Ionospheric antenna spanish to english complete translate.

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Translated spanish document named RESONANCIA MEC?NICA , page 1 out of 10

AMPLIFICATION OF MECHANICAL RESONANCE

(picture here some broken bridge)

The figure shows a classic one of the amplification by Resonance simultaneously is a real case of the phenomenon, it is the famous bridge of Tacoma located Narrows in the USA in the region near Washington that was inaugurated in 1940 and only lasted 4 months, it came down and it fell to the water product of the resonance of the structure with the wind around it is a case world-wide accepted and it was as it shows the photo, the 68 wind gusts of wind that reached Km/h, the amplified repetitive force of the wind caused that the bridge rose and balanced until it was broken and fell to the water
The present publication finally must show that in the mechanical systems also we have energy amplification in resonance as a parallel equivalent to the amplification by electrical resonance through the ionosphere and to have one first impression of the obvious thing is east phenomenon.
All mechanical system or piece of matter has parameters such as: Mass, elasticity and viscosity or clear, especially the matter in solid state is what we analyzed here, when is applied to an external force to the system takes place an oscillation, especially if the applied force is oscillating, the objective is to demonstrate analytically that the final energy of the system in oscillation is greater to the muzzle energy has been applied on the system to a frequency near the resonance.
We consider the following scheme shows a mechanical system of a degree of freedom, that is to say, able to move in a dimension to only simplify the analysis:

page 2 below,

(diagram here)

The three parameters, inertia, elasticity and grazes is represented by parameters M, K, and C respectively and is measurable in any real physical system easily. When moving the mass of its position of balance the effect means will exert a force being against to its streching, and the shock absorber will be against the speed
We call F to the external force will be applied on the system, the differential equation of the movement will be:

(work out here)

The one that does not depend on the applied force reason why appreciates, whose solution is:

(work out here)

onde xs (U) =xU and dx/dt (U) = vU are initial conditions.
Thus then there will be 4 possibilities in the oscillating movement of the system: On cushioned (p >1), critically cushioned (p=1) and sub cushioned (p <1) respectively
In the ideal case cushioned (p=U) the movement it is not a maintained oscillation then as the function of the damping can be seen is to diminish the amplitude of the oscillations expotencialmente

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Practical examples of cushioned mechanical systems are: smooth lowering of the arm of a tornamesa of a tocadisco (not cushioned), suspension of sport car (critically cushioned for fast answer) and a springboard (cushioned Sub)

Measurement of the damping factor:

As the unique case in that is appraised we have free oscillation is in the case sub cushioned generally, for this case this factor of damping can be determined measuring the successive amplitude of the oscillation by n periods of duration T is watching the equation (2):

(work out here)

Applying logarithms and defining:


(work out here)

Clearing and remembering that is had

(work out here)

For values of p smaller than 0.2 the expression approximated to 2% of error can be used:

(work out here)

Another form to find this factor is to count the number of necessary oscillations n so that the initial amplitude decays to half. In such case the previous equation takes the form:

(work out here)

Simpler still, but with the abundance of software nowadays, it is enough to have a PC with sound card and vibration sensors, thus simply we struck the object we want to him to measure the damping factor and software will make the rest and it will give east factor to us with the exactitude we want.

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Generally we can say that vibratory systems with low factor of damping vibrate with almost equal frequencies that the system noncushioned, when increasing the damping lowers to the frequency extending itself the period of oscillation measured Values are for example, for the steel a factor of damping of 0.01 and rubber 0.1, and the reason between successive maximums is 0.9 and 0.5 respectively
VIBRATION FORCED IN RESONANCE
Before exposed it is the free vibration of the mechanical system without a permanent external force, that is to say the way of answer of the system to a force of short duration calculated leaves oscillating the system until it pauses in order to obtain conditions and parameters and knowledge before nothing if our system is going to oscillate and how, now the idea is to apply an external alternating force, an external vibration and to see what happens with its amplitude if the system will give to him more amplitude the route of that force, that is to say, will give additional energy and we obtain the wished amplification.
In these conditions the equation (1) instead of for being even to zero is even to the applied external force:

(work out here)


If harmonic force we suppose the applied it of the form

(work out here)


Being wf the frequency of the vibration applied on the system.
Of the solution of the differential equation it interests the particular solution to us or in stationary state it would have the form:

(work out here)


and the amplitude would be:

(work out here)

Where w is simply the final oscillation frequency of the system
It is appraised clearly that the numerator of this expression would be the possible maximum deformation of the means equivalent of the system when being applied the external force, if this amplitude B is greater to that value we would be obtaining more energy and therefore an amplification of



Page 5 below.

energy, we remember work = energy and the energy is force by displacement, defines then the amplification factor like:

(picture here strong DesplazamienWo/static Displacement)

The factor of frequency or syntony is also defined like:

