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Research Papers

J. Vib. Acoust. 2017;139(3):031001-031001-16. doi:10.1115/1.4035482.

A semi-analytic method is presented to analyze free and forced vibrations of combined conical–cylindrical–spherical shells with ring stiffeners and bulkheads. First, according to locations of discontinuity, the combined shell is divided into one opened spherical shell and a number of conical segments, cylindrical segments, stiffeners, and bulkheads. Meanwhile, a semi-analytic approach is proposed to analyze the opened spherical shell. The opened spherical shell is divided into narrow strips, which are approximately treated as conical shells. Then, Flügge theory is adopted to describe motions of conical and cylindrical segments, and stiffeners with rectangular cross section are modeled as annular plates. Displacement functions of conical segments, cylindrical segments, and annular plates are expanded as power series, wave functions, and Bessel functions, respectively. To analyze arbitrary boundary conditions, artificial springs are employed to restrain displacements at boundaries. Last, continuity and boundary conditions are synthesized to the final governing equation. In vibration characteristics analysis, high accuracy of the present method is first demonstrated by comparing results of the present method with ones in literature and calculated by ansys. Further, axial displacement of boundaries and open angle of spherical shell have significant influence on the first two modes, and forced vibrations are easily affected by bulkheads and external force.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031002-031002-7. doi:10.1115/1.4035485.

This paper presents an efficient impedance eduction method for grazing flow incidence tube by using a surrogating model along with the Wiener–Hopf method, which enables rapid acoustic predictions and effective impedance eductions over a range of parametric values and working conditions. The proposed method is demonstrated by comparing to the theoretical results, numerical predictions, and experimental measurements, respectively. All the demonstrations clearly suggest the capability and the potential of the proposed solver for parametric studies and optimizations of the lining methods.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031003-031003-18. doi:10.1115/1.4035480.

The vibration signal decomposition is a critical step in the assessment of machine health condition. Though ensemble empirical mode decomposition (EEMD) method outperforms fast Fourier transform (FFT), wavelet transform, and empirical mode decomposition (EMD) on nonstationary signal decomposition, there exists a mode mixing problem if the two critical parameters (i.e., the amplitude of added white noise and the number of ensemble trials) are not selected appropriately. A novel EEMD method with optimized two parameters is proposed to solve the mode mixing problem in vibration signal decomposition in this paper. In the proposed optimal EEMD, the initial values of the two critical parameters are selected based on an adaptive algorithm. Then, a multimode search algorithm is explored to optimize the critical two parameters by its good performance in global and local search. The performances of the proposed method are demonstrated by means of a simulated signal, two bearing vibration signals, and a vibration signal in a milling process. The results show that compared with the traditional EEMD method and other improved EEMD method, the proposed optimal EEMD method automatically obtains the appropriate parameters of EEMD and achieves higher decomposition accuracy and faster computational efficiency.

Topics: Bearings , Vibration , Signals
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031004-031004-8. doi:10.1115/1.4035378.

The coupling matrix in structural-acoustic systems carries the entire information about the coupled resonances. We have found an elegant way of presenting this matrix and computing its determinant analytically (in a closed-form) for light fluid loading cases. The determinant gets factorized into a product. This form can be used to gain an insight into the new order of the coupled resonances. The specific example of a rectangular panel backed by a cavity is taken to demonstrate the method. This being the primary objective of the work, secondarily, the form of the matrix so derived is used to compute the new coupled resonances using a simple iterative scheme requiring a starting guess. Numerical values are compared with those given in the literature and also using the commercial package virtual lab.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031005-031005-15. doi:10.1115/1.4035382.

Combined systems consisting of linear structures carrying lumped attachments have received considerable attention over the years. In this paper, the assumed modes method is first used to formulate the governing equations of the combined system, and the corresponding generalized eigenvalue problem is then manipulated into a frequency equation. As the number of modes used in the assumed modes method increases, the approximate eigenvalues converge to the exact solutions. Interestingly, under certain conditions, as the number of component modes goes to infinity, the infinite sum term in the frequency equation can be reduced to a finite sum using digamma function. The conditions that must be met in order to reduce an infinite sum to a finite sum are specified, and the closed-form expressions for the infinite sum are derived for certain linear structures. Knowing these expressions allows one to easily formulate the exact frequency equations of various combined systems, including a uniform fixed–fixed or fixed-free rod carrying lumped translational elements, a simply supported beam carrying any combination of lumped translational and torsional attachments, or a cantilever beam carrying lumped translational and/or torsional elements at the beam's tip. The scheme developed in this paper is easy to implement and simple to code. More importantly, numerical experiments show that the eigenvalues obtained using the proposed method match those found by solving a boundary value problem.

Commentary by Dr. Valentin Fuster

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