This paper presents a unified integral transform solution for the analysis of free and forced vibration of ribbed rectangular plate with arbitrary classical boundary conditions, whereas previous integral transform techniques have mainly focused on the analysis of the mechanical behavior of bare plates. The one- and two-dimensional integral transform techniques are applied to the higher-order partial differential governing equations of the beams and the plates, respectively, which are transformed into a system of linear algebraic equations after a rigorous derivation. The unknown coupling force and moment are determined by the compatibility conditions at the beam-plate coupling interface to obtain a unified solution scheme for ribbed plates with arbitrary classical boundary conditions. Good agreements are found between the results of analytical solution, finite element analysis and literature. Moreover, experiments on vibration analysis of a ribbed plate with completely free boundary conditions are conducted to further verify the validity and accuracy of the unified solution scheme. The effect of rib on the vibration response of rectangular plates is also investigated. It is shown that the vibration is controlled by the plate stiffness when the rib plays as a mass loading. The proposed unified analytical solution can be widely used to provide theoretical guidance for the vibration prediction of various structures with ribbed plates, such as offshore platforms, high-speed carriages, and aircraft wings.

针对具有任意经典边界条件的带肋矩形板的自由振动和受迫振动分析，本文提出了统一的积分变换解决方案，而以往的积分变换技术主要集中在裸板的力学行为分析上。将一维和二维积分变换技术分别应用于梁和板的高阶偏微分控制方程，经过严格推导后转化为线性代数方程组。由梁-板耦合界面处的相容条件确定未知的耦合力和力矩，得到具有任意经典边界条件的肋板的统一求解方案。解析解、有限元分析和文献的结果之间有很好的一致性。此外，对具有完全自由边界条件的肋板进行了振动分析实验，进一步验证了统一求解方案的有效性和准确性。还研究了肋对矩形板振动响应的影响。结果表明，当肋作为质量载荷时，振动受板刚度控制。所提出的统一解析解可广泛用于为海洋平台、高速客车、机翼等各种带肋板结构的振动预测提供理论指导。对具有完全自由边界条件的肋板进行振动分析实验，进一步验证了统一求解方案的有效性和准确性。还研究了肋对矩形板振动响应的影响。结果表明，当肋作为质量载荷时，振动受板刚度控制。所提出的统一解析解可广泛用于为海洋平台、高速客车、机翼等各种带肋板结构的振动预测提供理论指导。对具有完全自由边界条件的肋板进行振动分析实验，进一步验证了统一求解方案的有效性和准确性。还研究了肋对矩形板振动响应的影响。结果表明，当肋作为质量载荷时，振动受板刚度控制。所提出的统一解析解可广泛用于为海洋平台、高速客车、机翼等各种带肋板结构的振动预测提供理论指导。结果表明，当肋作为质量载荷时，振动受板刚度控制。所提出的统一解析解可广泛用于为海洋平台、高速客车、机翼等各种带肋板结构的振动预测提供理论指导。结果表明，当肋作为质量载荷时，振动受板刚度控制。所提出的统一解析解可广泛用于为海洋平台、高速客车、机翼等各种带肋板结构的振动预测提供理论指导。