Vol.24, No.3, 2024, pp. 393–397
https://doi.org/10.69644/ivk-2024-03-0393

TIME PERIOD OF TAPERED PARALLELOGRAM SHAPED PLATE WITH EXPONENTIAL PROFILE IN YOUNG’S MODULUS

Neeraj Lather1, Reeta Bhardwaj1, Naveen Mani2, Praveen Ailawalia2*, Amit Sharma1**

1) Department of Mathematics, Amity School of Applied Sciences, Amity University Haryana, Gurugram, INDIA

N. Lather  0000-0001-7896-844X; R. Bhardwaj  0000-003-2427-5108; A. Sharma  0000-003-4516-6955

2) Department of Mathematics, University Institute of Sciences, Chandigarh University, Chandigarh, Gharuan, Mohali, Punjab, INDIA    N. Mani  0000-0002-7131-2664; P. Ailawalia  0000-0003-4381-6299

*email: praveen_2117@rediffmail.com ; **email: dba.amitsharma@gmail.com 

 

Abstract

The current study estimates the time period of frequency (four modes) of parallelogram shaped plate having circular density and thickness in one and two dimensions, in respect, along with exponential profile in Young's modulus for two different edge conditions. The two different edge conditions of the plate are CCSS and CSSS. The Rayleigh-Ritz method is implemented to solve the frequency equation for the system mentioned above. The major conclusion made from the study is that we can optimise the time period for the system by choosing the circular profile in density and thickness for such plates. To validate our findings, we compare our results with previously published data and show in tabular form.

Keywords: density, exponential, skew plate, Young’s modulus, time period

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