A simple approach to investigate vibratory behaviour of thermally stressedlaminated structures

The aim of the present paper is to propose a simple method to investigate t he vibratory behaviour of laminated composite structures subjected to large thermal loads (may be beyond critical temperature T-cr). von Karman type n on-linear strain-displacement relationships are employed to derive non-line ar finite element equations of motion. These finite element equations are b ased on secant stiffness rather than tangential stiffness. The secant stiff ness matrix is separated into three parts, i.e., (i) linear stiffness matri x independent of field variables, (ii) non-linear stiffness matrix dependin g linearly on field variables and (iii) non-linear matrix depending quadrat ically on field variables. Linear thermal buckling and free vibration analy ses are performed as a first step to compute the critical temperatures, nat ural frequency and corresponding mode shapes. Assuming the mode shape corre sponding to fundamental frequency as the spatial distribution, large-order non-linear finite element equations are reduced to a single second-order or dinary non-linear differential equation. A direct numerical integration met hod is employed to compute the non-linear frequencies of thermally stressed structures. To demonstrate the method, vibratory behaviour of thermally st ressed laminated beams is investigated. The proposed method is validated by comparing the non-linear frequencies of beams (not subjected to initial st ress) obtained using the present method with those available in the literat ure. The influence of difference in buckling mode shape and vibration mode shape for certain boundary conditions on the non-linear behaviour is also s tudied. Some interesting observations regarding the finiteness of amplitude in the post-buckling regime are also made. (C) 1999 Academic Press.