FLEXURAL VIBRATION OF FIXED SUPPORTED BEAMS

1. FLEXURAL VIBRATION OF FIXED SUPPORTED BEAMS
SRINIVAS REDDY.S
R19MCE13

2. • The dynamic bending of beams, also known as flexural
vibrations of beams, was first investigated by Daniel
Bernoulli in the late 18th century.
• Resonance frequencies of beams with various types of end
supports were examined for flexural vibration.
• The natural frequencies associated with flexural vibrations are
of much lower magnitude than those of torsional and axial
vibrations.
• The purpose of flexural vibration analysis is to know the
structural behavior under the influence of various loads and to
get the necessary information for design such as deformation,
moments and dynamic forces etc
INTRODUCTION

3. Response of the beams due to moving loads:
• A single concentrated load is assumed to move with a uniform velocity the
practical application for this problem occurs in bridges ,aircraft , carriers
etc.
• Automobiles , aircrafts , etc., while moving over the deck produces a
number of effects , with increases the stresses in the structural members.
some of them are the impact effect due to unbalanced parts of the vehicle
,impact effect due to irregularities of the deck surface and the effect on the
structure due to smooth running of the vehicle.
1. The mass of moving load is considered to be small in comparison to the
mass of the deck. This case is to be analysed as an elastic beam subjected
to a moving load
2. The mass of moving load is considered to be larger in comparison to the
mass of beam is neglected and the weight of vehicle is considered as a
concentrated weight so the problem reduces to SDF system

4. fixed flexural vibration testing method of beams for timber
guardrails
• Young’s modulus is one of the properties that is related to the
strength and can be obtained without damaging the specimen.
One method for measuring Young’s modulus is a flexural
vibration test.
• A beam for a timber guardrail is fixed to a post by a bolt
through a bracket (Fig. 1). Therefore, the end conditions of the
beams used as timber guardrails are thought to be between
those of simply supported ends and fixed ones.
• the resonance frequency of a beam with fixed ends is about
twice as large as that of a beam with simply supported ends,
according to the Euler-Bernoulli elementary theory on
bending.
timber guardrails

6. VIBRATION TEST
To obtain the resonance frequency of the first mode by bending, flexural vibration
tests were conducted by the following procedure.
• An apparatus (End condition controller) shown in Fig. was used to provide
various end conditions.
• By screwing a bolt attached to a load cell, the test beam was compressed.
• The compressing load was measured by the load cell and recorded by a data
logger .Motion of the beam was detected by a microphone in the center part
• The signal was processed through a fast Fourier transform (FFT) digital signal
analyzer to yield high-resolution resonance frequencies.

7. Changes in resonance
frequency with compression for
5-mm-thick spruce (left) and
10-mm-thick spruce (right)

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