The theory of sonics is a branch of continuum mechanics

Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

 which describes the transmission of mechanical energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 through vibration

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

s. The birth of the theory of sonics can be considered the publication of the book A treatise on transmission of power by vibrations in 1918 by the Romanian

Romanians

The Romanians are an ethnic group native to Romania, who speak Romanian; they are the majority inhabitants of Romania....

 scientist Gogu Constantinescu.

ONE of the fundamental problems of mechanical engineering is that of transmitting energy found in nature, after suitable transformation, to some point at which can be made available for performing useful work. The methods of transmitting power known and practised by engineers are broadly included in two classes: mechanical including hydraulic, pneumatic and wire rope methods; and electrical methods....According to the new system, energy is transmitted from one point to another, which may be at a considerable distance, by means of impressed variations of pressure or tension producing longitudinal vibrations in solid, liquid or gaseous columns. The energy is transmitted by periodic changes of pressure and volume in the longitudinal direction and may be described as wave transmission of power, or mechanical wave transmission. – Gogu Constantinecu

Later on the theory was expanded in electro-sonic, hydro-sonic, sonostereo-sonic and thermo-sonic.
The theory was the first chapter of compressible flow

Compressible flow

Compressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure. Compressibility effects are typically considered significant if the Mach number of the flow exceeds 0.3, or if the fluid undergoes very large...

 applications and has stated for the first time the mathematical theory of compressible fluid, and was considered a branch of continuum mechanics

Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

.The laws discovered by Constantinescu, used in sonicity are the same with the laws used in electricity.
The book A treatise on transmission of power by vibrations has the following chapters:

1. Introductory
2. Elementary physical principles
3. Definitions
4. Effects of capacity
   Capacitor
   A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
   
   , inertia
   Inertia
   Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
   
   , friction
   Friction
   Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
   
   , and leakage on alternating currents
5. Waves in long pipes
6. Alternating in long pipes allowing for Friction
7. Theory of displacements – motors
8. Theory of resonator
   Resonator
   A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...
   
   s
9. High-frequency currents
10. Charged lines
11. Transformer
    Transformer
    A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...
    
    s

George Constantinescu define his work as follow.

Theory of sonics: applications

• CC Gear an interrupter gear
  Interrupter gear
  An interrupter gear is a device used on military aircraft and warships in order to allow them to target opponents without damaging themselves....
  
   device used on military aircraft in order to allow them to target opponents without damaging themselves.
• Automatic gear
• Sonic Drilling, was one of the first applications developed by Constantinescu.A sonic drill head works by sending high frequency resonant vibrations down the drill string to the drill bit, while the operator controls these frequencies to suit the specific conditions of the soil/rock geology.
• Torque Converter
  Torque converter
  In modern usage, a torque converter is generally a type of hydrodynamic fluid coupling that is used to transfer rotating power from a prime mover, such as an internal combustion engine or electric motor, to a rotating driven load...
  
  . A mechanical application of sonic theory on the transmission of power by vibrations. Power is transmitted from the engine to the output shaft through a system of oscillating levers and inertias.
• Sonic Engine

Elementary physical principles

If v is the velocity of which waves travel along the pipe, and n the number of the revolutions of the crank a

The wavelength λ is =v/n

Assuming that the pipe is finite and closed at the point r situated at a distance which is multiple of λ, and considering that the piston is smaller than wavelength, at r the wave compression is stopped and reflected, the reflected wave traveling back along the pipe.

Physics

Elementary physical principles	Description
Suppose the crank a to be rotating uniformly, causing the piston b to reciprocate in the pipe c, which is full of liquid. At each in stroke of the piston a zone of high pressure is formed, and these zones, shown by shading, travel along the pipe away from the piston; between every pair of high pressures zones is a zone of light pressure shown in the picture. The pressure at any point in the pipe will go through a series of values from a maximum to a minimum.
Assuming that the pipe is finite and closed at the point r situated at a distance which is multiple of λ, and considering that the piston is smaller than the wavelength, at r the wave compression is stopped and reflected, the reflected wave traveling back along the pipe.If the crank continues rotation at uniform speed, a zone of maximum pressure will start from the piston at the same time the reflected wave cme to the piston, as a result the maximum pressure will double. At next rotation the amplitude is increased, and so on, till the pipe burst.
If instead of a closing pipe we have a piston at r;the wave will be similar at piston b and piston m,the piston m therefore will have the same energy as the piston b; if the distance between the b and m is not a multiple of λ the movement of m will differ in phase compared with the piston b.
If more energy is produced by piston b then is taken by piston m the energy will be reflected by piston m in pipe, and the energy will accumulate till the pipe burst.If we have a large volume vessel d, compared with the stroke volume of piston b, the capacity d will act as a spring taking out the energy of direct or reflected waves at high pressure, and giving back energy when pressure fall. The mean pressure in d and in the pipe will be the same. The result of reflected waves will be a stationary wave in pipe with no increase of energy, and the pressure in the pipe will never exceed the pressure limit.
Waves are transmitted by reciprocating piston along the pipe eeee, the pipe is closed at p at a distance of one complete wavelength. There are branches at one half, three quarter and one full wave length distances. If the p is open and d is open, the motor l will rotate synchronous with motor a. If all valves are closed, there will be a stationary wave with extreme values at λ and λ/2in point b and d, points where the flow will be zero, and where the pressure will alternate between maximum and minimum values determined by the capacity of reservoir f. the maximum and minimum point no not move along the pipe,and no energy flow from generator a. If valve b is open, the motor m is able to take the energy from the line the stationary half wave between a and b being replaced by a traveling wave, still between b and p the stationary wave will persist. If only valve c is open, since at this point the variation of pressure is always zero no energy can be taken out by the motor n, and the stationary wave will persist. If the motor is connected in an intermediary point part of the energy will be taken out by the motor while the stationary wave will persist at reduced amplitude. If the motor l is not capable of consuming all the energy of the generator a, then there will be a traveling wave a and a stationary wave, so there will be no point in the pipe where the pressure variation will be zero, consequently a motor connected at any point of the pipe will be able to use a portion of generated energy.

