Abstract: Dynamic models are crucial for model-based control of multi-degree of freedom (DOF) systems, and learning the precise dynamics of the system directly from data is currently a prominent research focus. Existing data-driven methods, such as Hamiltonian neural networks and Lagrangian neural networks (LNNs), demonstrate the feasibility of physically interpretable methods in modeling conservative systems, but face limitations in modeling non-conservative systems with unstructured factors such as friction. Therefore, this paper proposes a novel physically constrained energy network (PELNN), which integrates LNN and multi-layer perceptrons. The conservative part represents the Lagrangian by learning the kinetic energy and potential energy of the system, and then uses LNN to reconstruct the acceleration of the system, while the non-conservative part is represented by a multi-layer perceptron. The first feature of PELNN is that it considers that the system mass matrix and potential energy are only functions of generalized coordinates and the mass matrix is symmetric, thereby reducing the complexity of LNN by limiting the input dimensions of the kinetic energy and potential energy network model; the second feature is the introduction of energy constraints, which enables the conservative part to maintain mechanical energy conservation to the greatest extent. Finally, this paper evaluates the effectiveness of PELNN through numerical simulation of a damped double pendulum system and a six-DOF manipulator system and experimental verification of a double-layer nonlinear vibration isolator. The results show that PELNN has high modeling accuracy and strong extrapolation prediction ability.