Recently, increasing attention has been devoted to analyzing nonlinear phenomena in engineering design due to rapid advancements in complex lightweight structures and novel materials. These structures are generally modeled using Finite Element Methods, resulting in large systems of ordinary differential equations. For large degrees of freedom, parametric studies are often infeasible, and thus, engineers look for techniques to reduce the computational cost and ultimately expedite the design process. Linear projection-based Reduced-Order Model (ROM) solves this problem by identifying a linear modal basis (e.g., using full-scale training data) that aims to embed the relevant nonlinear normal modes utilizing a subset of these modal vectors. Since this modal basis is usually identified using training data from the full-scale nonlinear system, the identified projection basis is expected to be robust for small variations of the forcing energy levels used in the training data. The Proper Orthogonal Decomposition (POD) has been the standard approach to identify this reduced projection basis. Since POD identifies the modes based on their energy contribution within the training data, arguments are based on including enough modes in the reduced projection basis to achieve some energy-preserving criteria. Unfortunately, this approach to model order reduction is highly specific to the training data used and, more importantly, lacks a physical meaning when considering the underlying dynamics of the system. This work uses a Generalized Characteristic Value Decomposition (GCVD) to construct physics-informed reduced-order models by considering the identified modes’ decay rates and oscillation frequencies when selecting the reduced projection basis. Thus, our reduced-order models can be built based on a slow, intermediate, and fast time dynamics hierarchy. A significant advantage of this approach is its versatility for free and forced vibrations over a wide forcing frequency range. The proposed model order reduction strategy is demonstrated on several geometrically nonlinear finite element models. A numerical continuation is performed on both the reduced order model and full-scale systems to verify the accuracy of the GCVD-ROMs for predicting the primary frequency response curves, stability of solutions, and sub- and superharmonic resonances.