According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics in phase space are multiplied by corresponding virtual quantities, integrated and then added algebraically. By considering the character of fellow body and surface forces, the generalized quasi-variational principles of non-conservative systems are established in elasto-dynamics in phase space. By doing inverse Laplace transformation, the convolutional generalized quasi-variational principles of non-conservative systems of elasto-dynamics are established in original space. Applying the generalized quasi-complementary energy principle to the mechanical vibration problem of two kinds of variables, the authors of this paper present a calculation method for solving two kinds of variables simultaneously: the internal force and the displacement of a typical fellow force system.
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