Discrete singular convolution method for one-dimensional vibration and acoustics problems with impedance boundaries

Kara, Murat; Seçgin, Abdullah

doi:10.1016/j.jsv.2019.01.028

Cited by 7 publications

(3 citation statements)

References 34 publications

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“…The similar equations may be used at x = l x , y = 0 and y = l y . One can refer to [39][40][41] for the details of boundary condition implementation procedure. Equation ( 13) can be written in a matrix form after implementing proper boundary condition equation (i.e.…”

Section: Dsc Methods For the Laminated Thin Composite Platesmentioning

confidence: 99%

Sensitivity analysis of laminated composite plates with different orientations in low to high order modes

Kara¹,

Güler²,

Seçgin³

2021

Smart Mater. Struct.

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Laminated composite plates are utilized due to their high strength/weight ratios. Since such structures are light and have less stiffness, their natural frequencies are lower than usual isotropic structures. Therefore, their behaviours in higher order modes are of interest. On the contrary, sensitivity analysis of vibrating structures is generally performed for lower order modes. In this study, sensitivity analysis of symmetrical/anti-symmetrical/asymmetrical laminated composite plates is performed in low to high order modes. In this regard, angular orientation, Young’s modulus, shear modulus, Poisson’s ratio and density of the plate are selected as design parameters whereas natural frequencies are selected as design objective functions. Discrete singular convolution method is used as solver due to its high computational capability. Although some other conclusions are drawn, it can mainly be concluded that, the natural frequencies are very sensitive to small differences in Poisson ratio for orientation angles of considered plates.

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Section: Dsc Methods For the Laminated Thin Composite Platesmentioning

confidence: 99%

Sensitivity analysis of laminated composite plates with different orientations in low to high order modes

Kara¹,

Güler²,

Seçgin³

2021

Smart Mater. Struct.

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“…5, maximum transmission loss is converged to about 23.92 dB if the mesh is smaller than 0.5 mm. However, if the element size is less than 0.7 mm, the maximum difference from the converged value was 0.1 dB (0.5 % difference), so considering the calculating time, all analyses were conducted at mesh size of 0.7 mm [30,31]. By comparing the change of STL according to frequency obtained from each experiment and analysis method, as shown in Fig.…”

Section: Euclid Curvementioning

confidence: 99%

Design of flat broadband sound insulation metamaterials by combining Helmholtz resonator and fractal structure

et al. 2021

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A new sound insulation metamaterial (SIM) is designed by combining a Helmholtz resonator and a fractal structure for sound insulation in the frequency range of 600 to 1700 Hz. Using a fractal-based internal structure, the designed hybrid SIM shows a relatively constant value of sound transmission loss (STL) over the target frequency range. The basic concept of this work is to develop two functional parts working in each effective frequency range. One is a Helmholtz resonance structure that operates with a high value of STL from 600 to 1000 Hz, and the other is an internal fractal structure that shows a high STL at higher frequencies in the 1000 to 1700 Hz range. In this work, the proposed metamaterial has a mean of 16.34 dB with a standard deviation of 1.73 dB within the wide target range of 600 to 1700 Hz. Additionally, the proposed SIM is approximately 40 % smaller in size than the previous resonator and has a higher mean STL with a small ∆STL of 1.7 dB between highest and lowest values.

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“…Proper boundary condition implementation procedure is performed to get rid of the displacement in the ghost domains. Note that, this procedure is given in detail in Ref (Kara and Seçgin, 2019; Seçgin and Sarigül, 2008, 2009) for clamped, simply supported and free boundary conditions.Next, equation (3) can be written in a matrix form as an eigenvalue problem…”

Section: Mathematical Considerationsmentioning

confidence: 99%

Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

Seçgin

Kara

Ferguson

2021

Journal of Vibration and Control

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This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.

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Discrete singular convolution method for one-dimensional vibration and acoustics problems with impedance boundaries

Cited by 7 publications

References 34 publications

Sensitivity analysis of laminated composite plates with different orientations in low to high order modes

Sensitivity analysis of laminated composite plates with different orientations in low to high order modes

Design of flat broadband sound insulation metamaterials by combining Helmholtz resonator and fractal structure

Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

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