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Fig. 1. Design drawing of WSG resonator (
а
), finite-element approximation of
geometry (
b
) and its deformation according to the second mode shape (
c
)
This structure (as well as the simulated mode shape) is of a certain
practical interest because it is used in a number of modern developments
[11, 12]. The temperature field along the circular angle, heat flows and the
loss of resonator’s enegry for one period were calculated for a specified
deformation of the cylidrical shells subject to the properties of its material.
The characteristics of materials used in simulation are given in the table
below. The geometry of WSG resonator are given in Fig. 1,
а
.
The thickness of the resonator working area
b
and the central radius of
the working area
R
exert the main influence upon the change of resonator’s
characteristic features. The other dimensions do not exert significant
influence upon the result. In simulating,
b
takes on values 0.5, 1.0, 1.5, 2.0
and 2.5 mm, while
R
changes in a wide range.
The finite-element formulation of the task is based on the approximate
method of solving interconnected tasks of the dynamic theory of elasticity
and nonpermanent thermal conductivity [13]. According to the theory of
thermoelasticity, the connection between vectors of stresses and deforma-
tions is set in the form
σ
= D
ε
= D(
ε
El
−
ε
T
)
,
(4)
where
ε
El
,
ε
T
— tensors of elastic and temperature deformations;
σ
— stress
tensor;
D
— 6
×
6 elastic constant tensor.
30
ISSN 0236-3933. HERALD of the BMSTU. Series Instrument Engineering. 2015. No. 2