Theoretical And Experimental Research On Complex Vibrations And Waves

Vibration and fluctuation are very common in daily production and life,and the study of vibration and wave has been carried out for a long time,and simple harmonic vibration and plane wave models have been proposed.In particular,the application of modern technologies such as computers has greatly promoted the study of vibration and fluctuations.In this paper,the linear coupling mechanism of two vibrations with equal eigenfrequencies and the skin effect of electromagnetic waves are theoretically studied.The relationship between the vertical vibration and rotational motion of the Wechsler pendulum was explored by experiments,and the radiation and reception of spherical waves were explored by theoretical and experimental experiments.This paper studies the coupling relationship between Wilberforce pendulum rotation motion and up and down vibration from theoretical and experimental perspectives.Starting from the constraint relationship between the wire diameter and the number of turns of the actual spring and the length of the spring,the coupling mechanism of the two movements is studied from the theoretical point of view.Then,an experimental device is set up,the stiffness coefficient and torsion coefficient of the spring are measured,the coupling coefficient is calculated and verified experimentally.When the intrinsic angle frequency of vertical motion and the intrinsic angle frequency of rotational motion are equal,record a motion video of the experiment.Combined with the motion theory analysis of the two vibrations,the mutual conversion of the two vibrations is discussed.The problems of vertical and rotational vibration under different initial values when the eigenangle frequency of vertical motion and the intrinsic angle frequency of rotational motion are equal,and the initial value problems in stable mode are explored.Combined with the radiation pattern of electric dipole antenna and magnetic dipole antenna,the difference between the radiation of the fed magnetic dipole antenna and the ideal magnetic dipole antenna radiation is explained by the filling method.Experiments verify the directionality of antenna radiation and the skin effect of receiving antenna.The experimental antenna emits spherical waves,and if the receiving antenna is far enough from the transmitting antenna,the spherical waves received by the receiving antenna can be approximately regarded as plane waves.In this experiment,in order to visualize the radiation and propagation of electromagnetic waves,the receiving antenna is close to the transmitting antenna,so the electromagnetic waves received by the receiving antenna are treated as spherical waves.Under the polar coordinate system,the skin effect of the metal conductor of the receiving antenna is used to prove the rationality of the hypothesis that the current of the receiving antenna is the line current,and the correctness of the line antenna current analysis by standing wave theory of the receiving antenna is further proved.The standing wave theory is used to analyze the distribution characteristics of current and charge of half-wave antennas and verified experimentally.