This paper presents a new analytical and numerical method for modeling and synthesis of complex distributed parameter systems that are multiple continua combined with lumped parameter systems. In the analysis, the complex distributed parameter system is first divided into a number of subsystems; the distributed transfer functions of each subsystem are determined in exact and closed form by a state space technique. The complex distributed parameter system is then assembled by imposing displacement compatibility and force balance at the nodes where the subsystems are interconnected. With the distributed transfer functions and the transfer functions of the constraints and lumped parameter systems, exact, closed-form formulation is obtained for various dynamics and vibration problems. The method does not require a knowledge of system eigensolutions, and is valid for non-self-adjoint systems with inhomogeneous boundary conditions. In addition, the proposed method is convenient in computer coding and suitable for computerized symbolic manipulation.

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