Active Vibration And Buckling Controlof Lattice Sandwich Beams And Plates

In order to enhance the dynamical stability of lattice sandwich structures, the active vibration and buckling control of lattice sandwich beams and plates are studied using piezoelectric materials in this paper.The pyramidal lattice sandwich beam which is bonded with the piezoelectric actuator and sensor on its top and bottom surfaces is equivalent to the orthotropic structure that possesses the same physical properties with the sandwich structure. Only the shear deformation of the lattice core is considered in the structural modeling. As for the face sheets and the piezoelectric actuator and sensor, only the bending deformation is taken into account. Hamilton’s principle and the assumed mode method are used to formulate the equation of motion of the whole structural system. By solving the eigenvalue problem, the natural frequency of the structure can be obtained. First of all, the influences of different parameters on the natural frequency are analyzed. Then, the velocity feedback and linear quadratic optimal control (LQR) algorithms are applied to design the controller, and the active vibration control for the lattice sandwich structural system is conducted. Based on the time-and frequency-domain methods, the vibration responses and the actuator voltages of the sandwich beam under the velocity feedback and LQR control methods are investigated.In order to increase the accuracy of analysis for the vibration of the triangular grid sandwich plate, both the shear and bending deformations of the lattice core are taken into account. The piezoelectric materials are bonded on the top and bottom surfaces of the sandwich plate to act as the actuator and sensor. The equation of motion of the structural system is still formulated by the Hamilton’s principle. Velocity feedback and LQR control algorithms are used to design the controller, and the active vibration control of the sandwich plate is investigated. Solving the time-domain responses and the control voltages, the influences of the velocity feedback control gain on the active vibration control effect are analyzed. The vibration properties of the lattice sandwich plate are compared with those of the ordinary laminated plate. The superiority of the lattice sandwich structure on the dynamical properties is described. In addition, the influences of the size and location of the piezoelectric patches on the active vibration control effect are also investigated.On the basis of the active vibration control of the triangle grid sandwich panel, the influences of the in-plane compression and shear loads on the static stability, i.e. buckling, are analyzed, and the active buckling control of the structure is investigated. The vibration responses and the critical buckling load under the compression and shear loads are calculated. Velocity and displacement feedback control method are used to conduct the active buckling control of the structure. The influences of control gains of the velocity and displacement feedback control methods on the buckling control effect under the compression, shear and the hybrid loads are researched.The results presented in this paper may be helpful for the vibration analysis and active control design of the lattice sandwich structures.