**Executive Summary**

In this project, natural frequency of reinforced plate has been found either on Abaqus

Software and with the stiffness-frequency formulas. Since there are two different

analysis methods, of course there are two different results. Abaqus software’s

value(37.8) is %30 higher than the simple calculations result (29.2). Since, software

has many inputs like; material, interactions, model dimensions etc.., in hand

calcualtions, only property used from model was the mass and stiffness. There may

also be one more reason for that which is; when stiffness was calculated, only elastic

deformation took place.

In the second step; it is obvious that the stress generated on the model due to applied

load exponentially increases while frequency approaches to natural frequency. It will

have huge impact if an earthquake engineer does not know about the frequency of

structures.

**Problem Definition**

Main objective of this project is to measure the natural frequency of the model created

in “**Assessment of the Reinforced Plate with Linear Elastic Analysis and Non-Linear Analysis**“. This model has 3 reinforcement bars attached to a plate and fixed on one

end.

Methodology of finding the natural frequency of the model is; defining a frequency in

Step-1 without applying any load. If any load is applied, there will not be a problem

since Abaqus software will override the input onto the assigned load. After this

process, analysis will give the natural frequencies of the model as 10 different modes

of outputs.

In the second step, we are asked to use the first step’s outputs as an input to find the

structural damping and mass damping values and apply a 150 Newtons of distributed

load on flat surface of the model.

**Analysis Description**

Natural frequency of the model has been calculated in the first step;

Ready to use excel sheet has been used to obtain the structural damping ‘β’ and mass

damping ‘α’ values. Damping ratio ‘ξ’ taken as %5 in this process.

**Results and Discussion**

There have been 10 different failure scenarios occurred in 10 different frames during

first step. Some of the cases are just mirrored versions of the other one’s but it is

crucial to have that knowledge in design phase.

Natural frequency could also be found via using 2 formulas below;

k = F/u

f = (1/2π)*(k/m)^{1/2}

Where;

‘k’ is the stiffness,

‘f’ is the frequency

‘u’ is the displacement

‘F’ is the force

and ‘m’ is the mass.

Therefore;

k = F/u = 723N/5mm = 144.6 N/mm;

f = (1/2π)*(k/m)^{1/2} = (1/2π) * (144600/4.29)^{1/2 } = 29.2 Hz

Frequency found via Abaqus software is 37.8 Hz where simple hand calculations

gives us the value of 29.2 Hz. In this case, software’s value is more reliable because at

the modeling and assembling phases; interactions between reinforcements to plate,

material properties, section properties have been assigned. Difference between 2

results occurs because of this. In hand calculations, there is not any materials or

interactions defined. Those calculations may be used in springs and then it will give

reliable and accurate results but, in this case, where there is a complex model, it is

hard to obtain a reliable result.

Table 3 shows that; there is a jump through frequency 27 to 36. Since natural

frequency is known as 37.8 of the model, with an engineering judgement, model gets

under huge stress while frequency catches the natural frequency. Extra of 150N’s

distributed load creates destructive effect within frequencies close to natural

frequency. Any load applied on the model will have direct incremental effect on the

stress generation and indirect effect on the deflection of the model.