A differential quadrature procedure for free vibration of circular membranes backed by a cylindrical fluid-filled cavity

Eftekhari, S. A.

doi:10.1007/s40430-016-0561-3

Cited by 3 publications

(2 citation statements)

References 49 publications

(86 reference statements)

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“…Since it is difficult to solve analytically the coupled equations of motion under different boundary conditions, the differential quadrature method (DQM) as an accurate and low computational efforts numerical tool [9,[34][35][36][37][38][39][40][41][42][43][44] is applied to discretize the equations of motion and the related boundary conditions in the spatial domain. The main advantage of this method is that the equations of motion and the boundary conditions are discretized in their strong form and only limited number of grid points is required to achieve accurate converged results.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Hence, in this paper, the dynamic stability of nanoshells is presented based on the two-dimensional nonlocal elasticity of Eringen in conjunction with the first-order shear deformation theory (FSDT) of shells. The differential quadrature method (DQM) as an efficient and accurate numerical method [9,[34][35][36][37][38][39][40][41][42][43][44] is utilized to spatially discretize the equations of motion subjected to different boundary conditions. The discretized governing partial differential equations are converted to a system of Mathieu-Hill-type equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

Heydarpour

Malekzadeh

2019

J Braz. Soc. Mech. Sci. Eng.

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The dynamic stability of cylindrical nanoshells subjected to combined static and time-dependent periodic axial forces is studied by employing the two-dimensional nonlocal elasticity theory together with the first-order shear deformation theory of shells. The differential quadrature method as an efficient and accurate numerical technique is applied to discretize the equations of motion under different boundary conditions in the spatial domain and transform them into a system of coupled Mathieu-Hill-type equations in time domain. Subsequently, the Bolotin's first approximation method is employed to extract the dynamic instability regions of the cylindrical nanoshells. The approach is validated by showing its fast convergence rate and carrying out comparison studies with existing results in the limit cases. Afterward, the effects of the nonlocal parameter, length and thickness-to-mean radius ratios together with different boundary conditions on the principal dynamic instability regions of the cylindrical nanoshells are studied in detail.

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Section: Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

Heydarpour

Malekzadeh

2019

J Braz. Soc. Mech. Sci. Eng.

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State-of-the-Art of Vibration Analysis of Small-Sized Structures by using Nonclassical Continuum Theories of Elasticity

Nuhu

Safaei

2022

Arch Computat Methods Eng

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Band gap of structure coupling Helmholtz resonator with elastic oscillator

Chen¹,

Ye²,

Zhao³

et al. 2019

Acta Phys. Sin.

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<sec> In order to improve the low-frequency acoustical insulation performance of Helmholtz phononic crystals, a structure coupling Helmholtz resonator with elastic oscillator is designed. This structure combines the characteristics of Helmholtz resonators with those of the local resonant solid-solid phononic crystals. In this structure, the elastic oscillator is bonded to the inner wall of the conventional Helmholtz resonator by rubber. The structure has two bandgaps in the low-frequency range, i.e. 24.5−47.7 Hz and 237.6−308.6 Hz for a lattice constant of 6 cm. However, for the same lattice constant, the lower limit of the bandgap of the traditional Helmholtz resonator without the elastic oscillator structure is only 42.1 Hz. Our structure reduces the minimum lower limit of the bandgap by 40% compared with the traditional Helmholtz structure and has better low-frequency acoustical insulation characteristics. </sec><sec> In this study, the generation mechanism of the bandgap is analyzed with the sound pressure field and vibration mode. It is found that the elastic oscillator and the air in the air passage of the resonator vibrate in the same direction at the frequency of upper and lower limit for the first bandgap while they vibrate in the reverse direction for the second bandgap. Outside the resonator, air sound pressure is zero at the lower limit of the bandgap. The spring-oscillator system is established as an equivalent model. In the model, the elastic oscillator and the air in the passage are regarded as oscillators, and the air separated by the elastic oscillator, the air outside the resonator, and the rubber connected with the elastic oscillator are all regarded as springs. Besides, it can be found that the air in the resonator shows different equivalent stiffness for different vibration mode. </sec><sec> In the discussion, the effects of structural parameters on the bandgap are studied by theoretical calculation and the finite element method. The results show that when the lattice constant decreases without changing the side length of the resonator, the bandgap width increases without affecting the lower limit of the bandgap. The increase of the length of the air passage can increase the width of the first bandgap while the second bandgap decreases. However, the increase of the mass effect of the elastic oscillator results in the first bandgap width decreasing and the second bandgap width increasing. The increase of the length of the air passage and the mass of the elastic oscillator both can reduce the bandgap frequency. It can be found that the volume of the right cavity only affects the frequency of the second bandgap, while the volume of the left cavity can influence the frequency of each bandgap. Therefore, the shorter distance between the elastic oscillator and the passage, the better low-frequency acoustical insulation performance of the structure can be reached. Finally, the increase of the length of the rubber produces new vibration modes, which leads to the generation of new small bandgaps and the change of the frequency of the original bandgaps. However, it is found that the influence of the mode of vibration on the bandgap is smaller than that of the mass of the elastic oscillator, and the regularity of its impact is not apparent.</sec>

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A differential quadrature procedure for free vibration of circular membranes backed by a cylindrical fluid-filled cavity

Cited by 3 publications

References 49 publications

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

State-of-the-Art of Vibration Analysis of Small-Sized Structures by using Nonclassical Continuum Theories of Elasticity

Band gap of structure coupling Helmholtz resonator with elastic oscillator

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