| China is the largest loudspeaker manufacturing country in the world, but is far from a great power country producing quality loudspeakers. So the research exploring the mechanism of the loudspeakers' sub-harmonics makes the paper particularly significant not only in the theory of nonlinear dynamics of thin shells but also in practice of improving loudspeaker quality. Main studies are listed as follows.1. Nonlinear modal equations for closed revolution shells are derived according to the virtual work principle by using the Sanders nonlinear shell theory. The coefficients of the equations are well-suited for numerical calculation, and a special finite element method is developed to calculate the coefficients. The obtained results are verified by the previously published and analytical results. The coefficient values of the square terms derived from the Donnell's nonlinear shallow-shell theory are very close to the present results, whereas the coefficient values of the cubic terms are significantly under-estimated.2. Two modes, an axisymmetric mode plus a non-symmetric mode, are used to reveal the mechanism of the 1/2 sub-harmonic distortion in loudspeakers. The motion equations obtained show that the axisymmetric mode is driven directly but the non-symmetric mode is excited through the nonlinear coupling between the two modes, known as the parametric excitation. When the driven frequency is close to two times of the nature frequency of the non-symmetric mode, it can be excited under some conditions to generate 1/2 sub-harmonics.3. The material, electromagnetic and geometry parameters of the loudspeaker under investigation are determined experimentally. And then, the coefficients of the equations describing the generation of the 1/2 sub-harmonics are determined by the finite element method.4. The analytic solutions of the equations are obtained with the multi-scale method and the harmonic balance method. They agree well with the numerical results obtained from the Runge-Kutta method. |
PDF Full Text Request