锥形薄壳的低频薄膜振动解及其在扬声器振膜的应用

MEMBRANE SOLUTIONS FOR CONIAL SHELL VIBRATIONS IN LOW FREQUENCY RANGE WITH APPLICATION TO LOUDSPEAKER CONE VIBRATIONS

采用摄动法求解旋转薄壳的轴对称自由振动方程，在低频段可得到４ 个边缘弯矩解析解和２ 个通常采用数值计算的薄膜无矩解．本文把锥壳无矩方程表示为以频率参数和几何参数的组合———ｋｘｔａｎα为自变量的形式，采用幂级数法求得了锥壳薄膜无矩解．结合弯矩解，求解了扬声器锥形振膜的低频强迫振动，并采用有限元数值计算方法验证了结果的正确性．对解的分析表明：在低频段，求解扬声器振膜振动可采用纯薄膜近似———求满足薄膜边界条件的薄膜无矩解；还表明，在低频段存在环反谐振频率，该频率可作为扬声器锥形振膜活塞式振动的上限频率．

The solutions for free axisymmetric vibration equations of thin shell in low frequency range found in perturbation method consist of four analytic bending solutions which are only edge effects and two membrane solutions which are usually obtained by numerical calculation.In this paper,the membrane equations for conial shell vibrations are first expressed in terms of the new independent variable kx tan α that is combinations of frequency parameter and geometrical parameter,and the power-series solutions in low frequency range for these equations are obtained.The forced vibrations of loudspeaker cone in low frequency range are given with application the membrane solutions above and bending edge solutions,which are verified with FEM numerical calculation.The discussions about the results show that the diffrence between the vibrations of loudspeaker cone obtained above by applying six boundary conditions to all the six membrane and bending solutions and those obtained by applying only two membrane boundany conditions to two membrane solutions can be neglected,and that there is a ring antiresonance frequency within the low frequency range below which the loudspeaker cone vibrates as a piston.