将恢复力为ε·sign（x）·｜x｜r 的振子命名为具有单纯r 次幂型恢复力的振子，记为P（r）P 振子，给出了其自由振动频率的精确计算公式。提出了频率幂次常数和当量刚度等概念，将P （r）P振子自由振动频率归纳为频率幂次常数与当量刚度平方根的乘积。提出了P （r）P振子的分类方法：把幂次r在0和1之间的称为渐柔型P （r）P振子，振幅愈大，其自由振动频率愈小；幂次r大于1的称为渐刚型P （r）P 振子，其自由振动频率随振幅的增大而增大。%Oscillators with restoring forceε· sign(x)·|x|r are named oscillators with pure r-th po-wer type restoring force,abbreviated as P(r)P oscillators,and an exact free vibration frequency for-mula of this group of oscillators is presented.The concepts of frequency-power constant and equiva-lent stiffness are proposed,and the free vibration frequency of P (r)P oscillators is explained as a product of frequency-power constant and square root of equivalent stiffness consequently.The free vi-bration frequencies of P(r)P oscillators are related with the amplitude except linear oscillator.The exponent r is the key parameter of P(r)P oscillators,which influences the free vibration frequencies remarkably and determines frequency-power constants particularly.Frequency-power constant mono-tone decreases as exponent r increases.P(r)P oscillators can be divided into two groups.The softe-ning P(r)P oscillators have exponent r in the range of 0 to 1 ,whose free vibration frequencies de-crease with an increase in amplitude while the hardening P (r)P oscillators have exponent r bigger than 1 ,whose free vibration frequencies increase with an increase in amplitude.
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