(picture here)

Thus then it is possible to be rescribir:

(pic here)

the phase angle

(pic here)

A graph of (5) will help us to include/understand better the situation near the resonance as dep is appraised more down for different practical values and q:

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Observing these previous graphs of amplitude, the maximum amplification is not to the frequency of resonance (q = 1), but in a smaller value it is obtained from:

(work out here)

What means then that stops a factor of damping of p =1/V2 we are in the case limit, and dampings majors no longer produce maximum, except for obvious in wf=0 of equal value to the unit.
The maximum amplification, in maximum q will be then:

(work out here)

In the resonance frequency, q = 1, has an amplification of:

(work out here)

This last value receives the name of resonance amble

He is also interesting to appreciate the analogy of these equations and graphs with the electrical equivalents, in the resonant electrical circuits study in courses of mains, exist the curves of universal resonance there are the same shown here, the system mass-means is dice by an inductance and a condenser and the rubbing or viscous damping by the electrical resistance, thus in those circuits in resonance exists a current amplification or voltage, but never a power amplification because the energy always in those electrical systems contributes to the source and the load to it is passive, nevertheless here in the mechanical system when increasing the oscillation in resonance the work done by the force applied it alternates increases since the amplitude of the oscillation increases for the same force, that energy does not come from the external agent applies the force but it is given by the own mechanical system it stores energy and it is at heart the energy maintains to the solid like so, the stored molecular internal energies like potential energy, reason why this mechanical energy amplification does not break the conservation law of energy, is simply an energy transfer. To notice that the factor decides if we will have amplification is the one of damping and therefore not always this amplification is guaranteed, depends then on the elasticity degree of the solid or material and if its elastic range is very small we will not have results, normally all the current materials have ample elastic range and if we remembered the factor of

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damping of the steel for example we gave before was of 0.01, the amplification factor rises by on 50
Arises a question, how to enconWrar the frequency of resonance GE sisWema? , good, we can in first approach consider it by the classic formula of oscillations:


some science divider with (k line m) here can't be arsed with another pic.



That it would serve to begin with as point then as we already know also depends on the damping, but it helps us, elasticity we can consider it to k of the Young's modulus of the material to analyze, but it is very clear with this simple formula that this frequency will increase with the elasticity of the material and will lower with its mass, a very great system will vibrate to smaller VLF and to higher frequencies
Nevertheless if we are practitioners more and we watched the equation of phase angle between the force and the displacement in vibration (6) we see that to the frequency of resonance q =1, the phase angle must be of 90?, reason why experimentally can find it thus
The energy amplification in resonance is a phenomenon clearly explained and justified in Mechanics with solid a practical and theoretical base, it is a so important fact that the technicians and engineers must take care of that their equipment does not vibrate or enters vibration with some harmonica happens through the resonance of the system, especially that care takes themselves in the generating turbines from electricity, motors, etc, take place repetitive analyzes of vibration of the machines in order that this does not happen. The theoretical analysis has been made here is for showing the nature of the mechanical resonance and clearly it is appraised that the maximum amplification is not to the resonance frequency but a slightly smaller value, and depends strongly on the damping of the system, therefore to frequencies different from the one of more distant resonance or harmonicas the amplification is cushioned quickly, the resonance is welcome in fields like music, the violin arc excites the cords of the same in many frequencies, but the one of resonance only persists and its overtones and by all means for those who we worked in free energy. Violation in the principle of conservation of energy does not exist, the energy in excess leaves the amplification comes from the excited body same and is released to the outside and it is due to notice that to persist the force this one initiates the oscillation will grow indefinitely until the body colapse, that is to say, if we saw that for the steel the factor was of 50 that does not mean that if we applied to 1 Watt 50 the maximum to hope are Watt, to persist the initial force, that yes is valid in the first cycle, but in the second cycle of those 50 oscillation Watt will amplify 50 2500 thus times that is Watt and by each cycle until the body colapse if the operating force does not pause. In this respect another case similar to the one of Tacoma Narrows and its bridge was mentioned at the outset, has in Nikola experience Tesla realized during the construction of the famous Building of New York in the USA, the Empire State, Tesla took a small small box worked with batteries and only vibrated as today it makes a vibrator of cellular, that all the structure of the building began to move as in an earthquake and

last page of document - page 10.

workers were there were scared, made to Tesla enough to demonstrate it exactly the resonance produces mechanical energy amplification not only but electrical also the positive applications of the mechanical resonance see in mining today, rocks among others destroy with this one method, using it as generator is not very practitioner since a very great structure would be needed would end up slowly destroying itself and their waves would mechanically affect the environment, although nothing is impossible, but it is more obvious to do it with electricity that with mechanical energy
Doubts or consultations to the post office:
gigawattgratis@l 23mail.cl gigawattgratis@ubbi.com
Juan Araya M.
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