Modal Analysis of a Square Plate with Reinforcement with Number of Stiffeners

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/ by/4.0) ABSTRACT This Modal analysis is a major technique to determine the vibration characteristics of engineering structures and its component’s. It is a process by which the natural frequencies, mode shapes of the structure can be determined with a relative ease. It should be a major alternative to provide a helpful contribution in understanding control of many vibration phenomena which encompasses in practice. In this work comparison of the natural frequency of the square plate with different number of reinforcement is found by using FEA .The main objective of this paper is to determine the natural frequency and mode shape of a square plate with different number of reinforcements. The number of ribs is increased in each iteration.


A. INTRODUCTION
Modal analysis is the study of the dynamic properties of systems in the frequency domain. Examples would include measuring the vibration of a car's body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeaker.
Modern day experimental modal analysis systems are composed of 1) Sensors such as transducers as, or non contact via a Laser vibrometer, or stereo photogrammetric cameras 2) Data acquisition system and an analogue-todigital converter frontend (to digitize analogue instrumentation signals) and 3) Host PC (personal computer) to view the data and analyze it.
Classically this was done with a SIMO (single-input, multipleoutput) approach, that is, one excitation point, and then the response is measured at many other points. In the past a hammer survey, using a fixed accelerometer and a roving hammer as excitation, gave a MISO (multiple-input, singleoutput) analysis, which is mathematically identical to SIMO, due to the principle of reciprocity. In recent years MIMO (multi-input, multiple-output) have become more practical, where partial coherence analysis identifies which part of the response comes from which excitation source. Using multiple shakers leads to a uniform distribution of the energy over the entire structure and a better coherence in the measurement. A single shaker may not effectively excite all the modes of a structure Stiffening objects or processes brings rigidity and structural integrity. Stiffening is used in industry, architecture, sports, aerospace, object construction etc. In mechanics, "stiffening" beams brings anti-buckling, anti-wrinkling, desired shaping, reinforcement, repair, strength, enhanced function, extended utility. In medicalarts, aerospace, aviation, sports, bookbinding, art, architecture, natural plants and trees, construction industry, bridge building, and more. Mechanical methods for stiffening include tension stiffening, centrifugal stiffening, bracing, superstructure bracing, substructure bracing, straightening, strain stiffening, stress stiffening, damping vibrations, swelling, pressure increasing, drying, cooling, interior reinforcing, exterior loads or compression invite stiffening to stop buckling or reinforcing, wrapping, surface treating, or combinations of these and other methods. Beams under bending collapse while fulfilling desired functions, purposes, and benefits.

B. PROBLEM DEFINITION:
A square plate of (50X50) mm planar area is considered for analysis. Thickness of the plate considered is 2mm. The plate is then subjected to different number of reinforcements ie

IJTSRD23207
International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470 Page: 1158 ribs i.e one, two, three and four. The reinforcement area will increase from single rib to four ribs.
The boundary conditions for the plate with different cut outs is kept same i.e all the four corners of the plate are constrained in all DOF Four different square plates of above mentioned dimensions is considered with all four corners completely fixed in all DOF.
The geometry of square plate with single rib, two ribs, three ribs and four ribs is shown in figures from fig1 to fig4. Mode Shape

Mode shapes of Square plate with single rib
It has been observed that for mode shape 2 the natural frequency is decreasing. Fig.31 Variation of natural frequency for Mode shape 3 It has been observed that for mode shape 3 the natural frequency is decreasing. It has been observed that for mode shape 4 the natural frequency is increasing. Fig.33 Variation of natural frequency for Mode shape 5 It has been observed that for mode shape 5 the natural frequency is decreasing and increasing. It has been observed that for mode shape 6 the natural frequency is increasing.

CONCLUSION
The finite element formulation is used to study effect of reinforcements on the free vibration of Mild steel plate. The results obtained from finite element software are presented and discussed above. The conclusions that can be made from the present study are summarized as follows: It has been observed that the natural frequency for the plate with increasing number of ribs is decreasing for mode shape 1, 2 and 3 and is increasing for mode shape 4, 5 and 6. Hence in order to have decrease in frequency of plate number of ribs should be increased for mode shapes 1, 2 and 3 where as to obtain increase in frequency of plate number of ribs should be increased for mode shapes 4, 5 and 6. Hence depending on the requirement of the frequency the reinforcement on the plate can be selected.