A computationally efficient $C^0$ finite element model in conjunction with the nonpolynomial shear deformation theory (NPSDT) is extended to examine the free and forced vibration behavior of laminated composite plates. The employed NPSDT assumes the nonlinear distribution of in-plane displacements which qualify the requirement of traction free boundary conditions at the top and bottom surfaces. The present formulation utilizes both von Kármán and Green–Lagrange type of strain–displacement relations to model the geometric nonlinearity. Using Hamilton’s principle, the nonlinear governing equation of motion is derived and then discretized based on the nine-noded Lagrange element. The obtained equations are solved by utilizing unconditionally stable Newmark’s scheme in conjunction with Newton–Raphson method. A damping effect in the transient analysis has been introduced in the framework of the Rayleigh damping model. The steady state forced vibration analysis has also been carried out by employing harmonic force with excitation frequency around the natural frequency. The arc-length continuation method is applied to obtained the frequency response. The present model has been validated for a wide range of problems and a detailed numerical study has been carried out for several types of boundary conditions under various types of loading with different magnitude of the load.

计算效率高 $C^0$结合非多项式剪切变形理论（NPSDT）扩展了有限元模型，以研究层压复合板的自由振动和强迫振动行为。所采用的NPSDT假设面内位移为非线性分布，这符合上，下表面无牵引边界条件的要求。本公式利用vonKármán和Green-Lagrange类型的应变-位移关系来建模几何非线性。利用汉密尔顿原理，推导非线性控制运动方程，然后基于九节点拉格朗日元素进行离散化。通过使用无条件稳定的Newmark方案结合Newton-Raphson方法求解获得的方程。瞬态分析中的阻尼效应已在瑞利阻尼模型的框架中引入。稳态强迫振动分析也已经通过采用谐波频率和固有频率附近的谐波来进行。应用弧长连续法获得频率响应。目前的模型已经针对各种问题进行了验证，并且针对各种类型的边界条件，在具有不同载荷大小的各种类型载荷下，进行了详细的数值研究。