利用分数阶Kevin粘弹性模型,建立矩形薄板的动力学方程,并利用拉普拉斯变换及其逆变换给出四边简支粘弹性薄板的解析解,并着重分析在常值荷载作用下,分数阶Kevin粘弹性模型的分数阶参数、粘性参数和模量参数对挠度的影响.结果表明,随着粘性参数和分数阶参数的增大,粘弹性板的挠度变小；随着模量参数增大,粘弹性板的挠度变大.%Dynamic equations of rectangular thin plates based on fractional-order Kevin viscoelastic model were established. The analytical solution of the dynamic equations for a viscoelastic plate with four edges simply supported was obtained by using Laplace transform and inverter Laplace transform. The influences of the fractional order parameter, viscosity parameters and modulus parameters on the deflection of the fractional-order Kevin viscoelastic model with constant load were analyzed. The results show that the deflection of the viscoelastic plates decreases with the increasing of the viscosity parameters, while the deflection of the viscoelastic plates increases with the increasing of the modulus parameters.
展开▼
