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In this paper, optimal vibration control of a clamped-free conical shell is presented. A diagonal piezoelectric sensor/actuator (S/A) pair is proposed to control the axial, bending and transverse vibrations of the conical shell. The modal functions are adapted to satisfy the clamped-free boundary condition. Based on the independent modal control method, the response of conical shell to external excitations can be represented by the summation of all participating natural modes and their respective modal participation factors and each mode can be controlled independently. The modal equation is transformed into the linear state space form. The modal participation factor and its time derivative are chosen to be the state variables. The sensing signals are chosen to be the output vector. The modal force is chosen to be the control input vector. The linear quadratic (LQ) controllers are designed for each independent mode. The optimal gain matrix is related to the ratio between control voltage and sensing signal by the modal control force per unit voltage and the sensing signal. Numerical examples show that, the proposed optimal control method can achieve significant active control effects and the optimal gains are mainly related to the modal velocity. This effect varies with the locations of S/A pair and the mode of the shell. The results indicate that, to achieve the best control effects for all wanted modes, the optimal controller and the optimization of the S/A location should be taken into account in the design of the optimal controller.

The passive constrained layer damping (CLD) treatments have been used widely for vibration suppression of various flexible structures. Fully covered CLD treatment is extensively used to depress the vibration over a wide frequency range in engineering applications. In most of these treatments it is required that the CLD treatment should not significantly increase the weight or volume. This paper focuses on damping optimization of fully coating beam with a constrained viscoelastic layer. The governing equation of motion of a CLD covered beam is derived using an energy approach and Lagrange’s method. The assumed modes method is employed in solving the equation to obtain the modal loss factors which are used as the objective of optimal layout. A genetic algorithm with large-scale mutation method is employed to search for the optima of the thicknesses of both the constraining layer (CL) and the viscoelastic layer (VL) and the shear modulus of the viscoelastic material (VEM) with the restriction of added volume of the total CLD treatment. Numerical results show that the optima of three design variables, the thicknesses of the CL and the VL and the shear modulus of its viscoelastic material, are highly relevant to each other. The softer or thinner constraining layer requires a softer viscoelastic material for an optimal damping treatment, and high value of the elastic modulus of the base beam matches high shear modulus of the viscoelastic material. The variation of the CL thickness decreases slowly and that of the VL thickness increases with the increase of the thickness of the CLD treatment. Stiffer constraining layer assure greater modal loss factors.

Mechanisms associated with interaction of the wheel and the rail in the vertical and horizontal direction are investigated. The noise-generating characteristics and the calculation model of wheels are studied theoretically. An improved railway wheel added with viscoelastic constrained damping layers has been researched out theoretically and experimentally. Design equations and graphs are developed for the geometrical parameter of viscoelastic constrained damping layers used in wheels. Using existing theory, the procedures are developed for predicting the structure loss factor of structural composites with different numbers of constrained damping layers. The structure loss factor of wheels attached with symmetrical three constrained layers is optimally calculated using MATLAB. A number of experiments with pulse excitations in the laboratory are carried out from the number of constrained damping layers, the material of constrained layers, as well as the position added to the wheel. From the experiments, steel is chosen as the material of constrained layer, and rubber with high loss factor and wide temperature range is chosen as the material of elastic layer. Both materials are experimentally measured. The theoretical predictions of the noise reduction effect is compared with the experimental measurements. The results shown that the wheel noise is obviously reduced.