Extending the previous work done by the authors, this paper develops a time domain synthesis method for the classical guitar based on substructuring concepts and using the Udwadia-Kalaba modeling strategy. Adopting a modal description of the dynamics of the separate flexible subsystems in terms of their unconstrained modes and enforcing coupling constraint conditions for the assembly, the result is an explicit dynamical modal formulation for the coupled system that directly lends itself to time-stepping methods for simulation. The guitar model couples six strings through an experimentally based body model of an actual instrument, includes two string polarizations, and the string geometrical nonlinear effects, as well as the string/fret interaction as the instrument is played. Details are given for putting all the vibrating components together in a satisfying manner, and a specific strategy is explored to allow for a nonrigid fret using flexible-dissipative-inertial constraints. The reliability of the approach is demonstrated with simulation examples that confirm the features one would expect regarding the dynamical behavior of classical guitars. Finally, a pragmatic approach is made to calculate the radiated sound by convolution, combining the computed bridge force with a measured vibro-acoustic impulse response of the instrument, which proved to give satisfactory sounding results.

中文翻译：

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使用Udwadia-Kalaba模态公式对六弦吉他弹拨进行物理合成。

在扩展作者先前的工作的基础上，本文开发了基于子结构概念并使用Udwadia-Kalaba建模策略的古典吉他时域综合方法。通过对单独的灵活子系统的动力学进行模态描述（根据其无约束模式并强制装配的耦合约束条件），其结果是为耦合系统提供了明确的动力学模态公式，直接适用于时步法进行仿真。吉他模型通过实际乐器的基于实验的人体模型耦合六根琴弦，包括两个琴弦极化，琴弦几何非线性效应以及弹奏乐器时的琴弦/琴弦相互作用。给出了以令人满意的方式将所有振动组件放在一起的详细信息，并探索了一种特定的策略，以允许使用柔性耗散惯性约束的非刚性品格。通过仿真示例证明了该方法的可靠性，这些仿真示例确认了人们期望有关古典吉他的动态行为的功能。最后，采用一种实用的方法通过卷积计算辐射声，将计算出的桥力与仪器测得的振动声脉冲响应相结合，事实证明可以得出令人满意的测深结果。通过仿真示例证明了该方法的可靠性，这些仿真示例确认了人们期望有关古典吉他的动态行为的功能。最后，采用一种实用的方法通过卷积计算辐射声，将计算出的桥力与仪器测得的振动声脉冲响应相结合，事实证明可以得出令人满意的测深结果。通过仿真示例证明了该方法的可靠性，这些仿真示例确认了人们期望有关古典吉他的动态行为的功能。最后，采用一种实用的方法通过卷积计算辐射声，将计算出的桥力与仪器测得的振动声脉冲响应相结合，事实证明可以得出令人满意的测深结果。