The present paper deals with the dynamic resonance of composite curved panels subjected to periodic dynamic loadings. The effects of various parameters of foursided clamped composite curved panels at elevated temperatures and moisture concentrations on the principal instability regions are investigated by finite element method which is used to study the antisymmetric angleply square plates. The results show that instability of composite plates occurs for different parameters in adverse hygrothermal environment. The experimental and numerical investigation is also carried out for foursided clamped boundary condition for vibration and buckling of curved panels in hygrothermal environment.
Structural elements under inplane periodic forces may undergo unstable transverse vibrations, leading to parametric resonance, due to certain combination of the values of inplane load parameters and natural frequency of transverse vibration. This instability may occur below the critical load of the structure under compressive loads over a range or ranges of excitation frequencies. Several means of combating parametric resonance such as damping and vibration isolation may be inadequate and sometimes dangerous with reverse results. A number of catastrophic incidents can be traced to parametric resonance. In contrast with the principal resonance, the parametric instability may arise not merely at a single excitation frequency but even for small excitation amplitudes and combination of frequencies. Thus, the parametric instability characteristics are of great technical importance for understanding the dynamic system under periodic loadings. The distinction between good and bad vibration regimes of a structure, subjected to inplane periodic loading, can be made through an analysis of dynamic instability region (DIR) spectra. The calculation of these spectra is often provided in terms of natural frequencies and the static buckling loads. So, the calculation of these parameters with high precision is an integral part of dynamic instability analysis of composite plates and shells in adverse hygrothermal environment.
A review of earlier works on vibration and stability of plates subjected to thermal loadings is given by Tauchert [
Studies involving behavior of composite plates subjected to inplane loading with hygrothermal condition are in scanty literature. Noor and Burton [
Some studies dealing with composite plates subjected to inplane periodic loads under ambient temperature and moisture are also reported. Bert and Birman [
The present work is based on experimental work on free vibration, buckling of curved panels in hygrothermal environment, and resonance characteristics of curved panels in advese hygrothermal environment to fill in the lacunae in the literature.
The experimental and numerical models are given in Figures
Arbitrarily oriented laminated plate.
Geometry of an
The governing equation of dynamic stability of laminated composite panel considering hygrothermal conditions and under inplane periodic loads in matrix form is the following:
where
Free vibration is given by
and the buckling load is given by
An eightnode isoparametric element is used for dynamic stability analysis of woven fiber composite plates subjected to hygrothermal environment. Five degrees of freedom
The element elastic bending stiffness matrix is given by
The element geometric stiffness matrix due to residual stresses is given by
Composite plates are fabricated using handlayup technique. In the present study, woven glass fiber and epoxy specimens were fabricated. However, to study the variation of ILSS, the polyester matrix is also tried along with three different fibers: matrix proportions. Woven roving EGlass fibers (FGP, RP10) were cut into required shapes and sizes. For preparation of epoxy resin matrix, hardener 8% (CibaGeigy, araldite LY556, and Hardener HY951) of the weight of epoxy was used, and for polyester matrix, 1% accelerator (cobalt octane 2%) was added first to the polyester resin;, then, 1.5% of catalyst (MEKP methyl ethyl ketone peroxide) was added to mixture and stirred thoroughly to get polyester matrix using woven roving glass fibers and epoxy/polyster matrix. Subsequent plies were placed one upon another with matrix in each layer to obtain required stacking plies. A hand roller was used to distribute resin uniformly, compact plies, and to remove entrapped air to minimize void contents in the samples. The mould and layup were covered with a release film to prevent the layup from bonding to the mould surface. The laminates were cured at normal temperature (25°C and 55% relative humidity) under a pressure of 0.2 mpa for 3 days. The specimens were cut for vibration and buckling testing by brick cutting machine into plate of size 235 mm × 235 mm, forthree point bend test into 45 mm × 6 mm size, and for tensile test into 200 mm × 25 mm as per specification.
The specimens were hygrothermally conditioned in a humidity cabinet where the conditions were maintained at a temperature of 323°K and relative humidity (RH) ranging 0%1% for moisture concentration. The humidity cabinet had an inbuilt thermometer for temperature and hygrometer for relative humidity measurements. The temperature variation was maintained between 300°K and 425°K, whereas the RH was 0 in temperature bath. The hygrothermal conditioning was carried out for every six hours in a total period of thirtysix hours.
The present study deals with the vibration, buckling, and parametric resonance characteristics of woven fiber laminated composite panels. The results are presented as follows:
Convergence Study,
New results.
Convergence study of free vibration for cccc fourlayered laminated composite plates for two different lamination sequences at 325°K temperatures.
Mess division  Nondimensional frequencies at 325°K temperature  

