Finite Element Free Vibration Analysis of Soft-Core Sandwich Beams

Abstract

b = width of the beam C1, C2, C3, C4 = Lagrange cubic interpolation functions Ec = Young’s modulus of the core material h, hf = height of the beam, face sheet hb, hc, hp = one-half the height of the bottom, core, and top layer L, Le = length of the beam, a representative element NE, NT = matrix of shape functions for face sheets modeled using Euler-Bernoulli or Timoshenko beam theory qeE , qeT = vector of nodal displacements of a representative element for when the face sheets are modeled using Euler-Bernoulli or Timoshenko beam theory uE, uT = vector of field variables for when the face sheets are modeled using Euler-Bernoulli or Timoshenko beam theory ub, uc, up = longitudinal displacement of a differential element of the bottom, core, and top layer wb, wc, wp = transverse displacement of the bottom, core, and top layer zb, zc, zp = local through the thickness of the bottom, core, and top layer