Vibration Analysis of Circular Plates With Eccentric Hole

Chen

Journal of Sound and Vibration

2007

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of circular plates with multiple circular holes using indirect BIEMs

Chen

Journal of Sound and Vibration

2007

“…These include the Rayleigh-Ritz method in publications [4,5]. Finally, there are the most widely used discretization methods, such as the finite element method, the finite strip method and the difference method as can be found in the papers [6,7]. The development of active materials and actuators [8][9][10] gives new possibilities.…”

Section: Introductionmentioning

confidence: 99%

Quasi-optimal locations of piezo-elements on a rectangular plate

Koszewnik

Gosiewski

2016

Eur. Phys. J. Plus

Abstract. The optimal location of piezo-actuators and piezo-sensors for the vibration control of a rectangular plate with SFSF (Simply Supported -Free -Simply Supported -Free) boundary conditions is presented in the paper. Based on bending moments, M x(x, y) and My(x, y), the modal control forces generated by the piezo-stripes are calculated for the first five mode shapes. Calculations are carried out for different locations of two piezo-strips directed along the X and Y axes. The obtained results are used to define performance indexes of modal control forces for the two considered directions of vibration. In a similar way the modal unit elongations of the piezo-sensors are calculated for two different orientations of the piezos on the plate. Based on these results the objective cost functions J ε-odd and Jε-even are defined separately for odd and even modes. The quasi-optimal locations of the piezo-actuators and piezo-sensors are determined by maximizing the proposed cost functions. After analytical and numerical investigations the process of the full model identification is carried out at the laboratory stand. A chirp signal is applied in the identification process. The rectangular plate is excited with the chirp force while output signals are measured by the piezo-sensors oriented in the perpendicular directions X and Y . In such a way two mathematical models are obtained to control the vibration of the plate separately for odd and even natural modes.

“…Circular plates with multiple circular holes are widely used in engineering structures [1], e.g. missiles, aircraft, etc.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a circular plate with multiple circular holes by using the addition theorem and direct BIEM

Lee¹,

Chen²

2009

Mesh Reduction Methods

The purpose of this paper is to propose an analytical method to solve natural frequencies and natural modes of a circular plate with multiple circular holes by using the null field integral formulation, the addition theorem and complex Fourier series. Owing to the addition theorem, all kernel functions are represented in the degenerate form and further transformed into the same polar coordinate from each local coordinate at center of all circles. Not only avoiding the computation of the principal value but also the calculation of higher-order derivatives in the plate problem can be easily determined. According to the specified boundary conditions, a coupled infinite system of simultaneous linear algebraic equations is derived and its solution can be obtained in an analytical way. The direct searching approach is adopted to determine the natural frequency through singular value decomposition (SVD). After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the direct boundary integral equations for domain points. Some numerical results are presented. Moreover, the inherent problem of spurious eigenvalue using integral formulation is investigated and the SVD updating technique is adopted to suppress the occurrence of spurious eigenvalues. Excellent accuracy, fast rate of convergence and high computational efficiency are the main features of the present method.