In this paper, the non-harmonic resonance of Bernoulli viscoelastic beams, Kirchhoff viscoelastic plates, Timoshenko viscoelastic beams, and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time. The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus. The displacement vector is approximated by employing the separation of variables method. The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa. The novel point of the proposed method is to express, prove and calculate the critical time in which the displacement will be several times the displacement at time zero. In addition, this new method calculates the maximum deflection at the critical time, explicitly and exactly, without any need to follow the time-displacement curve with a low computational cost. Additionally, the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero.

本文首次研究了伯努利粘弹性梁、基尔霍夫粘弹性板、铁莫申科粘弹性梁和明德林粘弹性板在随时间呈指数递减横向分布载荷作用下的非简谐振动。本构方程是利用具有恒定体积模量的玻尔兹曼积分定律来表达的。采用变量分离法来近似位移矢量。拉普拉斯变换用于将方程从时域转移到拉普拉斯域，反之亦然。该方法的创新点在于表达、证明和计算了位移将是零时刻位移数倍的临界时间。此外，这种新方法计算了关键时刻的最大挠度，明确且准确，无需遵循时间-位移曲线，计算成本低。此外，所提出的方法引入了时间的临界范围，使得响应大于时间零时的响应。