Vol. 12, No. 2 (1956)
1956, 1601 (2): 85-95.
The face that the amplitule of the nth order sideband of a frequency modulation signal is equal to Jn(Mf) allow us to discover some useful properties of the frequency modularion signal. By means of an approximate expression of the Bessel function (14), we discover some new properties of the frequency modulation signal: The position and amplitude of the maximum maximum sideband are well defined, as shown in fig.3 moreover the ratio of the amplitude of this maximum maximum sideband to that of critical sideband is also known, as shown in fig.4.The total number of secondary maxima of sidebands is given by (21). Utilizing another form of this asme approximate expression of the Bessel function Jn(x), we can proceed to determine the required width of frequency modulation spectrum for satisfactory transmission; for this purpose we may also use a family of empirical curves as shown in fig.4.
1956, 1601 (2): 139-151.
The non-linear theory of elastic thin-walled bars of open cross-sections proposed by the auther is applied to the study of large torsion of such bars. The fundamental equations are simplified for the case of bisymmetrical ane central symmetrical cross-sections. For non-symmetrical cross-sections, it is generally impossible to obtain pure torsion without bending in the non-linear theory. The problem is solved by a perturbation method. Two specific examples are considered.
1956, 1601 (2): 152-169.
In this paper the non-linear theory of thin 一 walled beams of open cross sections Proposed by the author  recently is applied to the investigation of the stability of such beams. Fundamental equations of the previous paper [ 1 ] are firstly linearized and simplified for the determination of the critieal load and the mode of buckling.In the ease of eccentrie compression, the fundamental equations of this paper differ from those in the theory of V.Z.Vlasov in the following two points : l) A new generalized displacement P is in troduced.2 ) The initial bent state of the beam is taken in to account. A numerieal exaple (an angle of unequal legs ) shows that in the case of central uniform compression, P has little in fluence on the magnitude of the critical load, The re fore P is then neglected in this paper.In the ease of beams loaded by pure bending momments , two numerical examples are carried out (a cross beam and an I-beam , see Figs.4 and 6 ). Critieal moments are ploted against a d imensionless parameter a as shown in Figs.5 and 7(curves I), where a is the ratio of width to depth of the cross section of the beam·Our critical moments are greater than those given by V.Z. Vlasov (curves II in Figs.5 and 7).This is because in this paper the initial bent state of the beam is taken into : account. It is interest to point out that according to our theory, beams may lose lateral stability under pure bending moment only when the ratio of width to depth of the cross section is less than a certain critical value. This fact is in agreement with common exprience .