Alternating fluid currents

Considering any flow or pipes,if:

ω = the area section of the pipe measured in square centimeters;

v =the velocity of the fluid at any moment in centimeters per second;

and

i =the flow of liquid in square cubic centimeters per seconds,

then we have:

i =vω

Assuming that the fluid current is produced by a piston having a simple harmonic movement, in a piston cylinder having a section Ω.
If we have:

r =the equivalent of driving crank in centimeters

a =the angular velocity of the crank or the pulsations in radians degree per second.

n =the number of crank rotations per second.

Then:

The flow from the cylinder to the pipe is: i = I sin(at+φ)

Where:

I = raΩ (the maximum alternating flow in square centimeters per second; Amplitude of the flow.

t = time in seconds

φ = the angle of the phase

If T= period of a complete alternation (one revolution of the crank) then:

a = 2πn; where n = 1/T

The effective current can be defined by the equation:

and the effective velocity is :

The stoke volume δ will be given by the relation:

Alternating pressures

The alternating pressures are very similar with alternating currents in electricity.
In a pipe were the currents are flowing, we will have:

;where H is the maximum alternating pressure measured in kilograms per square centimeter. the angle of phase; representing the mean pressure in the pipe.

Considering the above formulas:

the minimum pressure is and maximum pressure is

If p₁ is the pressure at an arbitrary point and p₂ pressure in another arbitrary point:

The difference is defined as instantaneous hydromotive force between point p₁ and p₂, H representing the amplitude.

The effective hydromotive force will be:

Friction

In alternating current flowing a pipe the friction appear at the surface of the pipe and also in liquid itself. Therefore the relation between the hydromotive and current can be written:

; where R= coefficient of friction in

Using experiments R may be calculated from formula:

;

Where:

• is the density of the liquid in kg per cm.³
• l is length of the pipe in cm.
• g gravitational acceleration in cm. per sec.²
• section of the pipe in square centimeters.
• v_eff the effective velocity
• d internal diameter of the pipe in centimeters.
• for water this is an approximation made by experiments.
• h is instantaneous hydromotive force

If we introduce in the formula, we get:

this is equivalent with:

; introducing k in formula, result thar

For pipes with greater diameter greater velocity can be achieve for same value of k.
The loss of power due to friction is calculated with:

, putting h=Ri result:

Therefore:

Capacity and condensers

Definition: Hydraulic condensers are appliances for making alterations in value of fluid currents, pressures or phases of alternating fluid currents. The apparatus usually consists of a mobile solid body, which is dividing the liquid column, and fixed elastically in a middle position, in such way that it follows the movements of the liquid column.

The principal function of hydraulic condensers is to counteract inertia effects due to moving masses.

Hydraulic Condenser Drawing

Theory

The principal function of hydraulic condensers is to counteract inertia effects due to moving masses. The capacity C of a condenser consisting of a piston of section ω on which the liquid pressure is acting, held in mean position by means of springs, is given by the equation: ΔV=ωΔf=CΔp where: ΔV=the variation of volume of the space for liquid; Δf=the variation of the longitudinal position of the piston, and Δp=the variation of the pressure in the liquid. If the piston is held by a spring at any given moment: f=AF where A= a constant depending on the spring and F=the force acting on the spring. In the condenser we will have: ΔF=ωΔp and Δf=AωΔp Considering the above equations: C=Aω2 and For a spring wire of circular section: Where B is the volume of spring in cubic centimeters and σ the allowable stress Yield (engineering) The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed... of metal in kilograms per square centimeter. G the coefficient of transverse elasticity of the metal. Therefore: B=mFf m being a constant depending on σ and G. If d is the diameter of the spring wire and the D the mean diameter of the spring. Then: so that: if we consider :: then: The above equations are used in order to calculate the springs required for a condenser of a given capacity required to work at a given maximum stress.