Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

Wu, J J; Chou, H. M.; Dw, Chen

doi:10.1243/146441903321898656

Cited by 6 publications

(7 citation statements)

References 32 publications

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“…The solutions from the eigenfunction expansion (EE) method presented by Avalos et al [10] and Wu et al [12] and the solutions from the finite element (FE) method presented by Wu et al [12] are taken as the reference. Moreover, the solutions from the Lagrangian multiplier (LM) method presented by Kim and Dickinson [3] are taken for comparison for the case of a rigid vertical point-support.…”

Section: Comparative Studymentioning

confidence: 99%

“…Wong [11] applied the Rayleigh-Ritz method to study the effect of distributed mass on plate vibration behaviour. Wu et al [12] used the mode expansion method to investigate the effect of various concentrated elements. Jacquot [13] used the two-dimensional Fourier series to study the random vibration of rectangular plate attached with absorbers.…”

Section: Introductionmentioning

confidence: 99%

“…Adhikari et al [18,19] experimentally studied the effect of uncertainty quantification on structural dynamics. Although some investigators [10,12,13] used the two-dimensional Fourier sinusoidal series to obtain the exact solutions of the dynamic characteristics of plates attached with elastic/rigid masses, such a method is only applicable to plates with four edges simply supported. It should be mentioned that the existing studies mainly focused on plates with classical boundary conditions and with one sprung mass.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Zhou

2012

Shock and Vibration

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Abstract.A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical point-supports.

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Section: Comparative Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Zhou

2012

Shock and Vibration

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“…Some papers studied the free vibration of rectangular plates with discrete elements such as concentrated sprung/rigid masses or elastic/rigid point-supports (Wu et al, 2003; Zhou and Ji, submitted for publication; Wu and Luo, 1997). Moreover, some papers have studied the free vibration of rectangular plates with continuous elements such as elastic foundation and distributed solid mass (Avalos et al, 1989;Kopmaz and Telli, 2002;Wong, 2002).…”

Section: Comparison and Validationmentioning

confidence: 99%

“…Some papers studied the free vibration of rectangular plates with elastic/rigid point-supports, based on the energy method, using different approaches such as spline finite strip method (Fan and Cheung, 1984), finite layer method (Zhou et al, 2000), the Lagrangian multiplier (Kim and Dickinson, 1987), the static beam functions (Cheung and Zhou, 1999;Zhou, 2002), the orthogonal polynomials (Liew et al, 1994) and the exact solution (Gershgorin, 1933;Bergman et al, 1993;Zhou and Ji, submitted for publication). Moreover, some papers studied the free vibration of rectangular plates with elastic/rigid concentrated masses by using different methods such as the exact solution (Bergman et al, 1993;Li, 2001Li, , 2003Zhou and Ji, submitted for publication), the optimal Rayleigh-Ritz method (Avalos et al, 1994) and the mode expansion method (Avalos et al, 1993;Wu and Luo, 1997;Wu et al, 2003;Chiba and Sugimoto, 2003). Keane (1996, 1997) investigated the possibility of using attached masses to control the vibration of rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of rectangular plates with continuously distributed spring-mass

Zhou

2006

International Journal of Solids and Structures

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The vibratory characteristics of rectangular plates attached with continuously and uniformly distributed spring-mass in a rectangular region are studied which may represent free vibration of a human-structure system. Firstly, the governing differential equations of a plate with uniformly distributed spring-mass are developed. When the spring-mass fully occupies the plate, the natural frequencies of the coupled system are exactly solved and a relationship between the continuous system and a series of discrete two degrees-of-freedom system is provided. The degree of frequency coupling is defined. Then, the Ritz-Galerkin method is used to derive the approximate solution, when the spring-mass is distributed on a part of the plate, by using the Chebyshev polynomial series to construct the admissible functions. Comparative studies demonstrate the high accuracy and wide applicability of the proposed method. Finally, the frequency and modal characteristics of the plate partially occupied by distributed spring-mass are numerically analysed. It has been observed that both the natural frequencies and the modes appear in pairs. Moreover, a parametric study is performed for rectangular plates with three edges simply supported and one edge free. The effects of occupation size and position of the distributed spring-mass on natural frequencies of the coupled system are studied in detailed. The present investigation provides an improved understanding of human-structure interaction, such as grandstands or floors occupied by a stationary crowd.

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Health Monitoring for Damage Initiation & Progression during Mechanical Shock in Electronic Assemblies

Lall

Choudhary

Gupte

et al.

56th Electronic Components and Technology Conference 2006

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Electronic products may be subjected shock and vibration during shipping, normal usage and accidental drop. Highstrain rate transient bending produced by such loads may result in failure of fine-pitch electronics. Current experimental techniques rely on electrical resistance for determination of failure. Significant advantage can be gained by prior knowledge of impending failure for applications where the consequences of system-failure may be catastrophic. This research effort focuses on an alternate approach to damage-quantification in electronic assemblies subjected to shock and vibration, without testing for electrical continuity. The proposed approach can be extended to monitor product-level damage.In this paper, statistical pattern recognition and leading indicators of shock-damage have been used to study the damage initiation and progression in shock and drop of electronic assemblies.Statistical pattern recognition is currently being employed in a variety of engineering and scientific disciplines such as biology, psychology, medicine, marketing, artificial intelligence, computer vision and remote sensing [Jain, et. al. 2000]. The application quantification of shock damage in electronic assemblies is new.Previously, free vibration of rectangular plates has been studied by various researchers [Leissa 1969, Young 1950, Gorman 1982, Gurgoze 1984, Wu 2003] for development of analytical closed-form models. In this paper, closed-form models have been developed for the eigen-frequencies and mode-shapes of electronic assemblies with various boundary conditions and component placement configurations. Model predictions have been validated with experimental data from modal analysis. Pristine configurations have been perturbed to quantify the degradation in confidence values with progression of damage. Sensitivity of leading indicators of shock-damage to subtle changes in boundary conditions, effective flexural rigidity, and transient strain response have been quantified. A damage index for Experimental Damage Monitoring has been developed using the failure indicators.The above damage monitoring approach is not based on electrical continuity and hence can be applied to any electronic assembly structure irrespective of the interconnections. The damage index developed provides parametric damage progression data, thus removing the limitation of current failure testing, where the damage progression can not be monitored. Hence the proposed method does not require the assumption that the failure occurs abruptly after some number of drops and can be extended to product level drops.

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Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

Cited by 6 publications

References 32 publications

Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Free vibration of rectangular plates with continuously distributed spring-mass

Health Monitoring for Damage Initiation & Progression during Mechanical Shock in Electronic Assemblies

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