0/90/90/0  45/−45/−45/45  
4 × 4  8.079  11.380 
6 × 6  8.039  10.785 
8 × 8  8.036  10.680 
10 × 10  8.036  10.680 
Nondimensional frequency:
The geometrical and material properties of the laminated composite plates are
The present formulation is then validated for buckling analysis of composite plates as shown in Table
Convergence of nondimensional critical load for ssss fourlayered laminated composite plates for two different lamination sequences at 0.1% moisture concentration.
Mess division  Nondimensional critical load at 0.1% moisture concentration  

0/90/90/0  45/−45/−45/45  
4 × 4  0.6095  0.7255 
6 × 6  0.6079  0.7041 
8 × 8  0.6078  0.7003 
10 × 10  0.6078  0.7003 
Critical load:
Elastic moduli of glass fiber/epoxy lamina at different temperatures.
Elastic moduli  Temperature in (°K)  

300 K  325  350  375  400  425  

7.9  7.6  7.1  6.7  6.5  6.3 

7.4  6.8  6.4  6.2  5.9  5.7 

2.9  2.6  2.3  2.1  1.8  1.6 

0.4  0.43  0.41  0.35  0.36  0.35 
Elastic moduli of glass fiber/epoxy lamina at different moisture concentrations.
Elastic moduli  Moisture concentration in %  

0.0  0.25  0.5  0.75  1.0  

7.9  7.6  7.5  7.3  7.2 

7.4  7.4  7.3  7.1  7.0 

2.9  2.9  2.8  2.7  2.6 

0.4  0.4  0.4  0.39  0.39 
Numerical results are presented to study the effects of different parameters for vibration, buckling, and dynamic instability behavior of woven fiber composite curved panels in adverse hygrothermal environment. The geometrical and material properties of the composite plates are
The frequencies of vibration of woven fiber composite plates subjected to hygrothermal environment are obtained by using the experimental setup and numerically using the finite element method. The variation of frequencies of vibration in Hz of laminated plates (both experimental and numerical) for the lowest four modes subjected to temperature is shown in Figure
Variation of frequency in Hz with temperature for clamped supported (cccc) in the lowest four modes of 16layer [0/0]_{4S} woven fiber composite plates.
Variation of frequency in Hz with moisture concentration for clamped supported (cccc) in the lowest four modes of 16layer [0/0]_{4S} woven fiber composite plates.
However, with increase of moisture concentration from 0.25% to 1%, the frequencies of vibration of laminated composite plates reduce by 25.76%, 52.72%, 44.94%, and 36.63%, respectively, due to reduction of stiffness for the first four lowest modes. As shown in Figures
The results for buckling loads in KN of both the numerical analysis and experimental values with increase in temperature from 300°K to 425°K in every 25°K rise in temperature and from 0% to 1% in every 0.25% rise in moisture concentration of sixteenlayered woven roving glass fiber/epoxy composite plates are presented for four sided clamped (cccc) boundary condition. The variation of critical buckling loads with increase in temperature and moisture concentration of the curved panels is shown in Figures
Variation of critical buckling load in KN with temperature of 16layer [0/90]_{4S} woven fiber laminated composite plates (cccc).
Variation of critical buckling load in KN with moisture concentration of 16layer [0/90]_{4S} woven fiber laminated composite plates (cccc).
The variation of excitation frequency with dynamic load factor of composite laminated simply supported symmetric crossply square shells subjected to temperature from 300°K to 325°K is shown in Figure
Variations of instability region with temperature of composite laminated symmetric crossply (0/90/90/0) curved panel (
Variations of instability region with moisture of composite laminated symmetric crossply (0/90/90/0) shell (
The results of the dynamic resonance studies of the composite curved panels in adverse hygrothermal environment can be summarized as follows.
There is a good agreement between the numerical and experimental results on vibration and buckling of composite panels under hygrothermal environment.
The natural frequencies of vibration and buckling loads of fiber composite panels decrease with increase of temperature and moisture concentration due to reduction of stiffness for all laminates.
The onset of instability occurs later with increasing number of layers of the laminated composite panels with hygrothermal loads.
The excitation frequencies of laminated composite curved panels decrease with increase of temperature and moisture concentration due to reduction of stiffness for all laminates.