The response enhancement (autoresonance) in a weakly dissipative nonlinear chain subjected to harmonic forcing with a slowly-varying frequency may be of interest for both a fundamental standpoint as well as practical applications. However, the cumulative effect of dissipation and forcing parameters on the emergence and stability of autoresonance in an anharmonic array has not been discussed thus far in the literature. Recent theoretical and numerical developments were focused on the study of unbounded autoresonance in a non-dissipative strongly nonlinear chain. In this work, the asymptotic methods are employed to construct the evolutionary equations, which describe the long-term behavior of a weakly dissipative strongly nonlinear chain under the condition of 1:1 resonance. Analytical approximations and numerical examples demonstrate that weak dissipation permits the emergence of autoresonance on a bounded time interval but an increase of dissipation leads to escape from resonance of either the entire chain or a part of the chain distant from the source of energy. Numerical simulations for a series of examples confirm close proximity of the exact (numerical) results to their analytical approximations, together with the dependence of the duration of autoresonance, its localization length, and the amplitudes attainable on dissipation and detuning parameters.

受到频率缓慢变化的谐波强迫的弱耗散非线性链中的响应增强（自谐振）可能对基本观点和实际应用都很感兴趣。然而，迄今为止，文献中尚未讨论耗散和强迫参数对非谐阵列中自谐振的出现和稳定性的累积影响。最近的理论和数值发展集中在非耗散强非线性链中无界自谐振的研究上。在这项工作中，采用渐近方法构建进化方程，该方程描述了弱耗散强非线性链在 1:1 共振条件下的长期行为。分析近似和数值例子表明，弱耗散允许在有界时间间隔内出现自谐振，但耗散的增加导致整个链或远离能量源的部分链的共振逃逸。一系列示例的数值模拟证实了精确（数值）结果与其解析近似值非常接近，以及自谐振持续时间、其定位长度以及可达到的振幅对耗散和失谐参数的依赖性。