An accurate solution method for vibration analysis of multi-span lattice sandwich beams under arbitrary boundary conditions

An accurate solution method for analyzing free vibration of multi-span lattice sandwich beams under arbitrary boundary conditions is proposed in this investigation. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions. In this paper, at boundaries and supports, the linear displacement springs and rotational springs are introduced to simulate the boundary and support forces of multi-span lattice beams, and by adjusting these elastic stiffness values, the arbitrary boundary conditions can be simulated furthermore. All the displacement field functions of multi-span lattice beams are uniformly expanded into an improved Fourier cosine series supplemented with four sine series, which are introduced to eliminate the discontinuity or jump at the boundaries and supports during the solution process. The unified vibration equation of multi-span lattice sandwich beams under arbitrary boundary conditions is constructed based on the energy method. The Rayleigh–Ritz method is used to solve the free vibration characteristics of multi-span lattice sandwich beams. Based on the current method, the free vibration characteristics of multi-span lattice sandwich beams under arbitrary number of spans, arbitrary boundaries and supports can be studied without modifying the solution algorithm and program. The correctness as well as the accuracy of the current method are verified through comparison with those obtained from other analytical approach. Numerical results are presented to show that the current method is very suitable for analyzing the free vibration of multi-span lattice beams under arbitrary boundary conditions. In addition to this, the geometric parameters, as well as the elastic modulus and damping of materials, are analyzed for their effect on the vibration characteristics of multi-span lattice sandwich beams under different boundary conditions.