Bloch wave based method for dynamic homogenization and vibration analysis of lattice truss core sandwich structures

Abstract

A unified semi-analytical method for dynamic homogenization and vibration analysis of lattice truss core sandwich beams is proposed. The method is developed based on prediction of both propagating and evanescent Bloch waves in the periodic truss core sandwich beam using a wave finite element method. This is accomplished very efficiently with the requirement of modeling only one unit cell of the periodic sandwich beam, which can be implemented simply by employing a conventional finite element package. A dynamic equivalent Timoshenko beam model is thereby built by matching its propagating and evanescent flexural wavenumbers to those predicted from the original sandwich beam. Dynamic equivalent beam parameters including equivalent flexural stiffness, equivalent shear stiffness, as well as equivalent Young’s modulus and shear modulus are identified and expressed as explicit formulations relating to the two matched flexural wavenumbers. Free vibrations of finite-length lattice truss core sandwich beams with various common boundary conditions are further examined based on analytical natural frequency equations and normal mode functions. It is demonstrated that the proposed method shows excellent agreement with conventional finite element method and provides much better accuracy of natural frequency prediction than a representative existing method.