The viscoelastic damping structure is widely applying for vibration and noise reduction. The viscoelastic damping layer, most of which is rubber or rubberlike polymers, represents hysteresis under a dynamic load. Part of the mechanical energy is absorbed and finally dissipated as heat due to the internal friction of the molecular chains. Continuous cyclic load and poor conduction of heat may cause extensive heat to build up in the structure. The mechanical response of the viscoelastic materials is often highly sensitive to temperature [

1,

2,

3]. Heat may change the mechanical characteristics of the structure and the damping capability [

4,

5,

6]. Excessive heat may lead to early fatigue failure or even explosive rupture. Therefore, it is essential to evaluate the temperature distribution and damping characteristics of the viscoelastic damping structure due to the mechanical energy dissipation during cyclic loading.

Numerous analyses have been proposed to estimate the temperature distribution and damping characteristics of viscoelastic material and its structure. Macro-mechanical or micro-mechanical material models were proposed to describe thermo-viscoelastic behavior [

7,

8,

9,

10]. The complexity of the theory restricts their engineering application. Habibi et al. investigated structural bamboo at the microscopic and macroscopic level [

11]. Two kinds of biological cells separately have the responsibility of viscoelasticity at lower or higher frequencies. David I. G. Jones introduced simple and effective approaches for describing the damping-related properties of viscoelastic materials, with emphasis on the effects of frequency and temperature, and proceeded to illustrate simple techniques for measuring the desired properties and for selecting and applying the materials [

12]. Johnson and Chen employed a linear viscoelastic model (the Maxwell solid model) to solve the coupled thermal and large strain history integral. Due to under-prediction of the size of the hysteresis loop in the linear viscoelasticity, the error in dissipated energy prediction at large strain is unacceptable [

13]. Shah et al. studied the coupled problem of deformation of a linear-viscoelastic composite cylinder by applying the correspondence principle [

14]. Pesek et al. proposed a mathematical model based on a weak formulation of the partial differential equation by FEMLAB (original release of COMSOL Multiphysics) to investigate the thermo-mechanical interaction in a pre-stressed rubber block used for resilient elements of composed tram wheels. A proportional damping model and the equality of the heat energy density and the dissipation energy density were computed to perform coupling between the mechanical and thermal equations under selected simple stress states [

15]. Banic et al. investigated the temperature of a rubber damper under cyclic loading due to hysteresis losses by finite element analysis (FEA). The visco-plastic constitutive model established by Bergstrom-Boyce was used to predict the heat generation and hysteresis in the rubber-metal spring of railway draw gear [

16]. Luo et al. predicted the heat generation of a rubber spring instrument during the spring-accelerated fatigue test. A static hysteresis loop was obtained via the FEA approach experimentally [

17]. Kamran and Anastasia used a non-linear visco-elastic constitutive model (proposed by Schapery) to analyze the effect of coupling between the thermal and mechanical response, which was attributed to the dissipation of energy, heat conduction and temperature-dependent material parameters on the overall response of visco-elastic solids [

18]. Hwang and Yeong analyzed the temperature distribution of a coupled 3D dynamic rolling simulation of a tire by finite element method (FEM) [

19]. The heat generation rate was assumed to be equal to the strain energy density function multiplied by the hysteresis coefficient. Fenza et al. investigated the damping characteristics of a viscoelastic embedded composite fuselage structure by experiments at different temperatures [

20]. Kerchman and Cheng [

21] evaluated the heat generation and transient temperature using linearized constitutive model and FEM. Frequency-dependence on the Viscoelastic Damping VED structure is also a matter of major concern. The sandwich viscoelastic damping structure is analyzed by the method of model reduction to reduce the high-order finite element models to a smaller size in direct dynamic analysis [

22]. The frequency response analysis of viscoelastic beams and plane frames with an arbitrary number of Kelvin-Voigt viscoelastic dampers was concerned. The exact frequency response in all frame members was also obtained in closed analytical form [

23].

Since the damping characteristics of viscoelastic material are sensitive to temperature, also due to the low conductivity of the material, the damping ability is a dynamic coupled process. Some works treated the coupled problem with a one-way coupling approach, especially common in the rolling resistance field of rubber tires. Some coupled thermo-mechanical constitutive models need to user-defined material (UMAT) subroutine by support. Meanwhile, due to the coupled effect, the temperature distribution of the viscoelastic damping structure may not be constant or homogeneous. In this paper, a fully coupled analysis of the viscoelastic damping structure will be investigated to describe the change of the damping characteristics more accurately. The investigation by commercial finite code ABAQUS (Dassault Systèmes, Vélizy-Villacoublay, France) will be validated by comparing it with the available field data in the present literature.