Experimental investigation on natural frequencies of thin rectangular plates using contact and non-contact methods

Authors

1 Mechanic,Engineering,Fedowsi University of Mashhad, Mashhad, Iran

2 Mechanic,Engineering,Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

In this paper, two excitation methods, namely contact and non-contact methods were used to excite a thin rectangular plate with clampled boundary conditions at all four edges. A modal hammer was used to apply an impact on the surface of the plate in the contact method while for the non-contact method, three loudspeakers were utilized to excite the plate by emitting a white noise signal. The loudspeakers covered low, medium and high ranges of frequency. Different positions for excitation point were suggested in order to find the best position in which the accelerometer is more capable of measuring the vibration of plate surface at natural frequencies. By comparing two types of excitation, the non-contact method was discovered to have advantages over contact method in medium and high frequency ranges and the contact method had better performance in low frequency range. An approximate analytical method based on Rayleigh-Ritz method was also studied in order to compare and validate the experimental results in predicting natural frequencies of a thin rectangular plate.

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References

[1] Leissa AW (1969) Vibration of plates. Technical Report, Ohio State University Columbus.
[2] Mukhopadhyay M (1978) A semi-analytic solution for free vibration of rectangular plates. J Sound Vib 60: 71-85.
[3] Dickinson S, Di Blasio A (1986) On the use of orthogonal polynomials in the Rayleigh Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates. J Sound Vib 108: 51-62.
[4] Lee H, Lim S (1992) Free vibration of isotropic and orthotropic rectangular plates with partially clamped edges. Appl Acoust 35: 91-104.
[5] Mizusawa T (1986) Natural frequencies of rectangular plates with free edges. J Sound Vib 105: 451-459.
[6] Bardell N (1991) Free vibration analysis of a flat plate using the hierarchical finite element method. J Sound Vib 151: 263-289.
[7] Bhat R, Mundkur G (1993) Vibration of plates using plate characteristic functions obtained by reduction of partial differential equation. J Sound Vib 161: 157-171.
[8] Rajalingham C, Bhat R, Xistris G (1996) Vibration of rectangular plates using plate characteristic functions as shape functions in the Rayleigh–Ritz method. J Sound Vib 193: 497-509.
[9] خورشیدی ک، بخششی ع، قدیریان ح (1395) بررسی تاثیرات محیط حرارتی بر ارتعاشات آزاد ورق مستطیلی از جنس مواد تابعی مدرج دو بعدی مستقر بر بستر الاستیک. مجله علمی پژوهشی مکانیک سازه­ها و شاره­ها 147-137 :(3)6.
[10] قدیریان ح، قضاوی م ر، خورشیدی ک (1395) تحلیل ارتعاشات و پایداری ورق­های مرکب چند لایه تحت اثر رطوبت و دما. مجله علمی پژوهشی مکانیک سازه­ها و شاره­ها 166-155 :(2)6.
[11] Wang D, Yang Z, Yu Z (2010) Minimum stiffness location of point support for control of fundamental natural frequency of rectangular plate by Rayleigh–Ritz method. J Sound Vib 329: 2792-2808.
[12] Ramu I, Mohanty S (2012) Study on free vibration analysis of rectangular plate structures using finite element method. Procedia Eng 38: 2758-2766.
[13] Senjanovic I, Tomic M, Vladimir N, Hadzic N (2015) An approximate analytical procedure for natural vibration analysis of free rectangular plates. Thin-walled Str 95: 101-114.
[14] Yeh YL, Jang MJ, Wang CC (2006) Analyzing the free vibrations of a plate using finite difference and differential transformation method. Appl Math Comp 178: 493-501.
[15] Mochida Y, Ilanko S (2008) Bounded natural frequencies of completely free rectangular plates. J Sound Vibration 311: 1-8.
[16] Malik M, Bert C W (1998) Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method. Int J Solid Str 35: 299-318.
[17] خورشیدی ک، عنصری نژاد س (1395) تحلیل دقیق ارتعاش آزاد ورق­های قطاعی کوپل شده با لایه پیزوالکتریک با بکارگیری تئوری تغییر شکل برشی مرتبه اول. مجله علمی پژوهشی مکانیک سازه­ها و شاره­ها 138-125 :(4)6.
[18] ‌Benamar R, Bennouna M, White R (1993) The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures, Part II: fully clamped rectangular isotropic plates. J Sound Vibration 164: 295-316.
[19] Low K, Chai G, Tan G (1997) A comparative study of vibrating loaded plates between the Rayleigh-Ritz and experimental methods. J Sound Vibration 199: 285-297.
[20] Singhatanadgid P, Songkhla AN (2008) An experimental investigation into the use of scaling laws for predicting vibration responses of rectangular thin plates. J Sound Vibration 311: 314-327.
[21] Nieves F, Gascon F, Bayon A (2004) Natural frequencies and mode shapes of flexural vibration of plates: laser-interferometry detection and solutions by Ritz’s method. J Sound Vibration 278: 637-655.
[22] Howard CQ, Kidner MR (2006) Experimental validation of a model for the transmission loss of a plate with an array of lumped masses. Proc. Acoust. Christchurch, New Zealand 169-177.
[23] Crocker M J (207) Handbook of noise and vibration control. John Wiley & Sons.
Journal of Solid and Fluid Mechanics
Volume 8, Issue 1
April 2018
Pages 1-11

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