Examples of vibrations are used and theories are briefly described

Summary. According to the relevant formula, it can be known.

The displacement with time forms the following mathematical form of motion is known as simple harmonic vibration.

Amplitude a, which indicates the maximum offset of the vibration.

The period t indicates the time to complete a vibration.

Frequency f, which indicates the number of vibrations per unit time.

Angular frequency represents the radian value of phase change per unit time.

Phase indicates the state of vibration at time t.

The initial phase indicates the state of the initial vibration.

Hold on. According to the relevant formula, it can be known. The displacement forms the following mathematical form with the closure of the tung ridge with time, which is called the simple harmonic vibration amplitude a, which represents the maximum offset period t of the vibration, represents the time frequency f of completing a vibration, represents the angular frequency of the number of vibrations per unit time, represents the radian value phase of the phase change per unit time, represents the initial phase of the state of partial cracking of the vibration at time t, and represents the state of the initial vibration.

(1) Measurement of the natural frequency of the structure: the method of sudden discharge load or sudden load of initial displacement or initial velocity can make the structure be subjected to a shock load and produce free vibration, and in the field test, the recoil exciter can be used to generate impact load on the structure.

After obtaining the damped free vibration curve of the structure, the period of the vibration waveform can be measured according to the time coordinates on the vibration curve, and the natural vibration frequency f=1 t of the structure is obtained from this (2) Structural damping measurement: the damping ratio is determined by the amplitude change obtained by the measured vibration shape, and the peak-peak amplitude value can be used when measuring the damping of the structure, which is relatively simple and correct. (3) Mode shape measurement:

When the structure vibrates at a certain natural frequency, the displacement of each point presents a certain proportional relationship, and the displacement of each point can be connected along the structure to form a curve of a certain shape, that is, it is an invariant vibration form of the structure corresponding to a certain natural frequency, which is called the mode shape of the corresponding frequency. Generally, only the first-order vibration type of the structure can be measured by the free vibration method.

27.Briefly describe the principle of the resonance method to test the dynamic characteristics of structures?

The resonance method is a method for measuring the dynamic characteristics of structures, which is based on the dynamic equations of the structure and the static equations in the excitation system, according to the frequency spectrum method and time-frequency analysis technology, to solve and analyze the mode shape characteristics and modal parameters of the structure, so as to obtain the dynamic characteristics of the object, and provide quantitative indicators for the design and analysis of components. The resonance method uses an exciter to add a small amplitude vibration to the structure, and resonance occurs when there is a natural frequency in the structure being measured. The resonance method uses the natural frequency of the measured structure to obtain the modal characteristic parameters and dynamic characteristic parameters of the structure.

This approach is influenced by many factors, so the test system needs to be rigorously checked to ensure the reliability of the test results.

Summary. Hello, I am glad to answer for you, through the analysis of forced vibration under the action of simple harmonics, the resonance peak found is the amplitude of the simple harmonic motion represented by the ordinate of the cd resonance curve, the abscissa represents the frequency of the driving force, and the peak value represents the amplitude of the resonance when the frequency of the driving force is equal to the natural frequency.

Through the analysis of forced vibrations under the action of simple harmonics, the resonance peaks of what are found.

Hello, I am glad to answer for you, through the analysis of forced vibration under the action of simple harmonics, the resonance peak found is the amplitude of the simple harmonic motion represented by the ordinate of the cd resonance curve, the abscissa represents the frequency of the driving force, and the peak value represents the amplitude of the resonance when the frequency of the driving force is equal to the natural frequency.

Pro, forced vibration is also known as "forced vibration". Vibration (oscillation) The vibration (oscillation) of a system under the action of an external force (driving force). When a vibrating (oscillating) system reaches a stable vibration state under the action of periodic driving force, the frequency (or period) of the forced vibration is the same as the frequency (or period) of the driving force.

Is the acceleration of simple harmonic motion related to the frequency of vibration.

Hello dear, I am glad to answer for you, the acceleration of simple harmonic motion is related to the vibration frequency, the displacement in the vibration is derived from time, and the velocity is derived from time, so in the simple harmonic vibration, the acceleration amplitude = vibration frequency * velocity amplitude = the square of the vibration frequency * displacement amplitude.

