Improved Birth-Death Element Method Enhances Variable-Mass System Dynamics Predictions

Researchers have developed an improved birth–death element method to analyze the non-stationary dynamics of multi-degree-of-freedom time-varying mass systems commonly found in aerospace engineering. The updated numerical approach addresses a long-standing limitation in conventional finite element modeling by explicitly accounting for the reverse thrust effect produced by mass change rates.

In standard structural dynamics, time-varying mass systems exhibit complex, non-stationary responses that require precise prediction during design and evaluation. Traditional finite element analyses typically apply the standard birth–death element method by directly modifying the structural mass and stiffness matrices over time.

To overcome these limitations, the authors proposed an improved birth–death element formulation that simulates mass reduction through systematic element deactivation while explicitly incorporating instantaneous velocity feedback. By introducing instantaneous velocity into the governing equations, the method mathematically captures the reverse-thrust term and reproduces the true underlying physical mechanism governing variable-mass structures.

The research team investigated the free-vibration responses of variable-mass systems under both linear and exponential mass variation profiles. Their parametric evaluations revealed that the rate of mass change exerts a direct influence on the natural frequencies, response amplitudes, and operational damping characteristics of the oscillating structures.

A key theoretical finding from the investigation is the identification of a critical damping rate associated with rapid mass loss.

The proposed modeling methodology was implemented using finite element software coupled with MATLAB, and the governing equations of motion were solved step-by-step using the Newmark numerical integration method. When benchmarked against theoretical predictions, the updated simulation framework showed good agreement and demonstrated higher accuracy than the traditional birth–death element approach. The authors concluded that the improved method exhibits strong accuracy and universality for dynamic response predictions and design evaluations in variable-mass engineering applications.

Subject of Research: Time-varying mass system dynamics and finite element modeling

Article Title: Time-Varying Mass System Dynamics Analysis Based on an Improved Birth–Death Element Method

Article References: Zhai, X., Zhang, Y., Du, Y., Zhang, Y., Ma, L., Li, Y., Luo, Y., & Xie, S. (2026). Time-Varying Mass System Dynamics Analysis Based on an Improved Birth–Death Element Method. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01323-3

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01323-3

Keywords: aerospace engineering, birth-death element method, critical damping rate, dynamic response, finite element analysis, free-vibration response, instantaneous velocity, linear mass variation, MATLAB simulation, MDOF systems, Newmark method, non-stationary dynamics, reverse thrust effect, structural dynamics, time-varying mass, variable-mass systems