylindrical Shells With General Boundary Conditions Using Modified Fourier Series Method

Dynamic behavior of cylindrical shell structures is an important research topic since they have been extensively used in practical engineering applications. However, the dynamic analysis of circular cylindrical shells with general boundary conditions is rarely studied in the literature probably because of a lack of viable analytical or numerical techniques. In addition, the use of existing solution procedures, which are often only customized for a specific set of different boundary conditions, can easily be inundated by the variety of possible boundary conditions encountered in practice. For instance, even only considering the classical (homogeneous) boundary conditions, one will have a total of 136 different combinations. In this investigation, the flexural and in-plane displacements are generally sought, regardless of boundary conditions, as a simple Fourier series supplemented by several closed-form functions. As a result, a unified analytical method is generally developed for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions including all the classical ones. The Rayleigh-Ritz method is employed to find the displacement solutions. Several examples are given to demonstrate the accuracy and convergence of the current solutions. The modal characteristics and vibration responses of elastically supported shells are discussed for various restraining stiffnesses and configurations. Although the stiffness distributions are here considered to be uniform along the circumferences, the current method can be readily extended to cylindrical shells with nonuniform elastic restraints.

Experimental Investigation of a Two-Stage Nonlinear Vibration Isolation System With High-Static-Low-Dynamic Stiffness

Shanghai Institute of Applied Mathematics and Mechanics Shanghai University, 149 Yanchang Road

Active control of sound transmission into an acoustic cavity surrounded by more than one flexible plate

This paper presents an investigation into the active control of sound transmission into a structural-acoustic coupled system. An enclosure with four acoustically rigid walls and two flexible plates is considered. One of the two plates through which a harmonic sound wave is transmitted into the enclosure, is called the incident plate, and the other as the receiving plate. Based on a fully coupled vibro-acoustic model, seven different control strategies, i.e. control configurations, are considered. They are: (a) use of the incident plate actuator, (b) applying acoustic control source in the cavity (called as cavity control), (c) use of the receiving plate actuator, (d) hybrid control system combining the incident plate actuator and the cavity control source, (e) hybrid control system combining the receiving plate control and the cavity control source, (f) simultaneous use of both the incident plate actuator and the receiving plate actuator, and (g) use of the combined acoustic actuator and structural actuators on both flexible panels. The effectiveness and performance of the control system corresponding to each configuration are compared and discussed through numerical simulations. The results show that two control system configurations, that is, the hybrid control system combining the incident plate actuator and the cavity control source and simultaneous use of both the incident plate actuator and the receiving plate actuator are desirable configurations in terms of the acoustic potential energy inside the enclosure.

Free vibration analysis of doubly curved shallow shells reinforced by any number of beams with arbitrary lengths

This study focuses on the free linear vibrations of doubly curved shallow shells reinforced by any number of beams of arbitrary lengths. Distributed elastic restraints are used to specify generally the boundary conditions along the shell edges and the coupling conditions between the shell and its reinforcing beams. Both the shell and stiffening beams are considered as independent structural components carrying three-dimensional displacement fields. Each of the displacements is invariably expressed as a simple trigonometric series with accelerated and uniform convergence over the solution domains of interest. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. As illustrated by examples, the current method provides a unified means for solving a wide range of shell problems involving various practical complications with respect to, for example, the boundary conditions, the coupling conditions, the number of stiffeners, and the lengths and locations of the stiffeners.

Free and forced in-plane vibration of rectangular plates with non-uniform elastic boundary conditions

In this paper, the free and forced in-plane vibration analysis of rectangular plates are performed for the first time using an improved Fourier series method, in which the boundary restraining spring stiffness can vary in any functional pattern along each edge. Two-dimensional improved Fourier series displacement forms are constructed with four supplementary polynomials introduced into the standard 2-D Fourier series to make the field functions sufficiently smooth in the whole solving domain. Energy formulations are employed to describe the in-plane dynamics of plate system, in which the in-plane concentrated point force is taken into account in the form of work term. All the unknown Fourier series coefficients are then solved through the Rayleigh-Ritz procedure. Several numerical examples are given to demonstrate the correctness and effectiveness of the proposed model through the comparison with those calculated via finite element analysis (FEA). The results show that these two results can agree very well with each other for various non-uniform boundary conditions. Based on the established model, the in-plane vibration response is also studied. Some curves and contours are obtained to illustrate how the boundary restraining stiffnesses affect the in-plane point and transfer mobility of rectangular plate structure.

Vibration Control of a Floating Raft System by Synchrophasing of Electrical Machines: An Experimental Study

Power and Energy Engineering College Harbin Engineering University, Nangtong Street No. 145

Dynamic behaviour and active sound radiation control of a two-stage vibration isolation system equipped on a flexible plate

This paper presents a general model of a two-stage vibration isolation system involving a flexible base plate with arbitrary boundary conditions. The dynamic behavior of the coupling system was obtained by using an impedance method in which the impedance matrix of the base plate was derived from a combined use of an improved Fourier series expansion and the Rayleigh-Ritz method. Subsequently, with the purpose of attenuation of sound radiation from the base plate structure, the optimal force information is formulated under various active control strategies including: 1) minimizing the total vibratory power of the coupled structure, 2) minimizing the sound power radiation from the base plate, 3) minimizing the vibratory power transmitted to the base plate, and 4) minimizing the mean square velocities at the isolator locations on the flexible plate. Numerical results were presented and discussed in detail. Finally, some concluding remarks are made.

An active vibration isolation system for an air-compressor in marine applications

Similar to a diesel engine, the main vibration sources of an air-compressor are to and fro inertial forces of its piston, rod, and crankshaft. An active vibration isolation system is developed for an air-compressor in a tug boat. This system consists of four inertial actuators and a DSP processor. A four-input and four-output adaptive control strategy is applied and the reference input signal comes from a laser tachometer on the shaft of the motor. The active vibration isolation experiment is conducted in a tug boat when only the air-compressor is working. The experimental results demonstrate that good vibration reductions are obtained at not only error sensors locations but also the hull under the compressor. Some discussion and conclusions are given at last.