Frequency equation of axisymmetric guided waves in composite structures of bonding metal bars
2.
Based on the equivalent circuit , the resonance frequency equation is derived and the resonance frequency is obtained
3.
By means of the numerical methods , the root of the resonance frequency equation is solved , and the relation between the roots and the poisson ' s ratio is obtained
4.
In order to avoid the domain integral , the above two equations are simultaneously solved , and the corresponding expression of frequency equations are obtained rapidly and accurately
5.
Based on equivalent four - terminal networks of the longitudinal ultrasonic transformer , the resonant frequency equation and the amplitude magnification coefficient , with reactive load , are studied
6.
In this article based on vibration theory of the flexural plate , the frequency equation , the equivalent mass and radiation impedance are derived and further , design theory is introduced
7.
According to several boundary conditions , the frequency equation of flexural circular plate is calculated . similarly some coefficients in the displacement distribution can also be acquired , which provide a preparation for further study
8.
Based on the transfer - matrix method , the general expressions of equivalent four - terminal network parameters of varying section torsional horn are derived , the relations between frequency equation and both the rotational velocity amplification and that of the surface tangential velocity of stepped type torsional ultrasonic horn with transitional section of cosine - like type are obtained
9.
At the same time , the first - order and the second order recurrence relations of transfer matrix and the vectors of every section are derived . based on the boundary conditions , the frequency equations of the zero - order , the first - order and the second - order perturbation of the bridges with random parameters are given as follows : the frequency equations are solved by numerical value method . and the results of eigenvalues of the zero - order , the first - order and the second - order perturbation are subsequently produced
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