A Modal Mass Computation Method for the Euler-Bernoulli Beam of Linear Multibody System Transfer Matrix Method

The multibody system transfer matrix method (MSTMM) has been widely used in multibody dynamics simulation and analysis due to its advantages such as eliminating the need for the global dynamics equation of the system and having lower matrix order. When computing the dynamics response of a linear multibody system using MSTMM, it is necessary to compute the modal mass of elements. For a continuous element like the Euler-Bernoulli beam, this requires integrating the modal displacement along the length direction of the beam. Conventionally, numerical methods such as the trapezoidal rule are employed by discretizing the beam into several small segments to compute the integral. This paper proposes an analytical approach to derive the exact expression for the modal mass integral of the Euler-Bernoulli beam using its transfer matrix. Comparative results demonstrate that the proposed method improves both the computational accuracy and efficiency compared to approximate numerical integration methods like the trapezoidal rule.