Dynamic Characteristics of an Elastic Structure with Thermal Effects

• Published in: International journal of acoustics and vibration 2020-06, Vol.25 (2)
• Main Authors: Xu, Guanhua, Gu, Bangping, Zhang, Jiafu
• Format: Article
• Language: English
• Subjects: Analysis; Temperature effects
• ISSN: 1027-5851
• DOI: 10.20855/ijav.2020.25.21578

The vibration table in a combination environmental testing device suffers from temperature changes, which cause the dynamic characteristics of the vibration structure to vary. The mechanism of the thermal effect on the dynamic characteristics of an elastic structure is presented, and a modal analysis with thermal effects based on the finiteelement method (FEM) is carried out. The results show that the natural frequencies for each order decrease as the temperature increases, while the mode shapes of the vibrator do not change with temperature. Although thermal stress may affect natural frequencies due to the additional initial stress element stiffness, this stress can be neglected in the modal analysis because it is negligible relative to the effect of the material property changes with temperature. NOMENCLATURE x Vibration displacement vector, m P(t) Nodal load vector, N M Mass matrix, kg C Damping matrix, N/(m/s) K Stiffness matrix, N/m [M.sup.[epsilon]] Element mass matrix, kg [K.sup.e] Element stiffness matrix, N/m [rho] Material density, kg/[m.sup.3] N Shape function B Geometric matrix, 1/m D Elastic coefficient matrix, GPa E Material elastic modulus, GPa [micro] Poisson's ratio [[phi].sub.i] Modal vector n Number of nodal degrees of freedom [[omega].sub.i] Vibration frequency, rad/s [GAMMA] Stress matrix, Pa G Shape function matrix [C.SUB.H] Heat capacity matrix, J/K [K.sub.H] Heat transfer matrix, W/K Q Node heat flow rate vector, W T Structural node temperature vector, K T Derivative vector of temperature versus time, K/s [mathematical expression not reproducible] Element heat capacity matrix, J/K [mathematical expression not reproducible] Element heat transfer matrix, W/K [Q.sup.e] Element heat load vector, W [G.sub.v] Heat generation per unit volume, W/[m.sup.3] [c.sub.p] Specific heat, J/(kgK) q Boundary heat flux, W/[m.sup.2] [alpha] Heat transfer coefficient, W/([m.sup.2] K) [T.sub.a] Ambient temperature, K [partial derivative][OMEGA] Boundary [[epsilon].sub.0] Initial thermal strain vector [epsilon] Total strain vector [beta] Thermal expansion coefficient, 1/K [sigma] Thermal stress vector, Pa [P.sub.f] Body load vector, N [P.sub.s] Surface load vector, N [mathematical expression not reproducible] Structural node load vector caused by initial thermal strain, N [K.sub.T] Stiffness matrix that varies with the temperature, N/m [K.sub.[sigma]] Initial stress stiffness matrix, N/m [T.sub.s] Temperature of the structure, K [k.sub.s] Thermal conducti