Under the excitation of simple harmonic force, the steady-state vibration produced by the forced vibration has the same frequency and phase as the excitation force, right?

In the process of multi-degree-of-freedom mechanical vibration, the displacement value of its natural mode shape is deterministic and invariant, right?

How to do it. Hello dear, I'm glad to answer for you, first of all, we have to remember what exactly is the form of equations for simple harmonic motion? That's x=acos( t+ ) According to the diagram, we can easily see that the amplitude is ten centimeters, so a=10.

We can also see from the graph that the half period is 4 seconds, so the period t 8s, =2 t = 4. Continuing to look at it, when t 0, x 5cm, then 5 10cos( )2 3 or -2 3, so the vibration equation is: x 10cos( t 4+120°) 10cos( t 4+2 3) or x 10cos( t 4-120°) 10cos ( t 4-2 3).

Not a single question.

Free vibration: After the external force makes the ball of the spring oscillator and the pendulum of the pendulum deviate from the equilibrium position, they vibrate under the action of elastic force or gravity inside the system, and no longer need to be pushed by external force, this vibration is called free vibration.

The vibration system can vibrate according to its natural frequency after the object leaves the equilibrium position under the action of external force, and no longer needs the action of external force, this vibration that is not under the action of external force is called free vibration Ideally, free vibration is called undamped free vibration The period of free vibration is called natural period, and the frequency of free vibration is called natural frequency They are determined by the conditions of the vibration system itself.

The impact of vibration on people depends on the intensity of the vibration and the frequency annihilation rate characteristics of the vibration. （）

a.That's right. b.Mistake.

Correct Answer: a

The displacement when the potential energy and kinetic energy are equal in the simple harmonic vibration is the amplitude.

times. The specific calculation process is as follows:

According to the law of conservation of mechanical energy.

It can be seen that the mechanical energy is conserved in the simple harmonic vibration, that is, ep+ek=e potential energy ep=1 2kx 2

Kinetic energy. ek=1/2mv^2

When the magnitude of the oscillator displacement is equal to the amplitude a, the kinetic energy is 0, the mechanical energy.

e=1/2ka^2

The displacement x when the potential energy and kinetic energy are equal in the simple harmonic vibration

ep=ek=1/2kx^2

2x1/2kx^2

1/2ka^2

x=√2/2a=

In the simple harmonic vibration, the displacement of the potential energy and the residual kinetic energy is as follows.

When the amplitude of the object is unchanged, and the displacement and acceleration of the object are maximum, the velocity is zero; When the displacement and acceleration are zero, the velocity is maximum. These facts illustrate that the potential energy and kinetic energy of the system of matter are constantly converted into each other, and the total energy of the system of matter remains constant. Therefore, the total energy of the system of matter at any moment is equal to its potential energy maximum, which is also equal to the kinetic energy maximum.

That is, the potential energy at any moment.

The simplest of vibrations is simple harmonic vibrations. In fact, the motion parameters of an object change with time according to the law of sine or cosine, which is the inevitable result of the external force on which the object is subjected to a force that is proportional to the displacement and in the opposite direction.

It is relatively easy to understand that the recovery force is proportional to the displacement of the object as a simple harmonic vibration, but it is not easy for beginners to understand the constant opposite direction, and mistakenly believe that in the process of moving the object from the equilibrium position to the maximum displacement, the displacement is directed to the maximum displacement, which is the opposite of the force subjected; In the process of moving from the maximum displacement to the equilibrium position, the displacement is directed towards the equilibrium position, which is in the same direction as the force subjected; In this way, it seems that the direction of the external force and the displacement are sometimes opposite, and sometimes the same. The main reason for this view is that in the simple harmonic vibration, the displacement always refers to the change in the position of the object with respect to the equilibrium position, that is, the displacement of the object to the equilibrium position is always opposite to the equilibrium position. The direction of the restoring force is always in the equilibrium position, so the direction of the two is always opposite.