This research analyzes a laminated double-curved panel’s free/forced vibrational features and Low-Velocity Impact (LVI) Accordingly, the Hertz contact scheme is introduced to model the contact force between the structure and the impactor. Additionally, Hamilton’s principle and four-variable refined quasi-3D logarithmic shear deformation theory (RQ-3DLSDT) are accessible for figuring out a structure’s motion and Boundary Condition (BC) equations for the LVI. Moreover, for computing the motion equation in the displacement and time frames, respectively, the Galerkin and Newmark methods are provided. Finally, there are two subsections within the results section. The first examines the influence related to the number of laminated layers, the geometry of doubly curved panels, and the ratio associated with Young’s module on the indentation and contact force in the time frame. The second discusses the impact of Young’s module proportion, the laminated layers’ form, and geometrical attributes related to the structure on the present simulation’s free and forced vibration features with the LVI.